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Fundamentals of Transportation Engineering: A Multimodal Systems Approach (2nd Edition) [2 ed.]
 9780130351241

Table of contents :
CHAPTER 1. TRANSPORTATION IN OUR DAILY
LIVES
1.1 The Role of Transportation
1.2 Fundamentals of Transportation
Engineering
1.3 Multimodal and Intermodal Transportation
1.4 Systems Approach to Transportation CHAPTER TRAFFIC FLOW: THEORYAND
ANALYSIS
2.1 Measuring Traffic Flow and Spacing 2.2 Measuring Traffic Speeds and Densities 2.3 Traffic Models for Continuous Flow
2.4 The Polssan Model for Continuous Flow
2.5 Measuring Roadway Performance CHAPTER HIGHWAY DESIGN FOR
PERFORMANCE
3.1 Capacity and Level of Service for Basic Freeway Segments 3.2 Queueing Systems 3.3 Systems with Stable Queues 3.4 Queueing Systems with Persistent Queues CHAPTER MODELING TRANSPORTATION
DEMAND AND SUPPLY
4.1 Basis for Transportation Planning 4.2 Trip Generation 43 Trip Distribution
4.4 Mode Cholce 4.5 Trip Assignment CHAPTER PLANNING AND EVALUATION FOR DECISION-KiAKING
5.1 The Transportation Planning Process 5.2 Brief Review of Engineering Economics 5.3 Economic Evaluation of Transportation Alternatives 5.4 Ranking Transportation Alternatives CHAPTER SAFETY ON THE HIGHWAY
6.1 Highway Safety Data and Analysis 6.2 Human Factors and Transportation Engineering 6.3 Vehicle Attributes That Affect Safety 6.4 Traffic Control Devices CHAPTER HIGHWAY DESIGN FOR SAFETY
7.1 The Chailenge of Roadway Alignment 7.2. Stopping Sight Distance and Alignment 7.3 Banking Curves (Horizontal Alignment) 7.4 Roundabouts CHAPTER DESIGN CF INTERSECTIONS FOR
SAFETY AND EFFICIENCY
8.1 Analysis of Non-Signallzed Intersections
8.2 Signai Warrants and Stopping Distance at
Signalized Intersections 8.3 Analysis of Signalized Intersections CHAPTER HIGHWAY DESIGN FCR
RIDEABILITY (PAVEMENT DESIGN) 9.1 Factors in Pavement Design
9.2 Determining Loads from Truck Traffic 9.3 Flexible Pavement Design 9.4 Rigid Pavement Design
9.5 Pavement Management Systems CHAPTER 10 PUBLIC MASS TRANSPORTATION
10.1 Transit Modes 10.2 Designing Rall Transit Line 10.3 Predicting Transit Ridership Changes 10.4 Performance Measures in Public Transportation
10.5 Life-Cycle Costs In Public Transportation CHAPTER 12 AIR TRANSPORTATION AND
AIRPORTS
11.1 Overview ofthe Air Transportation System
11,2 Alrport Planning and Forecasting 11.3 Airport Capacity 11.4 Delay at Airports 11.5 Airport Site Determination and Runway Orientation
11.6 Runway Length Design CHAPTER 1Z MOVING FREIGHT
12.1 Freight The Movement Behind Economic Well-Being 12,2 Moving Frelght by Truck 12.3 Moving Freight by Rail 12.4 Moving Freight by Barges on Inland Waterways 12.5 Oil Pipelines 12.6 Moving Freight by Air 12.7 Energy Analysis of Freight Modes CHAPTER i3 THE PATH TC SUSTAINABLE
TRANSPORTATION SYSTEM
13.1 Sustainability 13.2 Fueling Transportation Engineering for Sustainable Development 13.3 Infrastructure for Sustainable Transportation
13.4 Transportation Technology for Sustalnable Development 13.5 Transportation Demand Management Policies 13.6 Urban Design for Sustainability

Citation preview

Table of Contents Fundamentais of Transportation Engineering, 2nd Edition, 6th Printing Author: Robert K, Whitford; Jon D. Fricker Publisher: The Scholar Collection Capyright: 2018

Ch 0 Cover, Preface, Table of Contents

3

Ch

Transportation in our Community

7

Ch 2 Traffic Flow: Theory and Analysis Ch 3 Highway Design for Performance

31

1

96

Ch 4 Travel Demand Models

133

Ch 5 Planning and Evaluation for Decision-Making

196

Ch 6 Safety on the Highway

232

Ch 7 Geometric Design

294

Ch 8 Intersection Design

347

Ch 9 Pavement Design

385

Ch 10 Public Mass Transportation

437

Ch

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11

Air Transportation

Ch 12 Freight Transportation

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Ch 13 The Path to a Sustainable Transportation System

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Ch 0 Cover, Preface, Table of Contents

Fundamentals

of Transportation Engineering, Second Edition, 6" Printing.

© July 2018, Jon D. Fricker and Robert K. Whitford. All rights reserved. No part of this book may be reproduced, stored in a retrieval system, or transmitted in any form or by any means without prior written permission from the authors.

The first edition of this book was published by Pearson Education, Inc. Credit for cover art: All images copyright J. Craig Thorpe; from original paintings commissioned by Amtrak, Lynden, Inc., All Aboard Washington and General Electric Transportation Systems.

For instructor materials and details about the changes made since the first edition, go to https://engineering.purdue.edu/~ce361/JFRICKER/FTE/.

Preface to the Second Edition,

6" Printing

This is the sixth version of Edition 2. The first edition of Fundamentals of Transportation Engineering

(FTE1) was published in 2004. Since 2004, new editions of several well-known manuals and other references have been published. Furthermore, much of the data that appeared in FTE1 has become outdated. For these reasons, the second edition of FTE was published in June 2014 and distributed by

academicpub.com, followed by several subsequent versions (printings).

In the 6" Printing, the font size and line spacing of the text has been changes to make electronic versions of the book easier to read. Changes in content have been made to update data and topics, and to respond to suggestions by users

of the book. See https://engineering.purdue.edu/~ce361/JFRICKER/FTEY for

details.

As with the previous versions, Fundamentals of Transportation Engineering continues to: modes. (1) Cover topics beyond the highway mode. Chapters 10-12 cover the transit, air, and freight and new Chapter 13 on Sustainable Transportation includes non-motorized transportation

technologies. time for (2) Allow use of reading assignments to replace a traditional “lecture”. This increases class

discussions. taking student questions about the reading, working problems, and facilitating

Fundamentals of Transportation Engineering - Volume

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(3) Begin each chapter with a realistic scenario, build toward analyzing and solving related example problems, and invite students to ponder the “Think About It” boxes.

We continue to think about the future of the textbook. Should we continue the current online distribution, with its softcover, spiral bound, and eBook options? Should we return to a hardbound format? What topics should be added? Which topics could be deieted? We invite comments and suggestions from those who are using the book.

Thank you to those of you who have adopted the book. Please continue to tell us how the book has met your needs and how it could be improved.

Jon D. Fricker

Robert K, Whitford

West Lafayette IN

Seattle WA

13

July 2018

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Ch’0 Cover, Preface, Table of Contents

Table of Contents, Second Edition, 6" Printing CHAPTER 1. TRANSPORTATION IN OUR DAILY LIVES 1.1 The Role of Transportation 1.2 Fundamentals of Transportation

Engineering 1.3 Multimodal and Intermodal Transportation 1.4 A Systems Approach to Transportation

CHAPTER 2 TRAFFIC FLOW: THEORY AND ANALYSIS 2.1 2.2 2.3 2.4 2.5

Measuring Traffic Flow and Spacing Measuring Traffic Speeds and Densities Traffic Models for Continuous Flow The Polssan Model for Continuous Flow Measuring Roadway Performance

CHAPTER 3 HIGHWAY DESIGN FOR PERFORMANCE 3.1 Capacity and Level of Service for Basic Freeway Segments 3.2 Queueing Systems 3.3 Systems with Stable Queues 3.4 Queueing Systems with Persistent Queues

CHAPTER 4 MODELING TRANSPORTATION DEMAND AND SUPPLY 4.1 Basis for Transportation Planning 4.2 Trip Generation 43 Trip Distribution 4.4 Mode Cholce 4.5 Trip Assignment

CHAPTER 5 PLANNING AND EVALUATION FOR DECISION-KiAKING 5.1 The Transportation Planning Process 5.2 Brief Review of Engineering Economics 5.3 Economic Evaluation of Transportation Alternatives 5.4 Ranking Transportation Alternatives

CHAPTER 6 SAFETY ON THE HIGHWAY 6.1 6.2 6.3 6.4

Highway Safety — Data and Analysis Human Factors and Transportation Engineering Vehicle Attributes That Affect Safety Traffic Control Devices

CHAPTER 7 HIGHWAY DESIGN FOR SAFETY 7.1 The Chailenge of Roadway Alignment 7.2. Stopping Sight Distance and Alignment 7.3 Banking Curves (Horizontal Alignment) 7.4 Roundabouts

CHAPTER 8 DESIGN CF INTERSECTIONS FOR SAFETY AND EFFICIENCY 8.1 Analysis of Non-Signallzed Intersections

8.2 Signai Warrants and Stopping Distance at Signalized Intersections 8.3 Analysis of Signalized Intersections

CHAPTER 9 HIGHWAY DESIGN FCR RIDEABILITY (PAVEMENT DESIGN) 9.1 9.2 9.3 9.4 9.5

Factors in Pavement Design Determining Loads from Truck Traffic Flexible Pavement Design Rigid Pavement Design Pavement Management Systems

CHAPTER 10 PUBLIC MASS TRANSPORTATION 10.1 10.2 10.3 10.4

Transit Modes Designing a Rall Transit Line Predicting Transit Ridership Changes Performance Measures in Public

Transportation 10.5 Life-Cycle Costs In Public Transportation

CHAPTER 12 AIR TRANSPORTATION AND AIRPORTS 11.1 Overview of the Air Transportation System 11,2 Alrport Planning and Forecasting 11.3 Airport Capacity 11.4 Delay at Airports 11.5 Airport Site Determination and Runway Orientation 11.6 Runway Length Design

CHAPTER 1Z MOVING FREIGHT 12.1 Freight — The Movement Behind Economic Well-Being 12,2 Moving Frelght by Truck 12.3 Moving Freight by Rail 12.4 Moving Freight by Barges on Inland Waterways 12.5 Oil Pipelines 12.6 Moving Freight by Air 12.7 Energy Analysis of Freight Modes

CHAPTER i3 THE PATH TC A SUSTAINABLE TRANSPORTATION SYSTEM 13.1 Sustainability 13.2 Fueling Transportation Engineering for Sustainable Development 13.3 Infrastructure for Sustainable Transportation 13.4 Transportation Technology for Sustalnable

Development 13.5 Transportation Demand Management Policies 13.6 Urban Design for Sustainability

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TRANSPORTATION IN OUR DAILY LIVES

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SCENARIO Mythaca is not a small town any more. After decades of growth, it is beginning to have the transportation problems of larger cities. A drive across town no longer takes less than thirty minutes. Traffic congestion is becoming a common occurrence (Figure 1.1) and households are spending a greater share of their budgets on “mobility.” The transit company has purchased several new buses in response to a growing demand for public transportation. Access to important commercial markets will soon be enhanced because of upgrades to the nearby Port of Mazurka, the planned expansion of the nearby interstate highway, plus the new freight terminal and runway improvements at Mythaca’s airport.

Elected officials are asking transportation experts to work with citizens to develop policies and projects that will facilitate growth in the community’s transportation system at a cost that the taxpayers can afford. The officials need to consider a variety of strategies to improve

FIGURE 1.1 Traffic jam in Mythaca.

Photo: Jon D. Fricker mobility, but getting citizens to forgo driving and try walking, bicycling, and public transit may be difficult. To distinguish among alternatives, decision-makers need to have a reliable way to estimate the effectiveness and cost of each proposed Project or program. They need to turn to persons who can understand and implement the fundamentals of transportation engineering principles and methods that are introduced in this book. —

CHAPTER 1 OBJECTIVES At the end of this chapter, the student will be able to: 1

2 3

4 5

6

Describe the role transportation has played in the development of our communities and our society. Explain the role played by stakeholders in transportation decision making, Outline the fundamental structure of transportation systems and what activities transportation engineers may undertake. Explain the difference between multimodal and intermodal transportation. Develop a system specification for a particular transportation system. Identify and calculate performance measures needed to analyze a transportation system.

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THE ROLE OF TRANSPORTATION

Transportation is crucial to economic vitality and quality of life, because it is the movement of people and goods from place to place. Transportation engineers seek to make these movements safe, reliable, and efficient. Too often, we take transportation for granted, yet the average household devotes about 17.5 percent of its spendable income on transportation (BLS 2013, Table A). The journey on which we are about to embark in this book is an exploration of the realm of transportation, with emphasis on key aspects of its engineering and its close relationship to our social and economic lives. To provide an ongoing context, many of the problems presented in this book take place in the mythical City of Mythaca, the largest city in Mythaca County. Along Murdock Bay, there is the industrial port of Mazurka and the

recreation town of Shoridan. State Road 361 (SR361) between Mythaca and Shoridan is heavily traveled, including weekend traffic to recreation spots. Halfway between the two cities is the little town of Middleville. The map in Figure 1.2 shows the City of Mythaca and its surrounding area. As we examine transportation problems in and near Mythaca, we will explore methods that can lead to transportation engineering solutions in the real world.

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FIGURE 1.2

Map of Mythaca County

Most interstate, US, and state highways are numbered according to the direction that applies to most of the road. A highway that runs mostly east-west will end in an even number, A road that is predominately north-south will end with an odd number. Do the state, US, and interstate Highways in Figure 1.2 follow this convention? Hint: SR361 starts in the southern part of the state.

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1.1.1 Stakeholders

Transportation can affect different people in different ways. People who can be affected — positively or negatively — by transportation projects or policies are called stakeholders. One example of a transportation project is the construction of a new highway. A transportation policy example is the decision to add bus service to a particular part of town. Stakeholders can be individual citizens or groups

of people, representatives of government units, or business interests. Usually, flora andfauna are not treated as stakeholders, because environmental agencies and groups are expected to protect those interests. Good planning practice includes identifying stakeholders and bringing them into the early stages of the planning process.

Example 1.1 The Road from Mazurka

Activity at the Port of Mazurka is increasing, causing the growing number of large trucks using US86 and US39, through Mythaca to I-46, to become a major nuisance, Construction of a relocated US Highway 39 —a bypass highway that would follow a path to the west of Mythaca has been proposed. (See Figure --

1.2.) The basic concept is to cut across farmland between Middleville and Mythaca, with an interchange at SR361. Additional access to the new highway would be limited, except at locations set aside for as industrial The development parks. Mythaca County Planning Commission (MCPC) is beginning the planning process by contacting stakeholders to get their opinions about the concept.

A. Make a list of stakeholders that the MCPC should contact. B. For each stakeholder, think of at least one question, concern, or request regarding the potential good or bad aspect of the proposed bypass project.

C. How will the MCPC be able to measure the extent to which each stakeholder’s wishes or concerns have been addressed?

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THINK ABOUT IT Before looking at the solutions to this example, try answering Parts A and B. Put’: yourself in the place of each stakeholder that you identify, especially those who may have a viewpoint that is different from yours.

Solutions to Example 1.1

A. The exact nature of stakeholders may vary from city to city and project to project, but likely stakeholders in this example are:

(1) (2) (3) (4)

Residents of neighborhoods currently vexed by heavy truck traffic Individuals who own land in the path of the proposed bypass highway Business groups, such as a Chamber of Commerce The State Department of Transportation (DOT), which will provide much of the construction

funding and will be responsible for maintaining the new highway (5) Mythaca County and the City of Mythaca, which will assume responsibility for the portion of US39 that will be relinquished by the State DOT to the local governments (6) Environmental and farmland preservation groups, which will be concerned about loss of farmland and possible harm to water supplies and quality of life in rural areas,

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B. More specific questions, requests, and concerns might be: (1) Neighborhoods. Will vehicle noise, emissions, and safety issues be alleviated? (2) Land owners. How much of my land be taken? Will I get a fair price for it? Will I be able to use

what is left, especially if farmland? (3) Businesses. Will the diversion of traffic from US86 and old US39 hurt businesses that are located along those less-traveled segments? How will agricultural land along the new highway be

rezoned? (4) State DOT. What is the cost of the new highway? What are the economic benefits to the state and the region? When can money from the state highway budget be made available for the project? Will local governments contribute a share of the cost? (5) County and City. How much of the total construction cost can they contribute? In what condition will the US86 and old US39 segments be turned over to the local governments? (6) Environmental groups. How much farmland will be lost? Will any endangered species be threatened? Will the project cause unacceptable noise and air quality impacts? C. Measuring impacts on stakeholders. We will return to this question later in this chapter. —

The bypass highway project may not proceed if too many of the stakeholders’ concerns are not resolved. Often, not everyone will be entirely satisfied with the result of the planning process, but the process is not designed to take into account the input from all stakeholders, seeking consent where consensus may be possible. 1.1.2 Transportation’s role in history

The proposed bypass highway in Example 1.1 may affect the future of Mythaca and the surrounding area. The area’s economy may be helped. The residents’ quality of life may be enhanced. These are local impacts. On a regional and national scale, developments in transportation have had an important influence on the growth of the United States. A few illustrations:

Canals. The 360-mile Erie Canal, built in 1825 to connect the Great Lakes to the Atlantic Ocean, aided the development of the Upper Midwest. As shown in Figure 1.3, early canal barges were pulled by

FIGURE 1.4.

1825. Source: http://commons.wikimedia.org/wiki/File:Erie_

Golden Spike Ceremony at Promontory, Utah, May 1869. National Archives,

Canal_ Tow_Path_Utica-1905.jpg

http://research.archives.gov/description/594940

FIGURE 1.3. Mules pull a barge along the Erie Canal, ca.

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animals moving on towpaths next to the water. Another canal with great promise was built across Indiana to connect the Great Lakes to the Wabash, Ohio and Mississippi Rivers, to move goods to the Gulf of

Mexico. However, before the canal could earn enough revenue for its builders to recoup their investment, tailroads appeared on the scene. Railroads started carrying many of the grain and coal shipments that the canal depended on, and the Indiana canal did not survive. [Fatout 1985]

Railroads. Before automobiles, railroads were the primary mode of transportation in the United States for both people and materials, With the driving of the “golden spike” (Figure 1.4), the country became much better connected. Previously, settlers headed for California either took the arduous trip across the country in covered wagons or traveled on ships that took months to sail around the tip of South America. The California Gold Rush and other movements to seek natural resources in the West were aided by rail.

During the late 1800s and early 1900s, railroads were the principal means of moving agricultural products from the Midwest, and bringing coal for electric plants and ore to the steel-making foundries in the Midwest. Railroads also provided most intercity passenger travel. After the devastating Civil War, the faster transportation provided by rail helped the country begin to reunite. In fact, the railroads became so strong, especially in areas where there was no competition, that price-gouging and other predatory practices became commonplace. In response, the Federal Government intervened to regulate prices and the Interstate Commerce Commission was formed in 1887.

Automobiles. This mode did not enjoy widespread use until after 1925, Early competition was mainly between the electric automobiles (which required large batteries and didn’t go very far on a single charge) and internal combustion vehicles (which required difficult manuel cranking to start the engine). Ironically, it was an electric invention — an electric starter motor operated from a small battery that led to the demise of these first electric automobiles. The advances of the internal combustion engine technology, its affordability, plus the growing level of personal wealth, have enabled U.S. vehicle ownership to grow to an average of 1.86 per househoid. [Santos et al. 2011, Table 17] The automobile, when combined with about 4 million miles of roads in the United States, has offered most U.S. citizens a range of personal freedom of movement unsurpassed anywhere in the world. --

Waterborne Transportation. Early cities

--

great and small

--

tended to arise near the water. Because

of the convenience of water transport for the movement of resources across the vast oceans, great cities grew up around ocean ports. Ocean, lake, and river travel is still important today. About 39 percent of the United States population resides in coastal counties, which have less than 10 percent of the US land area (excluding Alaska). [NOAA 2013] Ocean shipping continues to be important to the US and world economies. A wide variety of goods are moved in containers, which will be covered later in this book. Interstate Highways. The Federal-Aid Highway Act of 1956 established the program for funding and building the National System of Interstate and Defense Highways. [FHWA undated] The original 42,000-mile network was completed in 1991, with the Interstate System serving interstate, regional, and intra-state traffic. More than 5000 additional miles have since been constructed. (See Figure 1.5.) The system has allowed personal and commercial vehicles to cover longer distances at higher speeds. Drivers were able to live farther from their workplaces, using Interstate segments within an urban area as commuter routes. Just as railroads replaced canals, Interstate highways provided stiff competition for intercity bus and passenger rail service.

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FIGURE 1.5,

Interstate Highway Network. Source:

FHWA undated.

Air Travel.

In a country as large as the US, an affordable way to reach distant destinations is a huge benefit. In the 1950s, passenger air travel was largely for business purposes. Families would dress up to take a traveler (usually the father) to the airport, and perhaps visit the observation areas to watch airplanes take off and land. Until 1978, airline operations were heavily regulated by the federal government. Entry by new airlines, permission to serve particular airports, and ticket prices were controlled by the Federal Aviation Administration. The Airline Deregulation Act of 1978 phased out these controls, allowing new

airlines to enter the market, fares to drop, and air travel to become affordable to more people.

FUNDAMENTALS OF TRANSPORTATION ENGINEERING

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1.2.1 Basic concepts

Transportation engineering is the application of the principles of engineering, planning, analysis, and design to facilitate the movement of people and goods. A transportation engineer must be concerned

with: e

The design and maintenance of physical infrastructure,

«

Efficiency, safety, environmental impacts, and energy usage in the movement of people and

goods. Transportation engineering involves the “hard” physical sciences, as the engineer evaluates pavements, geometric design, vehicle design, environmental effects, and the like. It also employs a variety of “soft” or social sciences, such as human behavior, welfare economics, urban planning, and political science, to conduct thorough analyses of the impacts of transportation design and operations. The competent transportation engineer must be capable of integrating the factors found in both the “hard” and the “soft”

sciences when searching for the best solution to a given transportation problem. Transportation is much more than people making trips. The movement of goods is a critical part of local, regional, and national economies. As goods move from origin to destination, transfer points can be rail yards, truck terminals, warehouses or distribution centers. Line-haul goods movement (i.c., between terminals) will be by rail, truck, water, pipeline or some combination of these modes. Again,

effectively located, properly designed and well-operated facilities are essential to an efficient

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transportation system. Ifa transportation facility or service is overdesigned, the result may be a waste resources. If it is underdesigned, bottlenecks that cause delays, lost productivity, or unsafe conditions

of

may arise.

Transportation engineering is much more than designing a facility. As the case of the proposed bypass highway in Example 1.1 illustrates, it involves working with the public, with industry, with

citizen’s groups, with elected officials, and with employees of government agencies to find the best solution possible. The transportation engineer may be part of a government agency, or he/she may work at a consulting firm that provides services to government agencies and private firms. In any case, the transportation engineer faces real problems that require engineering judgment plus the ability to work cooperatively with a wide variety of stakeholders. 1.2.2 Personal transportation. Personal transportation options range from non-motorized modes (walking and bicycling) to high-speed, long-distance highway, rail, and air modes. The shaded box in Figure 1.6 enclosed by dashed lines indicates categories that are usually apply to urban transit, Automobile

]

fitighway

[Motorcycle

]

Intercity

|

fige

= Transit Systems

]

[Airplane

Air Taxi Water Taxi

[Water

_| Ferries

{Non-motorized

|

FIGURE 1.6 Hierarchy of Personal Transportation Options

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MULTIMODAL AND INTERMODAL TRANSPORTATION

1.3.1 Using multiple transportation modes

The subtitle of this textbook contains the word “multimodal”. That is because this book includes coverage of modes besides the highway modes. Later chapters cover public transportation, air transportation, and freight movement. Intermodal transportation takes place when two or more distinct modes are used to carry persons or goods from origin to destination.

FYI Transportation, like many fields, has its own vocabulary. A Glossary of terms appears at the end of each chapter. The end-of-chapter Index will help will find the terms in the text. Transportation also has a very large number of abbreviations. For that reason, a list of abbreviations, with their meanings, is also included at the end of each chapter.

Example 1.1 was concerned with the possible construction of a bypass highway. The principal questions were: 1.

Should the highway be built?

2.

Ifit is built, how can the benefits to stakeholders be maximized and negative impacts be minimized?

Although a highway was the facility of concern, the problem was caused by freight arriving by ships at Mazurka. If the terrain is flat enough and a private investor can be found, it is conceivable that a rail line could carry enough of the current and future freight, so that investment in a new highway would not be necessary for many years.

—-4-— Example 1.2 The City Engineer goes to work. The Mythaca City Engineer lives about one mile from his office in City Hall. Depending on the situation, he chooses one of four modes for his trip to work. 1.

Bicycle. (In a typical year, he chooses this mode about 50 percent of the time.) His door-to-door travel time (home garage door to the bicycle rack near the entrance door at City Hall) is about six minutes.

2.

Bus. (25 percent) There is a bus stop one-half block from his home. Because Mythaca Bus Company has a passenger information system, he knows when the bus is about 3 minutes from his bus stop. After boarding the bus, the Engineer rides for about four minutes, and his walk from the destination bus stop takes about two minutes.

3.

Drive automobile. (15 percent) The drive to the parking garage near City Hall takes about 3 minutes. The walk from the parking garage to City Hall takes six more minutes.

4.

Walk. (10 percent) The City Engineer can walk to City Hall in about 14 minutes.

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The only transportation mode attribute that has been mentioned is door-to-door travel time, but the percentage of the time each mode is chosen aligns closely with the relative travel times — 6, 9, 9, and 14 minutes door to door. What other factors may explain why the City Engineer does not use one mode ail

(or most) of the time? One idea: List the advantages (+) and shortcomings (-) of each mode, as they might factor into the City Engineer’s mode choice decision.

Solutions for Example 1.2 1,

Bicycle. (+) Very low cost. (+) Shortest travel time. (++) Good exercise. (-+) He can start his trip when he wants. (-) Not pleasant in bad weather. (-) Difficult to carry heavy or fragile items, such as a personal computer. (-) Not practical if other trips during the day involve long distances or very busy streets.

2.

Bus; (+) May have lower cost than driving automobile, especially if parking cost is at least as large as bus fare. (+) In this case, less physical effort than any of the other modes. (-) Dependent on bus schedule and reliability. If the City Engineer is ready to leave home 15 minutes or more before the next bus is due to arrive, he must wait or use an alternative mode. If he misses a bus, he may have to wait 30-60 minutes for the next one. (-) Sometimes the ride could be unpleasant if the bus is crowded, pdssengers are rude, the bus driver makes abrupt starts and stops, etc.

3.

Drive automobile. (+) He can start his trip when he wants. (+) Can carry large items in the vehicle, then carry them a short distance to City Hall, or perhaps even drop the items off at City Hall before parking. (+) The greatest protection from bad weather. (+) Car is available for errands or meetings during the day that are not well served by the other modes. (+) Can carry passengers. (-) Cost of owning and operating the vehicle, especially fuel. (-} The inconvenience of searching for a parking space, and remembering where in the garage he parked. (-) Cost of parking.

4.

Walk. (+) Good exercise. (+) He can start his trip whenever he wants. (+) Very low cost. (-) Not pleasant in bad weather. (-) Difficult to carry heavy items. (-) Would have to use bus if other trips during the day involve long distances. (-) Longest trip time.

In Chapter 4, we will look at models that attempt to incorporate factors that explain mode choice behavier:

THINK ABOUT IT Notice that “helping the environment” was not an argument made for using any of the non-automobile modes in Example 1.2. Assuming that the City Engineer cares about air quality, what explains the absence of that argument? In Example 1.2, the City Engineer had several modes to choose from. Using our definitions, that was a multimodal case. In the next example, the City Engineer's boss is about to undertake an intermodal trip. —

ie

Example 1.3 The Mayor goes to 2 conference The Meyor of Mythaca is planning trip from her home (origin) to a conference hotel in a distant city a (destination). The trip could begin in her personal automobile, on a public transit vehicle, or in a taxi.

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This first link of her trip takes her from home to the airport terminal. This first segment is one of several line-haul portions of the trip. Here, we define “line-haul” as the movement between intermodal transfer points. If the mayor drives her car, she parks it at the airport parking garage, changing from the highway mode to the walking mode for a short distance, then perhaps taking a shuttle bus to the terminal. If the mayor leaves home by public transit or taxi, she gets dropped off directly at the door to the airport terminal. Each place where there is a change of mode is referred to as an intermodal transfer point. Table 1.1 indicates that this trip has several points where the mayor changes travel modes. While the main portion of her trip is by airplane, she uses several other elements of the transportation system. Make facilities used by the mayor during her trip. For each a list of the types of vehicles and transportation vehicle and facility, indicate whether it is likely to be privately or publicly owned and operated. Solutions to Example 1.3

The mayor drove her private automobile on city (public) streets to an airport parking garage that is probably owned and operated by a public airport authority. The shuttle bus, the airport roadway, and the airport terminal are under the jurisdiction of the public airport authority. The jetway and aircraft are owned by a private (non-government) entity, but the airport airside (apron, taxiway, and runway) at both the origin and destination airports are the airport authorities’. At the destination airport, the terminal is public. If a baggage claim area is dedicated to one airline, it is private; if it is shared among airlines, it is public. After leaving the airport-owned roads, the mayor travels on public streets to reach the conference hotel. She could drive a private rental car, take a private hotel shuttle, or hire a private taxi to do so. The lesson here is that a routine business trip makes use of a variety of travel modes and facilities, with a variety of public and private entities providing service in a coordinated fashion.

TABLE 1.1 Trip

Segment

START 1*

Transportation functions and activities during the mayor’s trip

Transportation Function

Activity

Location

Origin

Start trip

Home

Line-haul

Drives to the airport Parks car and boards shuttle bus Rides shuttle bus to terminal Leaves bus

City streets

Intermodal transfer point

2*

Line-haul Intermodal transfer point

3

Line-haul Intermodal transfer point

4

Line-haul Intermodal transfer point

8

Line-haul Intermodal transfer point

6

Line-haul

STOP *

Line-haul segments

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Walks to departure area Boards Aircraft Flies Lands Gets bags and walks Gets rental car, or boards taxior hotel shuttle bus Drives car, or rides bus or taxi

City streets

End trip

Destination 1

Airport parking garage Airport roadways Airport curbside Airport terminal Jetway Airspace Airport airside Airport landside Ground transportation facilities Hotel

and 2 in Table 1.1 can be replaced by a “transit or taxi” segment

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1.3.2 Freight Movement

Figure 1.7 shows the hierarchy of freight movement. The freight modes cover all forms of transportation. The pipeline mode is used to transport only liquids (e.g., oil) and various gases under pressure. The shaded portion of the diagram shows an important form of transportation called intermodal. Intermodal transport is when two or more modes are involved in the movement of goods from origin to destination. Several of the more common intermodal combinations are: ©

Rail & truck. Goods can be unloaded from one mode and loaded onto the other. These goods can be in containers or in truck trailers. Trailers on Flatcars

(TOFC) is included in Figure

1.7.

©

Water & rail. Increasingly, containers that arrive on a ship are transported by rail from the port, or vice versa,

©

Water & highway. Trucks can be driven on and off “roll-on/roll-off” ships (RO/RO in Figure 1.7), or catgo can be (un)loaded using a crane with lift-on/lift-off ships.

»

Air & highway. Trucks carry airfreight to and from the airport. Drayage. The short-distance movement of freight between major modes, such as trucks between port and railhead. (See Figure 1.7.)

Example 1.4 International Shipments and Tradeoffs has to move 100 containers from the A logistics manager

Far East to a plant in New Jersey. Each loaded container weighs 40,000 pounds. The container itself weighs 3600 pounds. It is loaded with a pharmaceutical product whose value is $4.25 per pound. Dunnage (packing material) accounts for about 15 percent of the cargo weight. The manager’s three choices can be seen in Figure 1.8. (1) He can move the containers by an all-water route through the Panama Canal, which takes 24

days.

(2) The goods can sail to Seattle/Tacoma in 10 days and take the railroad (called a Jand bridge) to

New Jersey, a trip that take 6 days, (3) The goods can sail to Long Beach in 12 days and be placed on a special double stack rail service that guarantees delivery within 72 hours. The prices for the shipping services are given in Table 1.2. Which route should the manager choose?

TABLE

1.2 Cost data for Example 1.4

Transport

Rate

All-water route

$2.45 per cwt. through Panama Canal $150 per container $1.25 per cwt to Seattle or Long Beach

Handling at Port in New Jersey Sail to West Coast port Handling at Port of Seattle Rail from Seattle to New Jersey Handling at Port of Long Beach Drayage at Long Beach to LA

Rail (double stack) from Los Angeles

$300 per container $3.25 per cwt $250 per container $150 per container $4.00 per cwt

Note: “cwt” = hundredweight = 100 Ibs Mad

ee

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18 FIGURE 1,7

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Hierarchy of Freight Transportation Options

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Water Reutes

Routes from Eure

FIGURE 1.8

Landbridge and all-water routes

Solution to Example 1.4. Table 1.3 summarizes the calculations for the 100-container shipment. One sampie calculation for each cost component in Table 1.3 is provided here.

(1.1) Transport cost through the Panama Canal is 100 containers * (40,000 Ibs /100 Ibs/ewt) *$2.45/cwt = $98,000, (1.2) Transport cost by rail from Seattle = 100 containers * (40,000 Ibs /100 tbs/cwt)

*$3.25/cwt = $130,000. (1.3) Handling cost at the Port in New Jersey is 100 containers * $150/container = $15,000.

Table 1.3 Solution to International Shipping Alternatives Panama Canal Sea-Tac+ rail

Options

Days of Shipping Transport (water) Transport (rail)

24

Handling Drayage Total cost

$98,000 $0

10+6=16 $50,000 $130,000

$15,000 $0

$30,000 $0

$113,000

$210,000

Long Beach + rail 12+3=15

$50,000 $160,000 $25,000 $15,000 $250,000

The route through the Panama Canal is the least expensive. Here is the explanation: © Option 1 (Panama Canal) is the longest, but there is no change of mode and handling is minimal, If there is no hurry to receive the goods, this option is best. © Option 2 (Sea-Tac + rail), and Option 3 (Long Beach + rail) have very similar transit times. Although Option 3 is one day shorter, it has additional costs related to drayage and railroad cost per pound. Therefore, Option 2 is better than Option 3, but not as inexpensive as Option 1.

This example shows the importance of considering characteristics of the commodities and the modes when analyzing freight operations. —

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SYSTEMS APPROACH TO TRANSPORTATION

1.4.1 Understanding Transportation Systems

Understanding transportation systems requires knowledge in three major areas. Just as a 3-legged stool

will not stand when one leg is missing, a transportation system performs best when all three “legs” listed below are present.

The Components of the System. A transportation mode can be defined by, among other things, the technology of the vehicle(s) used and the “way” that is used. A rail system uses different technology than a highway system. For passenger rail, steam has been replaced by diesel electric, which is being replaced in a few places by newer technologies. The “way” is the path used by a particular mode. Depending on the mode, the “way” could be a highway lane, a railroad track, a shipping channel, or a flight path. The control of the vehicle has usually been in the hands of a human operator, sometimes aided by technology. Emerging technology regarding connected, automated, and autonomous vehicles is likely to shift that relationship.

Leg

1.

Leg 2. Putting the System in Place. A common sequence in the life of a transportation project is

to planning, design, construction, and operations. Planning requires data collection and analysis, determine if the proposed project will meet the stated needs. The design phase must convert the planning The construction phase depends on the assurance that concepts into a practical facility or service. revenues adequate funding is available. Funding can be in the form of a government grant, a bond issue, from operations, or a combination. As used here, operations includes using the transportation system as efficiently (and safely) as possible and (through proper maintenance) to maximize its service life.

Leg 3. Issues for Viability. Viability here means the ability of transportation to meet its overall mobility requirements while meeting the social, health, economic, and accessibility goals of the community. In simplest terms, mobility is the ability to make trips. Accessibility has the additional qualification that desired destinations can be reached with reasonable effort or cost. Tripmaking often has negative impacts on others: noise, air and water pollution, equity issues, etc. These “externalities” need to be specifically addressed in the planning, design, and operations phases of a proposed transportation project. Other issues may also need to be considered — e.g., government regulations, local politics, behavior of users of the transportation system especially if they will affect the success of the project or service. --

THINK ABOUT IT Government regulations can affect transportation service and cost through regulations such as safety mandates. Seat belts, airbags, and car structure reinforcements are examples. If a better rollbar, side running lights, or a high-mounted rear brake light were options (not government-mandated standard features) on an automobile, how much more would you pay?

1.4.2 System Specifications

Transportation systems analysis is a way to design or modify a transportation system to meet the needs of the end user(s). It begins with a specification of the system’s objectives, and normally includes: (a) an investigation of the feasibility of the proposed system or its modifications (b) an estimate of the costs involved

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an evaluation of the alternative ways to achieve the objectives.

There will always be persons with an intense interest (or “stake”) in any proposed transportation project. These persons, called stakehoiders, who will need to have a voice in any decision, In this section, the systems analysis process will be introduced, The role of stakeholders will be covered more fully in Chapter 5, In specifying a transportation system, there are several important questions that the systems engineer/analyst should ask. The analysis of a system should begin with a clear understanding of its goals, purpose, or mission. The technology required for the system to perform its mission must be considered, as well as the system’s potential ability to meet the customer demands of accessibility, readiness, reliability, service and cost.

Most systems will have a hierarchy of specifications that begin with the system requirements. These requirements are, in turn, used in generating specifications for vehicles, the way, the communications and control components, and other subsystems within the transport system, Finally, these specifications will result in the detailed specification of components that comprise each subsystem. It is the designer’s responsibility to assure that specifications are generated at each level and that, when they are combined, the system will perform according to the overall or “top” system specification. The process of developing an overall specification generally results from answers to the following seven questions. [Volpe 1977] —

te



Example 1.5 Specifying an emergency medical response system for the County of Mythaca [Solutions given in italicfont] 1. What is the purpose of this system? The first statement in any specification contains a broad indication of the mission, scope, or objectives of the system. {The purpose ofthe Emergency Response (ER) system for the county is to provide quick, effective medical attention for all 500,000 residents in the county.] 2.

3.

4.

What is the

for this system’s operation? coverage area of

The answer to this question generally specifies the range or geographic area of use. It would also contain any special climatic conditions in which the system should work. {The ER system is to operate in Mythaca County, with emergency access to hospitals in nearby larger cities. It must operate in all weather conditions, with the help of other agencies, as needed] What are the technical specifics of the system’s intended mission/use? These specifics are usually defined in terms of the desired statistics that state the probability of achieving a given mission or by

defining the level of service or operational capability to be provided. (Note that these are not design specifications, but they are the first step leading to them.) /The system will have a 93% probability over the 24-hour day to be on the scene ofan emergency situation anywhere in the county in less than 15 minutes from the time the system is requested (usually via a 911 call). It must serve 80% of the population within 8 minutes oftime ofnotice Note: When safety is an important issue, it is made part of this specification. What is the capacity of the system? The demand for the system, especially in the peak periods, is critical. What level of use does it take to make the system ineffective? When is it saturated? What is the performance of the system near saturation? {Mythaca’s ER system will be able to handle at least 6 calls simultaneously

]

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What is the availability or operational readiness when the system is called into use? Sometimes the accessibility for the user to avail himself of the system is included. [The Mythaca ER system will have an availability of 96%. This includes communication from the caller to the system dispatcher and includes readiness ofthe vehicle(s) and Emergency Technicians to be deployed once the call is

5.

]

received al What is the reliability of the system in operation? A system that is available may fail while it is in use. Reliability is estimated on the probability of functioning properly when in use. The life expectancy of the system may also be specified. {The ER system reliability will be greater than 99.5%. Equipment will be replaced at the end of its service life.] What is the cost-effectiveness of the system? Every system needs to be evaluated on the basis of its

6.

7.

life-cycle cost, which includes the costs of research, development, implementation, investment, operation and maintenance. Often costs are weighed against the potential benefits of the system. Systems with a "benefit-to-cost ratio" in excess of one are usually funded. [The Mythaca ER system shall show a benefit-to-cost ratio greater than one when the benefit ofa life saved is estimated at one million dollars and the discount rate is 5%]

+

—4-

~

Vi

THINK ABOUT IT Some people get the availability and the reliability of a system confused. Can you explain the difference?

—--— Example 1.6 Mythaca As A Regional Airport Years ago, Mythaca’s small airfield was being considered for expansion to a regional airport to serve the region including Mythaca, Shoridan, Mazurka, and other towns within an hour’s drive. Apply the system specifications framework as what could have been a starting point for assessing the expansion of the old airfield and terminal. Solution for Example 1.6 Sample system specifications for Mythaca Regional Airport (MYT) are given in the table below. Note that Safety and other issues have been included as part of Technical Specification #3.

Top Level Specification 1.

--

Mythaca As A Regional Airport

PURPOSE/GOAL

2.

AREA OF COVERAGE

3.

TECHNICAL SPECS 3A. SAFETY 3B. SECURITY 3C. NOISE

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Grow to become a “small primary hub” airport serving all of Mythaca County. Provide facilities/runways for air service to destinations within 500 miles,

All Runways will have a Runway Protection Zone with expansiori potential. Be able to meet federal standards.

Emit no more than 60 dB of noise affecting local residents, schools, :

businesses.

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4.

CAPACITY

5. 6.

AVAILABILITY RELIABILITY

7

COST-

Handle 0.25% of national enplanements. Maintain competent services for General Aviation at a level up to 20% of total operations. Provide all-year all weather capability for air service. Maintain standards for flight cancellations, lost luggage, and on-time performance.

EFFECTIVENESS

Maintain competitive landing fees. Document contribution to regional economic activity.

To 14.3

Performance Measures as a Prime Tool of Systems Analysis

The systems analyst must consider the impacts of a project on the user, the operator, and the environment. The use of resources to create and operate the system is also of concern. Throughout this text, performance measures ere used to evaluate a design or assess the impact of proposed alternatives. People use performance measures every dey. For example, it takes 3 hours to go from point A to Point B via the shortest time route, or my automobile gets 32 miles per gallon of gasoline, or the price of gasolirie is $3.40 per gallon. The transit operator thinks in terms of operating cost per vehicle hour or farebox revenue per passenger. In design, the engineer will need to consider a number of performance measures

to effectively address engineering problems in transportation and to evaluate (sub)system capabilities. Because transportation investment decisions usually involve large expenses, performance measures should be chosen carefully. Several of the more pertinent performance measures are shown below. The list below is not exhaustive, but is intended to be illustrative. ©

© ©

« ®

© *

* ©

©

°

Average Speed and Maximum Velocity. Miles per hour (Kilometers per hour) Freight or passenger travel. Ton-miles or passenger-miles per year Operational use/capacity. Operations per hour or passenger cars per hour per lane or vehiclemiles traveled per year; percent of time an airport’s runway is occupied by an aircraft

Density oftraffic. Passenger car equivalents per mile per lane Range ofoperation. Miles Energy Use or Intensity. BTUs per ton-mile or BTUs per passenger-mile Acceleration and Braking. Feet per second per second, or G’s Cost of Transportation Operation. Cents per ton-mile (or per passenger -tile) Safety. Fatalities or crashes per year or per mile traveled. Crash rate per aircraft departure.

Reliability. Failures per unit time or per unit distance traveled; mean time between failures; minutes delay per aircraft operation Availability or Readiness. Percent of requests for service that are served; probability that a request is served

*

Weather Performance. Feet or meters per knot of crosswind

©

Tailpipe Emissions. Grams of hydrocarbons per vehicle-miles traveled Noise Emissions. Decibels

©

=

of braking distance on wet pavement; runway width

Productivity. Ton-miles delivered per labor hour

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—-eExample 1.7 Performance Measures for Stakeholders. In Example 1.1, stakeholders and their concerns regarding a new (relocated) US Highway 39 to replace those portions of US86 and US39 that pass through the City of Mythaca were identified. How will the or Mythaca Planning Commission be able to measure the extent to which each stakeholder’s wishes

concerns have been addressed? Use the illustrative list of performance measures above as a starting

point.

Solutions for Example 1.7

The values of the performance measures cited below will determine the degree of support (or opposition) by the stakeholder(s) involved. — (1) Neighborhoods. Vehicle noise acceptable decibel levels at sensitive locations along the old and

new highway alignments. Emissions — pollutant concentrations that meet air quality standards. — Safety crashes per year and crash severity are reduced. — (2) Land owners. Land taken — acres from each owner. Price government offer versus assessed value — for property tax purposes or sale price of comparable properties. Usefulness of remaining property

subject to negotiation or lawsuit, which may affect price paid. — (3) Businesses. Business impacts of diverted traffic Lost sales revenue as estimated by economic — What type of businesses will be allowed? impact models. Zoning changes — (4) DOT. Cost of new highway — engineer's estimate. Economic benefits estimates from economic — Check timing of projects with higher priority. impact models. When is state money available? Local share — dollars offered in specific year(s). — (5) County and City. Local contribution dollars in specific year(s), constrained by other commitments. Condition of old US highways at relinquishment — smoothness (International Roughness Index), structural condition (Pavement Serviceability Rating), and conditions of features such as curbs and

guardrails. — — (6) Environmental groups. Farmland lost acres, yield per acre. Endangered species degree of threat,

mitigation alternatives. Noise and air quality impacts concentrations that meet air quality standards



acceptable decibel levels and pollutant

CHAPTER1 SUMMARY Transportation plays an important role in society. Most human activity involves, or depends on, movement — directly or indirectly. Because they are important transportation links, lakes and rivers have been a main reason for the location of early settlements. Canals, railroads, roads, and airplanes followed — each influencing the way the US has developed. In today’s world, transportation projects benefit from on progress in technology and analytical methods. Transportation investment decisions are based procedures that have become standard practice. When appropriate, the procedures include participation by stakeholders. This chapter introduces concepts that are fundamental to the practice of transportation and a engineering. Examples illustrate the difference between multimodal and intermodal transportation,

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framework for a systems approach to designing a transportation project is introduced. Performance measures have become an important aspect of transportation systems analysis. The topics introduced in this chapter form the basis for a study in subsequent chapters of the Fundamentals of Transportation

Engineering, using a Multimodal Systems Approach.

ABBREVIATIONS AND NOTATION FOR CHAPTER 1 ewt

FHWA FTE

PUD RO/RO

TOFC

hundredweight Federal Highway Administration Fundamentals of Transportation Engineering (this textbook)

pickup and delivery roll-on/roll-off trailers on flatcars

GLOSSARY FOR CHAPTER 1 Accessibility: the degree to which desired destinations can be reached with reasonable effort or cost

Availability: the percent time the system can be accessed and used Capacity: the amount of goods and/or persons a system can handle before reaching saturation Coverage: range or geographic area of system operation Drayage: the short-distance movement of freight between major modes, such as trucks between port and railhead.

Dunnage: packing material Intermodal: when two or more distinct modes are used to carry persons or goods from origin to destination

Intermodal Transfer Point; place where persons or goods shift from one mode to another or one vehicle to another

Line-haul: the movement between terminals or intermodal transfer points Logistics: the management of the movement of goods, services, and information from origin to intended destination

Mobility: the ability to make trips. Multimodal: consideration of at least two transport modes

Reliability: the percent time the system performs according to its specification Relinquishment: change of ownership, most often when a state highway becomes a city street Roll-on/roll-off: ships that allow wheeled cargo to be rolled on and off the vessel Stakeholder: people who can be affected — positively or negatively — by transportation projects or policies

Transportation: the movement of people and goods from place to place. Viability: the ability of transportation to meet its overall mobility requirements while meeting the social, health, economic, and accessibility goals of the community. Way: the means by which a transportation mode moves — road, rail, water, air, etc.

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INDEX FOR CHAPTER 1 mobility, 1, 14

accessibility, 14 Airline Deregulation Act, 6

hundredweight, intermodal, 8, 9

drayage, 13

intermodal transfer point, 10

Drayage, 11 Federal Aviation

land bridge, 11

Administration, 6

Federal-Aid Highway Act, 5

11

multimodal, 8, 9 Mythaca, 2

line-haul, 6, 10

Shoridan, 2 stakeholders, 3, 15

logistics, 11 Mazurka, 2, 3

viability, 14 way, 15

REFERENCES BLS (2013). Consumer expenditures — 2012. US Department of Labor, Bureau of Labor Statistics. http://www.bls.gov/news.release/cesan.nr0.htm. Released 10 September 2013. Retrieved December 2013. Fatout, P. (1985) Indiana Canals, Purdue University Press, ISBN 0911198784.

11

FHWA (undated). The Dwight D. Eisenhower System of Interstate and Defense Highways. http://www.fhwa.dot.gov/interstate/homepage.cfm. Retrieved

8

November 2013.

NOAA (2013). Oceanfacts. National Ocean and Atmospheric Administration. http://oceanservice.noaa.gov/facts/population.html. Revised 26 March 2013. Retrieved 11 December 2013. Santos, A., N. McGuckin, H.Y. Nakamoto, D. Gray, and S. Liss. Summary of Travel Trends, 2009 National Household Travel Survey. Us Department of Transportation, Federal Highway

Administration. June 2011.

Volpe National Transportation Systems Center, Discussions at. USDOT, 1975-77

EXERCISES The Role of Transportation 1.1 The impact of transportation technologies. Choose one of the technologies below. Give a brief description and explain the impact it had, has, or possibly will have on society. Are any controversies associated with the technology you chose? Cite your sources

A. Airbags in passenger cars B. Bluetooth C. Cable car

I.

Global Positioning System (GPS) High-speed rail

J. K. Hybrid electric/internal combustion engine for automobile or transit bus L. Hyperloop M. Magnetic levitation vehicle N. Seatbelts in school buses

D. Drones for peaceful uses E. Ethanol as an alternative (or supplement) to gasoline

F. First bicycle

O. Seatbelts in private vehicles G. First steam engine P. Supersonic transport H. Funicular 1.2 The role of transportation in historic events. Choose one of the events listed below. Give a brief description of the role played by transportation in the event, or how the event affected transportation. Were any lessons learned? Cite your sources. B. Airliner aspects of September 11, 2001 A. Airline crash of particular interest to you

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C. Berlin Airlift D. “Carmegeddon” in Los Angeles

H. Evacuation of New Orleans after Hurricane Katrina E. Deregulation of the airlines I Fuel shortage in the 1970s F. Deregulation of the trucking industry J. Hindenburg, Crash of the G. Dunkirk K. Threat of terrorism L. Train crash of particular interest to you 1.3 Transportation facilities. Choose one of the facilities listed below. Give a brief description of the facility and its significance. Cite your sources. A. Appian Way E. Lincoln Highway (predecessor of US30) B. Burma Road F. National Road (predecessor of US40) C. English Channel Tunnel G. Paname Canal D. German Autobahns. H. Pennsylvania Turnpike 1.4 The “transportation disadvantaged". Think of an adult you know who does not drive a car. Why is it the case that that person is a non-driver? How does that person make the trips he/she needs to? What can the transportation professional do to increase that person's mobility? 1,5

A Campus People Mover — Objectives and Stakeholders.

The number of students at Mythaca State University has grown dramatically in recent years. Funds are being raised for new classroom, lab, and office buildings. The only places to put these new buildings are where parking lots now dot the central campus. Moving parking to parking garages at the edges of campus will increase walking distances, but may alleviate the growing safety problem of pedestrians, bicyclists, and motor vehicles using (end crossing) the streets that crisscross the campus. Most of those streets will closed, in favor a network of bicycle paths. A transportation professor suggests that an automated people mover

(APM) be considered to facilitate the movement of students and staff on the new car-free central campus. The professor invites members of the university’s Physical Facilities department to his Transportation Design class. After some discussion, two conflicting objectives for the APM emerge: © Get drivers from their vehicles parked in the perimeter garages to central campus, and return. e Get students between classes, especially if the classes are too far apart to reach by walking during the 10-minute class change period.

A. How would you describe an Automated People Mover? (See Chapter 10 of this book if you need help.) Have you ever ridden one? If so, where? B. Which objective do you think should be adopted? Why? C. For the objective you adopted in Part B, make a list of at least three stakeholders who should participate in the planning and design of the Campus APM.

Fundamentals of Transportation Engincering 1.6

A Campus People Mover (continued).

Where in the hierarchy of Figure 1.6 do you think an

automated people mover should be placed?

1.7 Determining the value of time. How valuable is your time, especially as it relates to travel? A. Imagine a case in which you could spend 75 cents to take a 5-minute bus ride, instead of walking 15 minutes to the same destination. How much would your time be worth if your decision is to take the bus?

-

Devise and clearly describe another experiment to determine the Value of Time (VoT). Provide actual or hypothetical values for the experiment, then calculate the VoT value from that experiment.

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C. What would be the flaws in “experiments” such as those in Parts A and B? Multimodal and Intermodal Transportation 1.8 Per capita freight movement. For a recent year, find the total ton-miles of freight shipped in the United States. Approximately how many ton-miles per US resident was that? Hint: A good source is the Commodity Flow Survey found at the Bureau of Transportation Statistics website www.bis,gov. 1.9 International Shipments with a Duration Cost. Repeat Example 1.4, but introduce a “duration cost” that penalizes a shipping mode $13,000 for each day the goods are in transit. Which route

should the logistics manager choose? Shipping bags of sand. Repeat Example 1.4, but now the product being transported is sand in bags. Each loaded container weighs 80,000 pounds and dunnage is negligible.

1.10

A Systems Approach to Transportation Leg 1 of the stool: The Components of the System. For the Campus People Mover proposed in Exercise 1.5, list the components that will comprise the system. 1.12 Leg 2 of the stool: Putting the System in Place. For the Campus People Mover proposed in

1.11

Exercise 1.5, describe the data collection and analysis activities needed to determine

if the proposed

project will meet the stated needs. 1.13

Leg 3 of the stool: Issues for Viability. Discuss the viability issues associated with the Campus

People Mover proposed in Exercise 1.5. Address the applicable issues raised in Section 1.4.1, 1,14 A Campus People Mover (continued). Base your responses to the questions below on the objective you adopted in Part B of Exercise 1.5. A. Develop a set of System Specifications for the Campus People Mover. List the specifications as was done in Example 1.5 or Example 1.6. If you can’t decide on specific values, use “XX” instead.

B. List four performance measures, including their units, that you think should be used to (1) set standards for the proposed People Mover and (2) determine the extent to which those standards are met.

1.15 Specifications for Trash Collection. The City Council of Shoridan is concerned about Saturday morning automobile traffic at the City Dump, because each household must dispose of its own trash. There also has been a rash of illegal dumping of trash by the residents in vacant lots and along roads. The city has purchased property in the hills at the edge of the city. That property is suitable for a landfill that will last 30 to 60 years. The council members now want to hire a company to provide curbside trash pick-up service and transport it to the landfill. The city will pay

for the landfill operations and the road needed to reach the landfill by charging commercial dumpers a "yet to be determined" fee. The private company will also need to provide some recycling services. The council, therefore, has asked you, a consultant, to help them prepare the specifications for the service that the prospective bidders will respond to. Using the general criteria for system specifications given in FTE Section 1.4.2 and your knowledge of the kind of services needed, prepare a set of specifications for the council to use in framing their Request for Proposal. Use the list format from Example 1.5, which will allow you to explain and justify your specifications, as needed. 1.16 Specifications for a Bicycle Network. The Mythaca City Parks and Recreation Department wants to expand and/or fill in the existing network of bicycle trails and bicycle lanes in and near the city.

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As part of the development of a Request for Proposals to be solicited from urban design firms, the Parks Department wants you to write up a set of system specifications for the designers to use. There are two principal users of the bicycle network — recreational riders and commuting bicyclists. level-of-service measure for bicycle facilities that is gaining acceptance is called the Bicycle Compatibility Index. The BCI is explained and illustrated at

A

http://www.hsre.unc.edu/research/pedbike/98095/index.html. See especially Table 2 at that site. Using the general criteria for system specifications given in FTE Section 1.4.2 and your knowledge of the kind of services needed, prepare a set of specifications for the council to use in framing their Request for Proposal. You are not being asked to design the new network; simply follow the 7item structure in FTE Section 1.4.2. The list format is preferred, because that format will allow you to better explain and justify your specifications, as needed. Your work will be evaluated according to how useful the Mythaca City Parks and Recreation Department Director would find your

specifications, Assume that the director knows what system specifications are and that he has access to FTE Section 1.4.2. 1.17 Specifications for 2 Fire Station. The City of Mythaca needs to find a location for a third fire station, so thet property in newly annexed territory can be properly served. The City Engineer is planning to conduct a study to identify and evaluate alternative locations for the third fire station. The study must incorporate Insurance Service Office (ISO) standards for fire station locations. Using the general criteria for system specifications given in FTE Section 1.4.2, create a systems

specification that could be used to help decide on the best site for the new fire station. You are not being asked to make the location decision; simply follow the 7-item structure in FTE Section 1.4.2. The list format is preferred, because that format will allow you to better explain and justify your specifications, as needed. Your work will be evaluated according to how useful the Mythaca City Engineer would find your specifications. Assume that the City Engineer knows what system

specifications are and that he has access to FTE Section 1.4.2. 1.18 Systems specification to help detect red light running. The incidence of red light running in the City of Mythaca seems to have increased in recent years. The City Engineer wants your firm to help him determine the extent of the problem. Answer the questions below in a clear, concise fashion, Hint: It would be helpful to observe a signalized intersection and discuss your ideas with someone else.

A. A definition for the average citizen. The City Engineer often finds himself talking to citizens of to members of the media. He needs a clear, concise definition of red light running that he can use when being interviewed or when talking to citizens. Give him a sentence (or two or three) to memorize.


TUCKS _ 168 tot vehs ~

Vd

199

=

33.3 percent.

THINK ABOUT IT Does 33.3 percent trucks seem high to you? Based on your intuition or experience, how does this value vary by highway type? How does percent trucks vary by time of day or time of night?

2.1.3 Accounting for Uneven Flows For many analyses, a simple 10-minute, 30-minute, or one-hour count may not be what is needed. Rather, the measure of the fluctuation in traffic flow during the period of analysis may be required. As we shall see in Chapter 3, some analyses of roadway capacity are based on the largest of the four 15-minute flow rates during the hour being studied. It is possible to have four egual 15-minute counts during an hour, but it is much more likely that those four counts will vary within the hour. The peak hour factor (PHF) for a

roadway (or lane of roadway) is calculated using the equation

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PHF = where

Vv

2. (22)

AV,

V = hourly volume and V;5 = peak 15-minute count.

Figure 2.3 summarizes measurements made August 1983 in the middle lane of three southbound ianes on Interstate 35W in Minneapolis, Minnesota, 4 miles south of the Central Business District. Each 5-minute count has been converted into an equivalent hourly flow rate, with units vehicles per hour (vph). The twelve consecutive 5-minute periods that produce the maximum one-hour vehicle count (1622 vehicles) begin at 7:20 AM. Within that hour, the 15-minute volumes and flow rates are as shown in

Table 2.2. Remember that the measurements are for only one lane.

aa

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=

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see

Relationship between long term and short term flows. From Highway Capacity Manual 2000. Copyright, National

Academy of Sciences, Washington, D.C., Exhibit 8-10, p. 8-10. Reproduced with permission of the Transportation Research Board.

16min Flow Rates

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| 1236

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Example 2.3 Determining a Peak Hour Factor Figure 2.3 shows a set of vehicle counts made in 5-minute intervals for the middle SB lane on an urban freeway. What is the peak hour factor (PHF) for the peak hour shown in Figure 2.3?

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Solution to Example 2,3 Figure 2.3 shows traffic flow data for the middle SB lane on I-35W. The peak hour for that lane begins at 7:20 AM. That lane's PHF is calculated by applying Equation 2.2 to the data in Table 2.2. The volume for the hour beginning at 7:20 AM is also the flow rate for that hour, or v= 1623. Of the four 15-minute periods that occur during the hour that began at 7:20 AM, the peak 15-minute period began at 7:35 AM. The count during that peak 15 minutes was 495 vehicles. The flow rate for the hour beginning 7:20 AM is 1623 vph. The maximum 15-minute flow rate in Table 2.2 is 4 *495 = 1980 vph. Equation 2.2 becomes

HF

1623

4x495

= 0.82

TABLE 2.2 Traffic volumes and flow rates on J-35W 15 minutes beginning

Vehicle Count

Flow rate

7:20 AM 7:35 AM

389 vehicles 495 vehicles

1556 vph

7:50 AM 8:05 AM

376 vehicles 363 vehicles

1504 vph

7:20-8:20AM

1623 vehicles

1623 vph

1980 vph 1452 vph

If only the flow rates (Column 3 of Table 2.2) had been provided, it would be a waste of time to recreate the counts from which the flows were computed, just to match the requirements of Equation 2.2. Instead,

using the flow rates directly in PHF =

~‘NF ~ |

1623

4* (1980/4)

= 0.82 produces the same result.

THINK ABOUT IT As traffic flow within an hour becomes more variable, i.c., fluctuates more, does the PHF increase or decrease? Is it ever possible that PHF > 1.00?

2.1.4 Traffic Flow Data Collection Techniques and Technologies Counting vehicles may seem like a simple concept, and it is— in concept. Traffic counts are also important for several applications. Among the uses are:

A. Documenting locations of congestion B. Establishing trends in traffic growth as a basis for future investment to increase the capacity of a roadway

C. Determining whether a stop sign or traffic signal is needed at an intersection D. Supporting the design and evaluation of new or improved traffic signal timing plans

E. Meeting the data reporting requirements of the federal government or other agencies.

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For some applications, the data needed may be simple traffic counts taken for a short period of time, such as during peak periods or during special events. In some cases, such as “D” above, even off-peak periods may be of interest, to help make the signal timing plan as efficient as possible for all times of day. Case “1” also requires that the number of vehicles making each tumming movement (left, through, or right) from each approach direction be recorded.

There are many different ways to collect traffic count data, depending on the intended use of the data, the nature of the roadway being studied, and the resources available to the counting agency. For example, a familiar way to do traffic counts is to use a pneumatic road tube stretched across one or more lanes

of roadway. (See Figure 2.4.) A tire passing over the rubber tube affixed to the road surface creates

a burst of air pressure that activates a ceramic diaphragm in a metal box to record the event. Tube counters can store the number of times a set of tires has activated the tube since it was set out. Tube counters have several shortcomings, however: 1) They count only axles, not vehicles. A vehicle with four exles will register as if two

2-axle vehicles have passed by. An “axle correction factor”, equivalent to the average number of axles per vehicle, must be used to convert axle counts into vehicle counts. Typical values for an axle correction factor range from 2.04 for local streets with few heavy trucks to 2.86 on Interstate highways.

2) The more advanced tube counters can store counts by one-hour or 15-minute intervals, but cannot store the arrival times of individual vehicle (or axle) arrivals.

fel

3) They often malfunction, are damaged, or are vandalized.

4) Many local governments cannot afford to own them. In such cases, local governments may be able to rent them from private companies or borrow them from other public agencies or from their state’s Local Technical Assistance Program (LTAP). Each statehas an LTAP, whose mission is to provide technical assistance to local public agencies

+

FIGURE 2.4

Pneumatic road tubes with traffic

counter. Photo: Jon D. Fricker

(cities, towns, and counties) on matters related to transportation.

Vi

§

THINK ABOUT IT How would you determine the value of the axle correction factor to use on a given roadway? What is the minimum possible value for an axle correction factor?

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Several alternatives to oad tubes exist. At the low-technology end, persons with clipboards (see Figure 2.5) or electronic count boards (Figure 2.6) can be used to record traffic volumes.

TABULAR SUMMARY OF VEHICLE COUNTS ofA

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© 1976 Institute of Transportation Engineers.

Source: B Ox Used by permission.

JAMAR TECHNOLOGIES; Int

oi

FIGURE 2.6 Electronic count board for turning movement counts. Source: Jamar Technologies Inc., used with permission

Devices higher than road tubes on the technology spectrum that you might see are:

A. Loop detectors (Figures 2.7 through 2.9). Sending an alternating current through the loop creates a magnetic field. Any conductor, such as the engine of a car, that passes through the field will cause changes in the magnetic field and a detectable change in the current. When the inductance or frequency of the loop passes a preset threshold, this indicates that a vehicle has been detected.

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———l

|

Loop

Loop l

Speed Honitoiing

Loo

Vehicle Counting FIGURE 2.7 Loop detector configurations

ale wi

iy

FIGURE 2.8

FIGURE 2.9 Loop detector to actuate traffic

Photo: Darcy Bullock

signal, after wire has been installed and sawcut has been sealed. Photo: Jon D. Fricker

Pavement marked for sawing machine to make cuts for loop detector wire.

B. Magnetometers (Figure 2.10). These wireless magnetic sensors are embedded in the pavement to record a vehicle’s magnetic signature and send the information to roadside controllers, traffic management systems, or other vehicle detection applications.

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C, Radar and Video methods. These technologies can mimic inductive loops in the pavement and detect the presence of vehicles. The devices shown in Figure 2.11 are mounted on traffic signal mast for testing at an intersection that is already equipped with in-pavement loops.

a

FIGURE 2.10. Magnetometer. Photo by Jon D. Fricker FIGURE 2.11

Radar and Video vehicle detectors. The radar device on the left is facing northbound traffic and the video camera on the right is facing southbound traffic. Photo by Jon D. Fricker

The more sophisticated technologies can provide greater reliability, accuracy, and detail in the data they collect, although each has its drawbacks and the performance of each must be frequently checked. A good summary and comparison of vehicle detection technologies can be found in Mimbela and Klein (2007).

~

Va

~“

THINK ABOUT IT What factors would you consider when evaluating any technology for use in counting traffic?

2.1.5 Turning Counts into Design Data Among the many possible examples of collecting and using traffic counts, let us concentrate on the ongoing effort by each State Department of Transportation (DOT) to monitor the amount of traffic that uses each segment of its highway system. The goal of a traffic monitoring system for highways (TMSH) is an accurate AADT value for each state highway segment. AADT stands for annual average daily traffic, expressed in vehicles per day that travel in either direction on the road segment. It is a two-way count. For most road segments (those that do not have a permanent traffic counter present), AADT is the result of two principal activities.

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Periodic 48-hour “coverage counts” taken on the roadway of interest. Ideally, these counts should be taken every year or two, but limited state DOT personnel, equipment, and budgets, coupled with a DOT's “special count” responsibilities, can make the time between coverage counts more like 3-6 years. “Special counts” are taken when traffic data are needed before the planned coverage count at a site. For example, traffic counts for a road segment or intersection with a recent increase in crashes

will permit a more accurate calculation of a crash rate. (This will be covered in Chapter 6.) Coverage counts are usually done during a 48-hour period between Monday noon and Friday noon, thereby avoiding the abnormalities of weekend traffic. [FHWA 2001]

2) Seasonal adjustments. Because of limited staff and counting equipment, coverage counts are done on different road segments within a jurisdiction at different times of the year. This means that the coverage counts must be adjusted to account for seasonal fluctuations in traffic levels. The degree of seasonal traffic fluctuation varies by classification of highway (see Table 2.3) and proximity to vacation areas or special event locations. The seasonal adjustment factors are derived from counts made at permanent count stations (PCSs) that are located around the state on a representative sample

of roads in each functional class.

TABLE 2.3 Class

1

Functional Classes of Roadways

= Rural Interstate

Class

11

= Urban Interstate

Class 2 = Rural Principal Arterial

Class 12 = Urban Other Freeways and Expressways

Class 6 = Rural Minor Arterial

Class 14 = Urban Principal Arterial

Class 7 = Rural Major Collector

Class 16 = Urban Minor Arterial

Class 8 = Rural Minor Collector

Class 17 = Urban Collector

Source: Highway Performance Management System Field Manual, Chapter IV, 30 August 1993

FHWA,

Design hourly volume. The number of lanes needed on a given roadway is based on the existing or anticipated demand for travel on a particular road segment. Traffic counts are the starting point for the design of roadways. The standard procedure uses the 30” highest 2-way hourly volume in a year as the design hourly volume (DHV). If the road segment happens to have its own permanent count station, all that needs to be done is to rank the most recent year’s worth of hourly traffic counts from highest to lowest, then choose the volume ranked number 30. For most roadways, however, a full year of hourly counts are not available. In Indiana, for example, there are approximately 100 permanent count stations, but about 11,000 miles of roadway on the state highway system. If the typical highway segment for traffic count purposes is two miles long, only about one in every 55 segments has its own PCS. For those segments without a PCS, the design hourly volume could be estimated either by

(8) Carrying out a “special count” for one year on the road segment in question, then ranking the onehour volumes so recorded, or

(b) Using relationships established by observing other roadway segments with similar characteristics.

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~

Vi

THINK ABOUT IT

-

What are the (dis)advantages of data collection methods (a) and (b) above to determine DHV? Which method do you prefer? Under what conditions would you favor either

(a) or (b)? Method (b) is implemented by using a plot like that in Figure 2.12. In the figure, the highest hourly volume for the year, expressed as a percentage of the annual average daily traffic (AADT) value, is plotted at the left edge of the graph. For exemple, if the highest hourly volume in a year for a particular freeway in a recreational area was 1044 vph, and its AADT was 4777 vpd, its highest “Traffic as a

Percentage of AADT” value would be (1044/4777)* 100 = 21.85 percent. This calculation could be repeated for an adequate number of roads of the same functional class having at least one year’s worth of hourly count data. In fact, this was done to establish the values for four road classes in Table 2.4. In

Figure 2.12, the average value for the highest hour on freeways in recreational areas is 25 percent of the AADT. Of greatest interest to us is the 30 highest average traffic volume as a percentage of AADT. This will help the analyst decide whether additional lanes should be considered for the roadway. Example 2,4 will demonstrate.

25

|

5 $

—#--Recreational

5

—a—Rural Freeway

8 @e

* 5

—x~ Urban Radial *

4

-—

at



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—@-Urban Ring Road 30th DHV

t

|

|

oO: 0

a

10

20

.

#30

40

~»#

50

Rank {by hour} of traffic volume FIGURE 2.12

Relationship between 2-way peak-hour volume and annual average daily traffic on four classes of roads for Design Hourly Volume. Based on HCM 2010, Exhibit 3-7

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THINK ABOUT IT Each of the curves in Figure 2.12 “slopes down” as the “Rank by hour” value gets larger (worse). Explain why this makes sense.

TABLE 2.4

Ranked hourly volume as percentage of AADT

Road class Recreational Rural Freeway Urban Radial Urban Ring Road — —

Average AADT

50th

23.0

30th 21.0

20.0

3862

15.0

13.5

13.0

10553

10.0

9.5

9.25

9.0

120173

75

7.35

7.25

72

141550

1st

10th

25.0 17.5

+

Example 2.4 Design Hourly Volume Mythaca County is studying the possibility of asking the state to increase a rural section of SR43 from two lanes to four lanes. The county engineering staff believes that Figure 2.12 applies to SR43, which has an AADT of8110 vpd according to the latest state traffic counts. What is the DHV for this section of

SR43? Solution to Example 2.4

For a rural freeway, the 30" highest hour in Table 2.4 is 13.5 % ofthe AADT. This makes the DHV = 0.135

*

8110= 1095 vph.

Discussion of Example 2.4 Under ideal conditions — adequate sight distance, equal traffic flow in both directions, no traffic signals or — stop signs, and no heavy vehicles this DHV would not justify additional lanes. In Chapter 3, a more detailed analysis will be introduced to determine the actual need for more lanes.

K-factor. Besides the peak hour factor and the design hourly volume defined above, another measure of the temporal variation in traffic is the X-factor. The K-factor is the proportion of daily traffic at a site that occurs during the peak hour.

=

Vea AADT

(2.3)

If Vpeax is important to the analysis or design of roadways or intersections, the best situation is to collect peak-hour data for the sites of interest. In many cases, however, there are too many sites and/or too little time to collect the data directly. In these situations, K-factor values must be assumed or borrowed. Local data may be available for similar facilities with similar demand characteristics, (HCM 2000, p. 8-9) but the K-factor can vary from site to site in the same city. Table 2.5 shows how K-factors tend to decrease as AADT increases.

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TABLE 2.5

Example K-factors

Average K-factor

AADT 0-2,500

0.151

2,500-5,000

0.136

5,000-10,000

0.118

10,000-20,000

0.116

20,000-50,000

0.107

50,000-100,000

0.091

100,000-200,000

0.082

>200,000

0.067

Based on HCM 2010, Exhibit 3-9, Note: K-factors are for the 30°-highest traffic volume of the year.

THINK ABOUT IT

™~

Make sure you are clear about the difference between the K-factor and the peak hour factor (PHF). —

Example 2.5 The K-factor According to counts taken three years ago that are available on the State DOT’s web site, SR361 had an AADT value of 17,140 in downtown Mythaca. While waiting for the State DOT to retrieve the hourly traffic counts for SR361 from its archives, the city engineer decided to use the default values in Table 2.5 to begin his analysis. A short time later, the State provided the requested data — the peak hourly volume was 1779.

A. What K-factor did the city engineer use in his preliminary analysis, while waiting for the State’s data? B. What K-factor did the segment of SR361 actually have, according to the State’s data? Solution to Example 2.5

A. The downtown road segment has AADT of 17,140, so K = 0.116 is the best value to borrow from Table 2.5. The peak volume would then be estimated as Vpeax = K * AADT = 0.116 * 17140 = 1988, B. From Equation 2.3,

K

=

=1779 Vea AADT 17,140

0.104. Using the default K-factor values in Table 2.5

would have overestimated the peak hour volume by 1988 - 1779 = 209 vehicles.

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The measures of temporal variation in traffic covered in this chapter so far have used two-way volumes as their bases. It is quite common to have traffic flow at a point that is not 50 percent in each direction during the time of interest, especially during the peak period. Traffic data on directional distribution should be collected, borrowed, or assumed, to better assess the ability of the existing or in more proposed roadway to accommodate the traffic flow in the major direction. This will be covered detail in Chapter 3.

To this point in Chapter 2, the reader has been introduced to ... basic traffic characteristics and how to measure them traffic data collection technology and limitations

©

e

examples of converting traffic data for use in roadway design. Now that the basic definitions of traffic characteristics have been introduced, the focus will shift to how to measure them, and how to use them for design. The next sections in Chapter 2 are concerned with ®

measuring traffic characteristics.

2.2

MEASURING TRAFFIC SPEEDS AND DENSITIES

2.2.1 Speed Calculations

Why collect speed data? Three common applications come to mind: 1. To monitor the quality of traffic flow. Reductions in speed are evidence of congestion. Relationships to be

SPEED

30)

introduced in this section will make inferences about flow quality from speed values possible.

2.

To monitor speeds with respect to the speed limit or with respect to driving conditions. If speeds on a road segment are excessive, then speed limit enforcement measures there may have to be intensified.

3.

To establish the basis for a speed limit, One common starting point is a legislative standard speed limit for urban or rural road segments. For example, the state may set 55 mph as a default speed limit for all roads in

rural areas and 30 mph as the default urban street speed limit. These default values can be adjusted after appropriate engineering studies, such as the one featured in an example later in this chapter.

= FIGURE 2.13 Solar mobile speed monitor. Source: Decatur Electronics, : Inc. Used with permission

There are two different ways to compute average speeds in a traffic stream. According to McShane, Roess, and Prassas [1998]: e

Time mean speed (TMS) is defined as the average speed of all vehicles passing a point on a highway over some specified time period.

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Space mean speed (SMS) is defined as the average speed of all vehicles moving over a given section of a highway over some specified time period.

The time mean speed is a point measure, such as that obtained by a radar gun. It is sometimes called a spot speed. The space mean speed is ascertained by timing vehicles over a known distance. The question is: Does the method affect the values that are calculated? Example 2.6 will help.

jExample 2.6 Speeds on Green Avenue Remember the mark on Green Avenue used for headway measurements in Example 2.1? The mark also serves as the beginning of a “speed trap” 100 meters long, The time needed for each vehicle to traverse the 100 meters has been measured and stored in Table 2.6, along with the computed value of space mean speed (SMS) for each vehicle,

A. Verify that the speed of each vehicle shown in Table 2.6 has been properly computed. B. Calculate the space mean speed (SMS) for the eight vehicles in Table 2.6.

TABLE 2.6 Vehicle Number (i) 1

2 3

4 5

6 7

i

Data for Space Mean Speed Calculations

_ Time for 100 meters 5.95 seconds 5.92 seconds 5.23 seconds 5.04 seconds

5.90 seconds 5.18 seconds 5.45 seconds §.51 seconds

Speed (Si) 60.50 kph 60.81 kph 68.83 kph 71.43 kph 61.02 kph 69.50 kph 66.06 kph 65.34 kph

Solutions to Example 2.6

A. The speed of each vehicle in Table 2.6 is calculated by dividing the distance traveled by the time needed to travel that distance. For Vehicle 1, the space mean speed is

_ 100meters =16.81 ops = 60.50kph kp

‘5.95 sec.

single vehicle can have a space mean speed, because its instantaneous speed could have varied over the 100-meter distance, however slightly.

A

B, In order to conform to the basis for the space mean speed definition, we cannot simply find the mean value of the eight “speed” values in the rightmost column of Table 2.6. Instead, we must use the total distance covered by the eight vehicles in the sample and the total time it took them (collectively) to cover that distance.

The space mean speed is:

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sMs-

8*0.lkm (5.95 +5.92+5.23+5.04+5.90+5,18+5.45+5.51)sect (1hr/3600 sec)

sms ~ =———0-80km__ 65 19kph 44, 18sec*

(hr /3600sec)

The equation for space mean speed of a group of vehicles can also be expressed as a harmonic mean of the “speed trap” speeds of the individual vehicles in the group: SMS

=

N

8

=

y §, 1

1

(asta tee en (60.50

66.06

60.81

8

= 65.34

0.1227

= 65.19

‘pn

The two SMS calculations above are equivalent.

~ Ni?

THINK ABOUTIT What is the basis for the first statement in the solution to Part B of Example 2.67 In other words, why not simply find the mean of the values in the rightmost column of

Table 2.67

If a point speed measurement were possible, wouldn’t that be a more convenient method, and

wouldn't the result be the same? To answer these questions, let us assume thet the each of the eight vehicles in Table 2.6 maintained precisely the speed given in column3 for the entire 100 meters of the speed trap. (Normally, a vehicle's speed will vary over the speed trap, even if intentional acceleration or braking is not taking place.) If the constant speed assumption is correct, the time mean speed calculation 18: N

TMS=—9'S, i=l

_ 60.50+ 60.81+

+65.93

-

+ 65.43

=

= 65.44kph

The difference between either SMS value and the TMS value is too large to be explained by round-off error. It is the consequence of using a different definition as the basis for computing mean speed in each It is also true that the difference between SMS and TMS is seldom big enough to worry about. This is good news, because the choice between them is usually the result of which method was used to collect the

raw data.

~

=

"4

THINK ABOUT IT In one case, a radar gun is used to record speeds. In a second case, a speed trap is set up using loop detectors. In which case would the resulting mean speed be space mean

speed? Which method would produce a time mean speed?

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2.2.2 Setting speed limits One of the considerations in setting speed limits is how fast drivers currently travel on the roadway. common rule of thumb is to determine what the 85" percentile speed is on a roadway. Eighty-five

A

percent of vehicles in a representative sample are being driven below that speed.

Example 2.7 Finding the 85" Percentile Speed Residents along County Road 750N in rural Mythaca County have been complaining about vehicles traveling at “excessive” speeds on that road in recent months. Because no speed limit is posted, the statewide rural default speed limit (55 mph) is in effect on the twolane road. As part of an engineering study, the

County Engineer’s office collects speed data for 48 consecutive hours beginning 4 PM. Tuesday. During this time, the speeds of 749 vehicles are recorded. The speeds are downloaded from the counting device to a spreadsheet file, where the speeds are sorted in descending order, from fastest (row #1) to slowest (row #749). On which row of the spreadsheet will the 85" percentile speed

FIGURE 2.14

Mythaca County Road 750N Photo by Jon D. Fricker

appear?

Solution to Example 2.7

The 85" percentile speed is the speed that is faster than 85 percent of the other speeds in the database. Row #1 in the sorted spreadsheet is the 100 percentile speed and row #749 is the zero percentile speed. Accordingly, the 85" percentile speed occurs on row X, where X/748 = (1.00 - 0.85). Solving for X gives us

112, Checking this, 112/748 than the speed in row 112. X=

= 0.1497, meaning that only 14.97 percent of the speeds are faster

Discussion of Example 2.7

Let us say that the 85" percentile speed found in Example 2.7 was 57 mph, Does this justify retaining the default speed limit of 55 mph? In the absence of other factors, yes. But there may be other factors that affect the setting of a speed limit. Several of these factors will be introduced in a later chapter.

~

Vi

THINK ABOUT IT What factors do you think might have to be considered in setting a speed limit on

CR7S0N?

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Chapter 2 Traffic Flow: Theory and Analysis that If, instead of 57 mph, the 85" percentile speed on CR750N was found to be 41 mph, this is evidence most (85 percent) of the drivers behave as if speeds greater than 41 mph are unwise. The presumption behind the 85" percentile method of setting speed limits is that most drivers know what a safe speed is for have been driving at prevailing roadway conditions. It may be that only a few drivers on CR750N driver without and behavior, will show if collected changing “excessive” speeds. The data, accurately of a 41 the case -mph 85" percentile how many excessively fast vehicles there are and at what speeds. In of other factors that may reduce the speed, a speed limit of 40 mph is justified, subject to consideration speed limit further. —

2.7? How many vehicles Sample Size. Did the County need to get speeds for 749 vehicles in Example would have comprised an “adequate sample” of all speeds on the roadway? If 749 was more than the minimum required, of what value was the enlarged sample size? A minimum sample size to achieve a desired degree of statistical accuracy for some percentile speed can be found by using Equation 2.4. [Robertson et al. 1994]

N= S*z7(2+U?) where

(2.4)

N= minimum number of measured speeds. IfN4

Number of vehicle arrivals each 15 seconds FIGURE 2.25 Fricker & Whitford

Frequency bar chart for Steak Street Direction One (Actual vs Theoretical)

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Regardless of the method you use, however, be sure to check the resulting P(n) values for reasonableness. Almost always, there is a peak value for P(n), with other P(n) values diminishing as n values get more distant from the mode. (The most frequently occurring value in a distribution is called the mode.) In this example, n=1 was the mode, because P(1) had the highest P(n) value. (See the right-

hand vertical bars in Figure 2.25.) Look for this kind of peaking pattern in any Poisson distribution. Another check comes with a little experience in using the Poisson model. In this example, we have A=

6.67 vehicles/minute. It seems that one or two vehicles every fifteen seconds would be typical. The two largest P(n) values we calculated were P(1) and P(2). C. In this example, P(n) values for n>3 are getting smaller and smaller as n increases. How many more P(n) calculations for n>5 do we have to do before P(n) gets “sufficiently close to zero” (however that is defined) for us to justify stopping? Actually, we need do no more P(n) calculations. We already have the basis for stating 5)=1.00-

3 P(n)

n=0

= 1.00 — (0.189 + 0.315 + 0.262 + 0.146 + 0.061 + 0.020) = 1.00 0.993 = 0.007 —

—-$-—

~

Vé THINK ABOUT IT Does the choice of t influence the values of P(n)?

If so, how does one choose t?

ht Example 2.17 Traffic in Direction 2 on Steak Street

Look at the data in Table 2.11 for Direction Two on Steak Street and reorganize the data into 10-, 15-, and 20-second intervals. (See Table 2.12 below.) For example, there were ten instances in which no Direction 2 vehicles were seen in a ten-second interval — including three consecutive intervals starting at 0:30 and ending at 1:00. For the same data using 20-second intervals, there were only 3 cases in which zero vehicles were observed. Will the appearance of the frequency distribution change as the interval width used to combine the data is changed? Does the Poisson model change in any important way as the choice of interval width changes?

Solution for Example 2.17 The observations for Direction Two lasted three minutes (180 seconds). The average arrival rate 4 is 15 vehicles in 180 seconds, or 0.0833 vehicles/second. When the interval width is ten seconds, Equation 2.24 is used to find the probability that no vehicles will be observed in an interval, as follows: PCO)

=

(0.0833 veh

/ seo*10sec)" O!vehs

&

OO9veH/seH"I08

110.435) _ 9 .sae

This is the first entry in the "0" row in Table 2.12.

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TABLE 2.12

Frequency distributions for various interval widths used in Example 2.17 (Direction Two) 10-second intervals

15-second intervals

20-second intervals

Events per| Probabilit Expected Actual | Probabilit Expected Actual | Probabilit Expected Actual Interval, n y freq ofn, freq of y freq of n, freq of y freq ofn, freq of

ofn

E(n)

n,A(n)}

events,

P(n)

0

0.435

1

0.362 0.151

2 3

0.042 0.009 0.002

4 5+

ofn

En)

on,

ofn

A(n)})

P(n) 7,82 6.52 2.72 0.75 0.16 0.03

10

18.00

18

4 2

0.287 0.358

E(n)

on,

A(n)

events,

events,

P(n) 3.44 4.30 2.69

3

1.12

2

0.189 0.315 0.262 0.146

5 1

1.70

3

2.83

2

2.36

1

1

0.224 0.093

1.31

1

1

0.029

0.35

1

0.061

0.55

0.009 1,000

0.11 12.00

0

0.028

12

1.000

0.25 9.00

2 0 9

0

Sums 1.000 Note: £P(n) for n= 0,1,..,5+ may not equal 1.000 because of rounding

There are eighteen 10-second intervals in the 3-minute observation period, so

P(0) *

18 intervals

= 0.435*18 = 7.82 intervals

This means that 7.82 intervals can be expected to have zero vehicles observed, according to the Poisson model. We can represent the expected number of times n observations will occur as E(n). In this case, long, P(0) = 0.287 and only 3.44 of the twelve 15-second intervals are expected to have zero vehicles observed. The remaining calculations are completed in a similar fashion, as summarized in Table 2.12.

E(0)-7.82. When the interval is

~

me

15 seconds

THINK ABOUT IT Does it make sense that P(0) and E(0) are smaller for the 15-second interval than for the 10-second interval? Why?

Figure 2.26 shows the "Actual frequency" distribution for each of the three interval widths in Table 2.12. Each A(n) entry in an “Actual freq” column in Table 2.12 stands for the number of times that n vehicles were observed during an interval. This is different from the frequency tally in the two rightmost columns in Table 2.11.

~

Ad

THINK ABOUT IT Are you clear about the distinction between "the number of vehicles observed during the interval" and "the number of intervals that had n vehicles observed"?

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Chapter 2.4

Actnal frequeticy for n axivals Q he

- Volume Fundamentals of Transportation Engineering

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12

10



[10-second intervals B 15-second intervals

4

5 20-sccand intervals

0

beta

ml

‘Number of vebicle atrivals in an interval.

FIGURE 2.26

Frequency distributions (observed data) for various interval widths (Direction

Two) While the appearance of the frequency distribution clearly changes with the choice of interval width, does the choice affect calculations using Equation 2.24? No, because no matter how you group = of data, the calculations using Equation 2.24 can be based on 4 0.0833 vehicles per second for a period let us is 5 vehicles Two arrival rate the Direction try per minute, analysis of any duration. Because 2.24 becomes minute. of one for a Equation period computing P(5) (0.0833 veh / sec* 60sec)” V°F3ven/see"608° _ 7 (3124.4)(0.006751) _ 9 176 120 5tvehs If A had been defined in terms of minutes, 2 = 15 vehicles/3 minutes = 5.0 vehs/minute and the Equation 2.24 calculation becomes e

P(5)=

P(5) =

(5.0veh/min*! min) S0ve/min"imin e

_- (3125)(0.006738) 120

5 175

5!vehs in the two difference computations would be due to rounding. The lesson: As long as you keep your Any units consistent (e.g., seconds vs. minutes), Poisson calculations such as P(n) can be done in several ways.

*

*

THINK ABOUT IT Inthe second P(5) calculation above, n=A. Wouldn't you expect P( 4.) to be much larger than 0.175? In fact, wouldn't you expect P(A ) to be the mode of the probability distribution?

Do you trust the Poisson model yet? Are you comfortable with it? Let's try some more experiments with it.

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Example 2.18 Poisson manipulations In using Equation 2.24, is there any difference between using one 15-second time interval and using 15 one-second time intervals?

Solution to Example 2.18 In Example 2.16, P(0) = 0.189 when t = 15 seconds for Direction One. Because

4 had the units “vehicles per second”, the (ary term was actually combining 15 one-second intervals, viz., (0.111*15)" = (1.667)°. If 2 had been defined in terms of 15-second intervals, 4 = 1.667 vebs/interval and t= interval for the same case, leading to (At)" = (1.667*1)". The result is the same, because the time units were 1

kept

consistent.

Example 2.19 Poisson models for natural events.

Year TS

list of Atlantic hurricanes over the previous 15 years, available at http://weather,ynisys.com/hurricane/atlantic/, is in the table at the right. TS = total storms, followed by given

A

the number of storms with Category 1-5.

A. For years 1-15, what was the average “arrival rate” for Atlantic storms? B. Calculate P(8) and P(14) based on the data for Years 1-15. C. What is the probability that there will be fewer than 8 Atlantic storms next year (Year 17)?

5

|

Total

15

14 13

12 13

10 12

Solutions to Example 2.19

A.

A=

_ 14.46 storms/yr. Tstorms Zi

14

15 years

a

B. (2.24)

P(n)=

_ P(17=

nat

(yer, nl

(14.46 *1)4e 14!

P(8) =

14.461

ay\t 1446"!

eens

= 0.0249.

13

= 0.1052

C. Although there were never fewer than 8 storms in the last 15 years, P(n1 or M/G/z>1.

C. The Engineer’s waiting time was W = 45 minutes. His service time was 8 minutes, equivalent to a service rate of u = 60/8 = 7.5 customers/hour. Time in the spent queueing system, t = waiting time + service time ~ 45

+ 8 = 53 minutes.

—— 3.3

SYSTEMS WITH STABLE QUEUES

3.3.1 Types of queueing models

As introduced in Section 3.2, the shorthand notation used to describe a type of queueing system is x/y/z. The value of z can be 1, 2, or any integer that indicates the number of servers active in the queueing system. For example, if toll road exit ramp has a single toll booth, and the driver of each car can pay the toll in about the same time, the arrivals are probably negative exponentially distributed, the service time is approximately constant, and the most appropriate queueing model is type M/D/1. Ifa grocery store selfcheckout lane has service times that are normally distributed, the best queueing model is probably M/G/1. If there are ten self-checkout lanes, the overall queueing model for those lanes would be represented by M/G/10, The performance of any queueing system can be measured by the performance measures introduced in the previous section: Q , W, tand P, To compute performance measures for any -

C

¢

queueing system, the required input values are: @ A: the arrival rate (customers arriving per unit time) at a queueing system ¢ 4: the service rate (customers served per unit time) by a single server

t ier

For the reader’s convenience, the equations that are most useful in transportation applications are grouped in Table 3.9. The ratio

4

is called the utilization ratio p. The most important thing about p is

that it must be /ess than one for the equations listed in Table 3.9 to be valid. The condition that 4 < y, that is, the arrival rate is less than the service rate. queue

If 4 > 2,

of increasing length. We could call the situation in which

IfZ < 4,

a steady state condition will result in terms

24>

p
1), the condition 2< # Must x2) queue. be

amended to be 2 < zu.

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M/D/1 in Table 3.9 is a special case of M/G/1 when o”= 0. For a much more extensive set of equations, see Appendix C in Allen [1978].

TABLE 3.9

Performance measure equations for stable queueing models

Queueing Model

Performance

M/D/1

M/G/1

Measure

go tho



"20=)

a

3.13 e3)

o=-—P

er) 3.10

80-9)

o”= variance of service time

_

W —

t

Po

~

_Q_pr+iict Wes 2MI—p)

_oil

t=

Wee

4



(3.11)

WwW

(3.14)

aul—p)

2-p =~ t

(3.12)

(3.15)

mp)

Po=1-p

Po=1-p

M/M/z with

wim

_

Q

=

w

-t P,

_ -/_

_

2

e-I yw-—* W=

Muay

._P

=—— pn

1 z__ t =——_

aod

P, =(1—-p)p”

py"! P,(z* FA

Q

(3.16)

p=A/(z*p)

Zz

and k customers

| 1

. (3.20)

3.21 OD

W= _(z*p)+Q_ -=— 1

=,

3.1 ON?

2

= _(*p)+Q t=

3.18 (3.18)

(3.22)

5

I (z*p)*

(3.19)

=

7 }

n-((§

(z 6)

Se

(3.234)

k

P.

=P,

re)

for kz

(3.230)

Sources: Allen 1978; Larson and Odoni 1981; Hillier and Lieberman 1986

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Chapter 3 Hghway Design for Performance

7

THINK ABOUT IT For any M/y/I queueing system with y = M, D, or G, always be some delay. Why is that true?

A> 0, and p> 0, there will

To clarify and reinforce some points, take a closer look at Equation 3.15 in Table 3.9. The value sought is the average time spent by a customer in the queueing system. This time includes both the average time spent in the queue waiting for service

(W) and the average time being served (1/p).

For

example, if the average service rate is 20.27 customers per hour, the average service fime is 1

P2027

cust /br

= 0,049hr / ae cust

*

60min hr

~

9

min/custo 96 muueustomer

Multiplying the

! — H

FOOD >

Equation 3.15 is the sum of Equation 3.14 and the average service time:

>

term by 2(1- p) produces f = ———

2(1—p)

TF

= et #

_ +—. 2uQl-p) B 1

p = = 2-p + 120-p)_p+2-2p_ 2uQ1-p) “21-p) 22ull-p) 2l-p)

.

Example 3.3 During afternoon peak periods, so much traffic tries to enter Freeway 16 at the Cheddar Street on-ramp that both safety and efficiency have been compromised. A signal has been installed on the ramp to restrict the number of vehicles entering the freeway. This is called ramp metering. The ramp from Cheddar Street has space for about 10 vehicles. The ramp metering signal is controlled a sensor that

r r

by

#

looks for gaps in the freeway traffic. The result is that no more than 500 vehicles per hour may enter the freeway from the on-ramp. During the typical weekday afternoon peak hour, 400 vehicles attempt to enter the freeway from Cheddar Street.

f

of

F

Which queueing model x/y/z best fits this problem? What is the average queue length for the situation described? What is the average time a driver will have to wait in the queue? How long will the average driver spend waiting on the ramp, i.¢., in the system? What is the probability that the on-ramp will be full at any time? Solutions to Example 3.3

A. For arrival pattern, the usual choice is between M (Poisson/negative

exponential) and D In the arrival is (deterministic/constant). traffic, pattern usually M, unless the assumption of random arrivals is invalidated by conditions such as a traffic signal upstream. The service pattern for this onramp is probably M, because the ramp meter operation is tied to traffic on the freeway, and the freeway arrivals are probably Poisson (random). Let us use the M/M/1 model in this example, saving other models for separate exercises, B. The average queue length in M/M/1 queueing system is found by using Equation 3.16. Because Equation 3.16 uses the utilization ratio p, it would be convenient to first calculate a

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=

A. He

veh hr 500veh/ hr

2

=f _

_ 0.8.

Substituting this value of p into Equation 3.16 gives us

(08) = 3,2 vehicles.

y

Note that, even though 4 < 7, the average queue length is not

zero. The randomness of arrivals will cause queues to form and dissipate, but the average queue length is estimated to be 3.2 vehicles, using the M/M/1 equation. C. Ifthere were never a queue on the ramp, the driver would only have to wait to be “served” by the vehicle ahead waiting for the ramp metering signal. However, there is sometimes at least one other will have to wait in the queue. time a driver the average signal to turn green. Equation 3.17 estimates _=0.008hr / veh 3500sec 28.8 sec/veh 400 vph W= 500 vph (500- 400vph) It is a good idea to develop the habit of showing the units at each step in your calculations. The errors relationships are not that difficult in the calculation above, but in other problems, embarrassing can be averted by keeping the units in order. TABLE 3.10 D. The total time in the queueing system known here as the Cheddar Street is used. M/M/1 model if the 3.18 p(n) calculations on-ramp can be estimated by Equation

-

aud)

-

_

1

t=—— = ———___———= 0.0 l hr / 1

u—2

(500—400) veh / hr

A simple, but useful, check is to

veh

*

verify that T >

3600sec _hr W .

36.0 BeeuN sec. veh.

Here, 36.0

sec. 28.8 >

sec., so nothing appears to be wrong. E, Equation 3.19 will allow us to estimate the probability that any particular number of vehicles will be in the queueing system (on the on-ramp) at any given time. For example, the probability that no vehicles will be on the on-ramp is pp =(1—p)p” =(1-0.8X(0.8)° =(0.2)(1) =0.2. Unfortunately, = the question is about n>10. We could recognize that P(n>10) 1 10

> p, and calculate by hand all the p, values for n= 0,1,2,...,10. Instead n=O

of eleven manual applications of Equation 2.21 forn=0,1,2

10,a

spreadsheet was used to generate the p, values. The results (Table 3.10) are worth examining, First of all, the most

common value

of n is zero. Secondly, although Q=3.2

P=

vehicles, 0.102, The modal value (Section 2.4.1) is not near the Q value. Finally,

_

for Example 3.2

lambda=

mu=

rho

400 500 0.8

npn) 0

0.200

; Os 3

0102

4

0.082 0.066

5

8

0.052 0.042 0.034

ie

Oy

6 7

“umn, 0-100914

= P(n>10) = 1.00 — 0.914 0.086.

~ Vé ~

THINK ABOUT IT In Example 3.3, the choice of an M/M/1 queueing model is not obvious, because the arrival do in such a case? pattern might not be “sufficiently random”. What should an analyst

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op Example 3.4 More than one identical server Before ETC was installed, motorists using the SR361 toll bridge across the Mythaca River had to pay cash. There were only two tollbooths for each direction of traffic. The average service time for each tollbooth had a negative exponential distribution, with a mean value of 8.8 seconds. Approach traffic followed the Poisson model.

A. Compute the first three performance measures

W and T for the WB toll plaza when the arrival rate is 718 vph. Assume k>z, i.e., there are more customers than set'vers. B. How many tollbooths had to be active, in order to < guarantee W 15 seconds? 0,

Solutions to Example 3.4

A. When z=2, Equation 3.20 in Table 3.9 becomes

game" 22 [t-py} |-RaceLt-py? 1

4

ToOcompute

:

fi for

use

:

|

= need are 2= 718 veh/br and

.20, all we in Equation 3.20,

3600sec/ hr

8.9 # =—————_ = 408,

§ Bsec/ cust

cust/hr for each tolibooth. The z * terms in Equations 3.20 through 3.23 account for the multiple Servers. In computing P) to use in Equation 3.22, use Equation 3.23a with (z* p)=2"*

0.878 = 1.756:

ro" k

f7e

zZtp)y"

eo

-

(E)- 225]

We are now ready to use Equation 3.20 to find the

Q= Ro(etey'|_1_|_o.06sya.7s6"[ 4

(-p)?

4

|

|

gy@*P)+Q W-——

_1.75645.91

1

a

718”

Zog.9

2*

A =

=

[(1+1.756) +12.633]

0.065.

average length of the queue: 1

= 0.088

*

queue, using Equation 3.21:

22910680 — 0.002446 0,002446

=



=

10680

~

67.1865.91 vehicles =

(1-0.878

We now need to determine the average waiting time in the 1

a"

0.008235 0.008235

nr hr

*

26008° _ 49 ——

29.6

=

seconds and the average time spent in the queueing system, using Equation 3.22 = (z*p)+ 1.756+5.91 600 = r 0.010677 hr 38.44 seconds.

=2'p+Q

=

ee

Notice that, inthe W and f equations, A. and have units “customers js per hour”, so the units of t will be hours. It is often necessary to convert hours to seconds to make the results easier to

B. How many tollbooths would have had to be active, in order to guarantee W was found to be 29.6 seconds with two tollbooths active. A natural to repeat the calculations of Part A using z=3, then check to see This process can be expedited by using a spreadsheet. A good

W

and

interpret.

W


zu. If done

by hand, a queueing diagram can be drawn on graph paper. The horizontal axis in Figure 3.8 measures time from some specified start of the analysis. The vertical axis measures the cumulative number of vehicles that enter the queueing system or depart from it.

Al ae



Tine

oe

eee

ee

es

ee ee

Time since queuc started ——

-

*

Arrival curve "maximum wait

FIGURE 3.8

— * +

—Departure curve

"maximum queve

Generalized Diagram for Analyzing Queues

Each queueing diagram has two "curves" — an arrival curve and a departure curve. In Figure the arrival curve is a solid straight line, having a slope equal to the arrival rate 4. in vehicles per hour. 3.8, The arrival curve is linear in the case shown, because the arrival rate stays constant throughout the analysis. The departure (or service) curve in Figure 3.8, however, is piecewise linear. This is because the server is shut off for a period (i.e., the horizontal dotted line with slope = 0) and then begins serving at a rate

(the dashed line). ny

ys

If the “server” is a roadway, a horizontal departure curve represents the

situation in which the roadway is blocked. The area between the arrival curve and the departure curve (Al + A2 in Figure 3.8) is the total vehicle delay and the longest vertical line between the two curves represents the maximum length of the queue.

Let us now look at the queueing diagram in more detail. In Figure 3.9, the arrival curve “AC1” illustrates a constant arrival rate of 2715 vehicles per hour. The departure curve represents the ability of the roadway to allow traffic to proceed, that is, its capacity. If the departure rate exceeds the arrival rate, a lasting queue will not form and no departure curve needs to be drawn. If, for some reason, one lane of

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roadway is blocked at time

t,, such that the capacity is reduced to 1340 vph, the departure curve “DC1”

will show the new capacity. If, as is shown in Figure 3.9, the slope of “DC1” (1340 vph) is not as steep as the arrival curve (2715 vph), a queue will begin to form. Clearly, we would expect the queue to grow by (2715-1340)/60 = 22.9 vehicles during each minute the capacity is reduced to 1340 veb/hr. A “ queueing diagram will do a good job of answering the “reasonable questions posed in the bullet list above. Example 3.5 will demonstrate.

a

—-+— —-

ne

Example 3.5: Only departure rate varies Because of a minor collision, one of the two SB lanes on Freeway 16 is blocked at 8:13 AM. The normal freeway capacity of 3600 vph (60 veh/min) is reduced to 1340 vph (22.33 veh/min). The SB flow rate on Freeway 16 at this time of day is 2715 vph (45.25 veh/min). The blockage is removed after fifteen Cumulative vehicles since 8:00 AM

minutes.

A. Did a queue form? If so, what was its maximum length? B. What was the longest time any single vehicle was in the queue? C. At what time did the queue clear? D. What was the total delay to traffic because of the lane blockage? E. Ifa vehicle entered the queue at 8:25AM, how many vehicles would be ahead of it in the queue and how long would the driver have to wait in the queue? 2000

1800+. 1800;

Os

118

1400-

1200+ 1000-

: a=000)

Maximum time

0

in

§

10

15

20

Minutes after

FIGURE 3.9 Fricker & Whitford

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2

30

35

40

46

AM lane blockage

Queueing diagram when only departure rate varies

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Solution to Example 3.5

A. Maximum queue length. Because the departure rate (capacity) during the lane blockage was less than the arrival rate (flow rate), a queue formed. The curve “DC1” was in effect until 8:28 AM departure in Figure 3.9), at which time the full capacity was restored. The restored capacity is in 3.9 the dashed represented Figure by departure curve “DC2”, beginning at time tz at point b. (time

t,

Whenever a departure curve in a queueing diagram is below the arrival curve, a queue is present, In fact, the number of vehicles in the queue at any time t is the length of the vertical line between the arrival and departure curves. Upon inspecting the “right triangle” in Figure 3.9, it is clear that the until time then queue grows t,, dissipates until the queue clears at time t,. (Whenever a departure

curve would appear above an arrival curve in a queueing diagram, it does not have to be drawn.) Because of the relative slopes of the arrival and departure curves between times t,andt,, the longest

vertical line between the two curves will occur at timet,. To determine the actual length of this vertical line, establish a coordinate system within the queueing diagram and use some algebra. (1) Let the coordinates (x,y) of the arrival curve at time t, be (0,0), where x = minutes since and y= t; number of vehicles arriving since t,. (2) At time the coordinates of the arrival curve will be x= t,,

y = (15 min. * 45.25 veh/min) = 678.75 vehicles. At time t,, the coordinates of the departure curve will be x = 15 minutes and y = (15 min. * 22,33 veh/ min) = 335.0 vehicles. 15 minutes and

Therefore, the maximum queue length was (678.75



335) = 343.75 vehicles.

B. Maximum time in queue. Whenever a departure curve in a queueing diagram is below (and to the

ror of #

right of) the arrival curve, the time spent in the queue by any single vehicle is the length of the horizontal line drawn from the arrival curve at the time that vehicle arrives to the departure curve. Just as the maximum queue length was reached at time t,, the maximum time in can be found queue

by drawing a horizontal line from the arrival curve, such that it reaches the departure curve at time

t,.

r

Because y=335.0 at t2, this means the 335% vehicle would be getting past the bottleneck on the 15 minutes after the blockage occurred. When did the 335“ vehicle enter the freeway queue? If the atrival rate is 45.25 veh/min, then the 335 vehicle arrived 335.0/45.25 = 7.4 minutes after the

blockage began. Because the blockage was removed at t2= 15 minutes, the maximum time in queue was 15.0 —7.4 = 7.6 minutes.

C. When does the queue clear? After time

t,, the departure curve DC2 has a steeper slope than arrival

“AC1”, Eventually, at time t, in Figure 3.9, the two curves will converge. At that time, the queue will have been cleared. To find that point in the queueing diagram, develop equations for the two curves, then determine when they intersect. The equation for the arrival curve is Yao = 45.25x curve

“DC2” starting at x,y coordinates (15.0,335.0) is + 335.0 60.0(x-15). To check these equations, verify Part A of this example using them: = — = Yac —Ypc2 45.25(15) [335 + 60(15-15)] 343.75 vehicles, and the equation for the departure curve

When the two curves intersect, Yao

Ypop

=

= Ypco :

= 335 5+ 60(x-15); = 45,.25x . ; = +

x = 900-335 6045.25

565 "14.75

:

38.3 minutes

Check this result in the original equations:

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yac

= 45.25(38.3) = 1733 vehs and yocz = 335 + 60(38.3-15) =

1733 vehs.

D. Total delay. A nice feature of a queueing diagram is that the units along its axes are time (minutes) and cumulative count of vehicles. If we calculate the area between an arrival curve and a departure curve to its right, the units associated with that area will be vehicle-minutes, which is a good measure of delay. The area of triangle abc in Figure 3.9 is found by defining a new point e at coordinates (15.0,0.0), which will form the lower right vertex of right triangles aec and aeb. Aste = Ace —Aseb =1(15.0-0.0)(678.75-0.0) ~>-(15.0-0.04335-0.0) = §090.625 - 2512.5 = 2578.125 veh-min = 42.97 veh-hrs.

A shortcut also works: Aste

= 145.0 -0.0) (678.75 —335.0) = 2578.1 veh —min—

60min

2

= 42.97

veh —hrs

The area of triangle bed can be found by defining a new point f at coordinates (15.0,1733), which will

cdf.

form the upper left vertex of right triangles bdf and

— —15.0X1733 —678.75) Atca = Apap ~Acar = 3(383 —15.0)(1733 —335) = 16286.70 - 12282.01 = 4004.69 veh-min = 66.74 veh-hrs.

583

Again, the shortcut also works:

Ato = +(38.3-15.0)(678.75 —335.0) = 4004.69

veh —min = 66.74 veh —hrs.

of the collision: Together, Au and Ated represent the total delay on Freeway 16 because = 42.97 + 66.74 109.71 veh-hrs. is of So, during the 38.3 minutes in which the queue builds and dissipates, 109.71 veh-hrs delay endured by drivers on

SB Freeway

16.

E. Queue position and waiting time for a specific vehicle. A vehicle that arrives at 8:25 AM does so minutes after 8:13 AM, when the queue started to build, Queue position can be determined by

12

at that time. drawing a vertical line from the arrival at 8:25 AM down to the departure curve in effect Because 8:25 AM occurs when curve “DC1” is in effect, we need the equation for that departure = = 22.33x. At 8:25 AM, x=12, ypc2 = 268 vehicles, and yac 45.25x 543 vehicles. CUIVe:

Ypcy=

= 543 — 268 = 275 vehicles. Strictly there would be 274 vehicles ahead of the vehicle that arrives at 8:25AM. The length of

This means that the queue length at 8:25AM is

ypc2

speaking, time this vehicle will spend in the queue is equal to the length of the horizontal line drawn from the 8:25 AM point on curve “AC” to the “DC2” curve to its right in Figure 3.9. Using the “DC2” = = for x gives us the time equation developed in Part C, Ypc2 335.0 + 60.0(x-15) 543 vehs. Solving the 8:25

AM arrival will leave the queue:

x,

=

ae

ee

=

=18.47 minutes. Recall that x is

measured from 8:13AM, so this vehicle will leave the queue just before 8:31:30 AM. Because the vehicle entered the queue 12 minutes after the queue formed, the waiting time for this vehicle will be 18.47 — 12 = 6.47 minutes.

ane



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Chapter 3 Highway Design for Performance

4

Example 3.5 concerned a freeway segment that was temporarily blocked. Queueing diagrams can also be applied to traffic signal cases, which have altemating red phases (when = 0 and queues form) and green phases (when queues are cleared if 4
z1.. They allow the analyst to "see" how and where queues build up and dissipate. If the problem being analyzed is too complex, or performance measures other than those that can be computed directly from a queueing diagram are needed for an analysis, then a special-purpose simulation computer package should be used.

CHAPTER 3 SUMMARY Backups on a roadway occur whenever the demand (traffic flow) on the roadway exceeds its supply (capacity). However, we have seen in the section on rural two-lane roads that several factors go into determining the capacity of the roadway. Some of those factors can change from day to day (or hour to hour). Or delays can be the result of an event that happens a significant distance ahead of the section being analyzed, such as a breakdown or collision that blocks part of the roadway. In Chapter 2, some basic traffic flow relationships were presented that help explain how such traffic behaves. In the last two sections of this chapter, methods for quantifying delay involving queues were introduced. Even

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experienced traffic engineers, when caught in a "traffic jam", have a hard time determining the cause as they proceed along the roadway. Given the information in Chapters 2 and 3, and the ability to make direct measurements and observations, traffic engineers can usually explain the cause of traffic congestion. More importantly, they can propose remedies. Remedies can be the result of better planning,

design, operations, or a combination of these fundamental activities.

ABBREVIATIONS AND NOTATION CAF EB Er

ETC fay

fic fiw fp

Capacity adjustment factor eastbound

passenger-car equivalent for trucks electronic toll collection heavy-vehicle adjustment factor adjustment factor for lateral clearance adjustment factor for lane width

driver population familiarity factor

FFS FIFO HCM LOS NB

free-flow speed first-in, first-out queueing operation Highway Capacity Manual level of service

Pa

steady state probability that exactly n customers are in queueing system

PCE

passenger-car equivalents

northbound

pephp!l passenger cars per hour per lane

PHF Pr Q

peak hour factor trucks as proportion of the traffic stream, expressed as a decimal average number of customers waiting for service radio frequency identification

RFID SAF Speed adjustment factor SB

southbound

t

Vp

= average time spent in the queueing system waiting time + service time total ramp density volume count for a specified time period flow rate expressed in terms of PCE, pc/h/In or pephpl

VMT

_vehicle-miles traveled

TRD Vv

average waiting time for each vehicle in the queue westbound number of servers in a queueing system

arrival rate (customers arriving per unit time) at a queueing system service rate (customers served per unit time) by a single server

utilization ratio

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GLOSSARY «

SBalking: a customer refuses to enter the queue. For example, driver may see that the left turn lane he/she wanted to use has a long backup, and decides to take a different route.

*

Base free-flow speed: the speed a driver would choose to maintain on a particular roadway, after that roadway’s characteristics have been taken into account. Capacity: the maximum flow rate expected along a roadway under specified conditions, usually expressed in terms of vehicles per hour Directional distribution: The share of 2-way traffic flow that moves in the major and minor

e

e

e ©

directions, e.g., 60/40. Federal aid road: roadways eligible for federal funding in the United States Free-flow speed: the speed a driver would choose to maintain on a particular roadway type, in the absence of other traffic and roadway characteristics that cause the driver to reduce his/her speed

©

Level of service: the quality of a roadway’s operation, praded on a scale from A (free-flow) to F

«

(breakdown) Major direction: the direction of higher flow on a two-way roadway.

=

Passenger-car equivalent: A result of converting a truck, bus, or recreational vehicle to its equivalent number of passenger cars in the traffic stream, to reflect how its size and operating characteristics affect the traffic flow. .

*

Peak Hour Factor: the ratio of the total traffic count during an hour to four times the highest 15minute traffic count during that same hour.

e

Persistent queue:

©

©

A queueing system with 2 > 4 , such that the eventual result is a queue of

increasing length Preemptive service: a server may suspend service to one customer, because a higher-priority customer (e.g., an emergency vehicle) has arrived. Reneging: a customer, having joined a queue, leaves before being served. Stable queues: a queueing system in which 4 < 2, such that a queue will not grow indefinitely,

INDEX FOR CHAPTER 3 atrival curve, 23 Arrival patterns,

FIFO, 14 13

arrival rate, 16 Balking, 22 base capacity, 7 base FFS§, 5

breakpoint, 8 CAF, 5, 11 density, 3 departure curve, 23 design analysis, 9 design application, 8 diverging, 2 driver population factor, 5 electronic toll collection, 12 federal aid roads, 2

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free-flow speed, 5 gaper's block, 28 general distribution, 16 HCM 2016 method, 2, 4 Highway Capacity Manual, 2 ideal freeway segment, 2 interarrival times, 16 lateral clearance, 5, 6 level of service, 3

LIFO,

14

Markovian, 16 Maximum queue length, 25 maximum service flow, 9 Maximum time in queue, 25 merging, 2

3.32

negative exponential distribution, 16 operational analysis, 4 passenger car equivalent, 7 passenger car equivalent flow rate, 7 peak hour factor, 5 persistent queue, 17 Preemptive service, 22 Priority in a queueing system, 14

queue clears, 25 Queue discipline, 14 queueing diagram, 23 queueing process, 12 queueing system, 12

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3

radio frequency identification, 12 ramp metering, 19 Reneging, 22

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service rate, 16 service times, 16 simulation, 23, 31 stable queue, 18 state of a queueing system,

Service patterns, 13

13

System capacity, 14 Total delay, 26 total ramp density, 5, 6 utilization ratio, 17, 19 weaving, 2 x/y/z, 16

REFERENCES

@

Allen, Arnold O., 1978, Probability, Statistics, and Queueing Theory with Computer Science Applications, Academic Press, Appendix C. Dudek, Conrad L. and Stephen H. Richards, 1982, “Traffic Capacity Through Urban Freeway Work

¢

Zones in Texas”, Transportation Research Record 869, p. 14-18. FHWA 2016, Highway Statistics 2016. Highway Statistics Series, Office of Highway Policy

e

Information, Federal Highway Administration, U.S. Department of Transportation, Washington DC 20590. Retrieved 26 December 2017 from https://www.fhwa.dot.gov/policyinformation/statistics/2016/. Data for the most recent year are

available via http://www.fhwa.dot.gov/pubstats.html. @

@

@

¢

HCM 2010. Highway Capacity Manual, Transportation Research Board, National Research Council, Washington DC, 2010. HCM 2016. Highway Capacity Manual, Transportation Research Board, National Research Council, Washington DC, 2016. Hillier, Frederick S. and Gerald J. Lieberman, 1986, Introduction to Operations Research, Fourth Edition, Holden-Day, Inc., Section 16.7. Larson, Richard C. and Amedeo R. Odoni, 1981, Urban Operations Research, Prentice-Hall, Section 4.6.2

@

@

Lovell, David J. and John R. Windover, Jul./Aug. 1999, Discussion of “Analyzing Freeway Traffic under Congestion: Traffic Dynamics Approach”, Journal of Transportation Engineering, Vol. 125, No. 4, p. 373-375, American Society of Civil Engineers. Nam DoH. and Donald R. Drew, May/Jun. 1998, “Analyzing Freeway Traffic under Congestion: Traffic Dynamics Approach”, Journal of Transportation Engineering, Vol. 124, No. 3, p. 208-212, American Society of Civil Engineers.

EXERCISES FOR CHAPTER 3 3.1 Capacity and Level of Service for Basic Freeway Segments Level of Service on an Old Freeway. A 4-lane urban freeway (2 lanes in each direction) was 3.1. built many years ago with a design speed of 60 mph, which is close to today’s measured free-flow speed. The lanes are 11.5 ft wide with only 3 ft of shoulder on the right-hand side. The peak hour mixed traffic flow is 2500 vph in the major direction with 25 percent trucks. Most drivers are familiar with this

roadway. The average distance between ramps is 0.33 mile. If any data are missing, adopt default values from Table 3.3. What is the density of the peak hour traffic? At what level of service is the freeway operating? 3.2. Freeway

LOS as J-46 enters the city. As I-46 crosses the city limits, it has six lanes (3 in each

users direction). The average distance between ramps is 0.72 mile. Enough of the drivers are infrequent

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of the freeway, such that f, = 0.93. Major direction V = 4787 vph with 14 percent trucks and PHF = 0.87. If any data are missing, adopt default values from Table 3.3. What is the density of the traffic? At what

level of service is the freeway operating? 3.3. Level of Service on a Freeway with 8 lanes. An urban freeway on level terrain has four 12-ft lanes in each direction, with a 3-ft shoulder on the right side and no shoulder on the median side. The freeway carries 12 percent heavy trucks within its mixed traffic flow of V = 7609 vph in the major

direction. Most of the drivers are commuters and know the road well, so 1.00. PHF = 0.90. If any data are missing, adopt default values from Table 3.3. What is the traffic density? At what level of service is the freeway operating? 3.4. Maintaining Level of Service C on a Freeway. A four-lane freeway is located on rolling rural terrain and has two 12-ft lanes in each direction and no lateral obstructions within 8 ft of the right-hand lane. The traffic stream consists of cars and trucks. A peak-hour volume of 3600 vehicles is observed in the major direction, with 1000 arriving in the most congested 15-min period. TRD = 0.24 ramps/mi. If

f=

any date are missing, adopt default values from Table 3.3. A. What is the PHF? B. What is the density of the peak hour traffic? At what level of service is the freeway operating? C. Ifa level of service no worse than C is desired, how many lanes are needed in each direction? 3.5 Number of Lanes Needed for LOS C. A 4-lane urban freeway must have lanes added in what is now a median so that 5249 vph in one direction can be served at LOS C. There are 8 percent trucks. The terrain is level and 5 ft of right-side lateral clearance can be provided. Ramp density will be 1.8 ramps/mi and most drivers are regular users of the freeway. Using PHF = 0.95, how many 12-ft-wide lanes will be needed to achieve LOS C on the freeway? If any data are missing, adopt default values from Table 3.3. 3.6 Will there be queueing? All but two lanes in one direction on a freeway must be closed for summer reconstruction. Midday traffic on the freeway is 4080 vph in the direction being studied. Six percent of the traffic is trucks. The terrain is level. No right-side lateral clearance can be provided. Ramp density will be 1.5 ramps/mi, but some drivers are new or occasional users of the freeway, making f, = 0.87. Using PHF = 0.86, will the two 12-ft-wide lanes be enough to avoid LOS F on the freeway? If any data are missing, adopt default values from Table 3.3.

Freeway Workzone Capacity Analysis. A freeway segment on rolling terrain has 14 percent trucks in its traffic stream. Because a 3000-ft section of the freeway must be patched, one of the heavy freeway’s lanes is closed, leaving two 12-ft wide lanes open with no right-hand side lateral clearance or

roe

3.7

ramps.

If any data are missing, adopt default values from Table 3.3.

CC

Ff

A. What is the maximum mixed traffic flow V in the workzone, such that a traffic jam (LOS F) will be avoided? One approach: Use Operational Analysis in a spreadsheet and search for V. B. What level of service does that flow correspond to for the six-lane freeway, which has 6 ft of right-hand side lateral clearance and two ramps every 4.6 mi?

3.2 Queueing Systems 3.8. Data collection for queueing analysis. If the county engineer wanted to verify or update the service times for express, non-express, and self-checkout lanes at his favorite grocery store, how should he collect and process the data he needs?

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3.9. Equations for Stable Queues. Derive Equations 3.13 and 3.14 for the M/D/1 model and Equations 3.16 and 3.17 for the M/M/1 model from the M/G/1 Equations 3.10 and 3.11, using o = 0 for an M/D/1 model and o =1/p for an M/M/1 model. 3.10. Queueing Analysis using Equations — Transit Fare Cards. A plastic stored value card is used by an increasing number of transit systems across the country. The card is read by sensor units located at turnstiles, When the rider enters the system, the sensor unit records the place and time of entry. If the

transit system’s fare structure is not distance-based, the amount of the fare is deducting from the value stored on the card at time of entry. If the fare is distance-based, the fare is deducted from the card by a sensor as the traveler leaves the system. The processing rate of transit riders through the turnstiles is about 20 passengers/minute. Which queueing model (x/y/z) would apply to the analysis of a turnstile

operating under periods of moderate passenger demand? Explain.

3.3 Systems with Stable Queues Queueing Analysis using Equations — Transit Fare Cards. See Exercise 3.10 on Transit Fare Cards. For a period in which the passenger arrival rate at a turnstile is 16 pax/minute, compute average length ofqueue and average wait time for both mag stripe and token turnstiles. Show your calculations

3.11.

clearly.

Review the solution. Think about the results in Example 3.3E. Do they make sense, or are they indications of an error in the analysis? If there is an error, where could it lie? 3.13. Left Turn Lane Analysis using Queueing Equations. The county staff thinks that the LT traffic from Coliseum onto Wakefield (see Exercise 2.37) follows an M/D/1 queueing regime. Recall that the arrival rate for LT vehicles is 5.7 per minute, the LT phase (a portion of the 60-second cycle) can 3.12.

serve 7 vehicles.

If the M/D/1

assumption is correct, show how to carry out the following calculations for

the off-peak arrival rates:

A. Average length of the LT queue

B. Average waiting time in the LT queue C. Average time spent in the system 3.14. Fast food queueing systems. Students at Mythaca State University were interested in comparing service at two nearby fast food restaurants. The two restaurants used different queue structures — one used a single server in each of several parallel queues, while the other employed two servers in series in a single queue. When the students collected data on the "peak hour" service rates at the two restaurants, they were surprised to find the hourly service rates were 71.46 and 69.76, respectively. Because these

values were so similar, the students decided to adopt a 1 value of 70 customers per hour for both restaurants. Assuming a 2 value of 558 fast food customer arrivals per hour, use the appropriate equations in Table 3.9 to determine: A. The minimum number of "channels" or queues a fast food restaurant would need to meet the service quality standard that the average waiting time in the queue does not exceed one minute?

Call this result kmin. B. The average queue length with kmin channels. C. The probability that the system will be empty (to five decimal places). D. What assumptions must you make to allow you to use Table 3.9? 3.15. Serial queue at McDonald’s. The city engineer has created a video of a serial queue at McDonald’s. The serial queue consists of three stations: (1) a “squawk box” at which the customer can

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place an order, (2) a window where the customer pays for the order, and (3) a window where the customer picks up the order. The average time spent waiting in the queue to Station] was 56.2 seconds. The average service time at Station 1 was 24.5 seconds, with a standard deviation of 13.3 seconds.

A. The average time between vehicles arriving at Station! is 43.6 seconds. What is arrival rate 7 (vehs/hr) at Station 17 What is 1 (vehs/hr)? Show your calculations for

Q,

W

if an M/M/1 queueing system is assumed for Station 1. and Pp if an M/G/1 queueing system is assumed for Station 1.

, and Po

Show your calculations for Q , W, Show your calculations for

Q,

W

, and Py

if an M/D/1

queueing systern is assumed for Station 1.

Twenty-two of the 86 vehicles observed in the video had no waiting time before being served at Station 1. Including those vehicles, the mean waiting time before Station 1 was 56.2 sec. Which queucing system x/y/z does the best job of describing the queueing system at Station 1? Explain. F, What is likely to be the best way to characterize the arrival distribution at Stations 2 and 3 —M, G, or D? Explain. 3.16. Queueing at Taco Terrace. A new fast food restaurant is opening in Middleville. The current plan to serve drive-up customers involves two servers. The first server window will take the customer's order with a mean service time of 38.5 seconds. The second server window will collect the money and give the order to the customer with a mean service time of 60.5 seconds. The expected arrival rate is 50 drive-up customers per hour. The interarrival and departure time patterns have negative exponential distributions.

A. If you neglect the “move-up" time from the first window to the second, what is the average time a Taco Terrace drive-up customer will spend in the system? B. How many car lengths of space need to be provided between the two server windows such that, under "average" conditions, the first server window is not blocked by a back-up at the second

window?

3.4 Queueing Diagrams Delays at toll bridge. The table below shows counts of arriving vehicles by 20-minute periods for a recent weekday morning. 3.17.

Time Period (beginning at): Vehicle Arrivals:

7:00

7:20

55

133

7:40 202

«8:00

=8:20

8:40

193

129

104

9:00 76

A. Ifthe arrivals between 7:00 AM and 7:20 AM are assumed to follow a Poisson Distribution, what is the probability that at least two vehicles will arrive during any given 30-second period? B. For the consecutive time periods) in which cumulative 4 > draw and label clearly a queueing diagram patterned after Figure 3.9 or Figure 3.12 that shows the build-up and dissipation of the queue.

C. Using the queueing diagram you constructed in the previous sub-problem... * When will the queue dissipate? ®

®

we

How long (according to the diagram) was the longest queue, and when did it occur? For the period in which a queue existed, estimate the total vehicular delay and average

delay per vehicle.

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Queueing at Amusement Park Vehicle Entrance. Vehicles begin arriving at an amusement park one hour before the park opens, at a rate of 4 vehicles per min. The gate to the parking lot opens 30 minutes before the park opens. If the total delay to vehicles entering the parking lot is 3600 vehicle-

3.18.

minutes,

A. How long after the first vehicle arrival will the queue dissipate? B. What is the average service rate at the parking lot gate, once it has been opened? C. Draw the queueing diagram. 3.19. Queueing on SR361. A rural section of SR361 has WB (westbound) lanes with capacity 1400 vph per lane. During the PM peak period, the flow rate is typically 1750 vph over the two WB lanes. One lane of WB SR361 must be closed for 30 minutes during the PM peak period. A. Draw the queueing diagram showing the queue build-up and dissipation. B. When will the queue clear? C. Estimate how much total vehicular delay will result. 1-96 Incident and queueing analysis. A truck overturned at 11:57 AM near milepost 138 on NB 3.20. 2

I-96, completely blocking that highway. Fortunately, the incident site is just beyond an off-ramp. This means that most vehicles will see the blockage and exit I-96 at the off ramp, avoiding a long backup and long delay. This also makes the detour of through vehicles simply a matter of using the off-ramp and the on-ramp to go around the incident site. For the first ten minutes after the truck's mishap, the ramp capacities were governed by the stop sign at the end of the off ramp and the priority given to cross traffic, which did not have a stop sign. The ramp’s service rate for detouring traffic was approximately 325 vph. After ten minutes, state police began controlling traffic at the end of the off-ramp, increasing the ramp’s service rate for detouring traffic to 650 vph. At exactly 1:00 PM, NB I-96 (capacity = 3600 vph) was reopened to through traffic. If the NB I-96 flow rate at this time of day is 1550 vph:

A. Draw a queueing diagram that shows the buildup and dissipation of the queue. B. At approximately what time (to the nearest minute) does the queue dissipate? Show this event on your diagram,

C. What was the longest vehicle queue? What was the longest vehicle delay? Show the longest queue and the longest delay on your diagram. 3.21. Queueing in “real life". You (and several thousand other music lovers) are driving to the Vulgaris concert at Fawn Creek Music Center just off I-46 north of Mythaca. Heavy traffic on the off-

ramp from I-46 to the county roads leading to FCMC is causing a backup onto I-46. Describe how you would try to estimate the value of 1 for this off-ramp as part of a queueing system without leaving your car, which is stuck in the off-ramp traffic. Use hypothetical but plausible numbers to clearly demonstrate

your method. 3.22,

Times measured in a queueing system. In Example 3.8E, the solutions used the symbol W to

represent average delay time at the I-25 work zone. Shouldn’t the symbol Why or why not?

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MODELING TRANSPORTATION DEMAND AND SUPPLY

|

SCENARIO State Route 361, which runs through Mythaca, is becoming congested ~ or at least the citizens of Mythaca think so. SR361 not only carries most of the traffic destined for downtown Mythaca from the

west and south (Figure 1.2), it is also the main route through the city. The trips through downtown include trips between the south part of the county and the campus of Mythaca State University. Because SR361 is a state highway, the local authorities must prove to the state’s Department of Transportation (DOT) that the problem is (or will become) serious enough to justify spending some of the state’s limited highway funds on a solution. Because Mythaca County is served by the Mythaca County Planning Commission, local officials call upon the MCPC staff to study the matter. The MCPC Executive Director agrees to have the MCPC staff document the current situation, forecast future trends, propose several possible solutions, and recommend the best course of action.

For the State DOT to accept any study of this sort, the MCPC must follow procedures that are well documented, supported by data, and can be replicated by the DOT. Over the past 50 years, certain procedures to carry out travel demandforecasting have become widely accepted. Although researchers

have looked at other procedures ~ and a major national effort to completely replace the current methods is now underway — this chapter will introduce the main features of each step in the current “state of the

practice”.

CHAPTER OBJECTIVES By the end of this chapter, the student will be able to ... 1.

List the four steps in the traditional travel demand modeling process.

2,

Explain the two-way relationship between land use and travel.

3.

Estimate the amount of trips that will be generated to and from a specified area.

4. Calculate the number of trips that can be expected to go to any particular destination from a specified origin. 5.

Estimate the proportion of travelers who will choose each transportation mode from a set of available modes.

6.

Explain equilibrium and use that concept to calculate the flow patterns that satisfy equilibrium conditions.

7. Discuss the strengths and limitations of standard travel demand models as the basis for major public investment decisions.

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4.1

BASIS FOR TRANSPORTATION PLANNING

4.1.1 Anticipating future network needs Transportation planning is a process that involves the analysis of current travel patterns, the forecasting of future travel patterns, the proposal of transportation infrastructure and services, and the evaluation of proposed alternative projects. The result of the process is a pian a set of proposed improvements in the --

transportation system to be considered by decision-makers for implementation.

SGRLOso

_LOSE F MI

LOSsS

FIGURE 4.1 AADT and LOS on Links in Base Year Urban Network [APC 2001, p. 61] Figure 4.1 shows part of an urban street network in the base year. Traffic counts for important street links in the network for that base year are shown in the diagram. The south end of the current path

of SR361 through Mythaca, mentioned in this chapter's scenario, begins with the label “8000” in the lower left part of Figure 4.1. The label "8000" represents two-way 24-hour annual average daily traffic Fricker & Whitford

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(AADT) volume of 8000 vehicles per day. The AADT for SR361 increases to 22,000, then drops off to 14,000 and 15,800 as it heads north toward downtown. Much of this traffic is heading for the university across the river, located in the northwest corner of Figure 4.1. The two bridges that cross the river have AADT values of 33,500 and 30,500. The base year AADT values in Figure 4.1 have been converted to levels ofservice. Links with LOS C or worse have special markings in Figure 4.1. If some of the forecast-year LOS values are poor, planners and decision-makers had better start immediately to consider strategies to alleviate the congestion. It is not unusual for a road construction project to take ten years to

go from decision to completion. In Figure 4.1, it doesn't make sense for the traffic that comes from the south and goes to the university to clog the downtown streets. What can be done?

THINK ABOUT IT Traffic on a state highway that runs through a city is causing congestion at intersections within the city. What options are available to transportation decision-makers to alleviate this problem? Be sure to include some options that do nof require major ~

construction.

The MCPC staff has created a computer model of the Mythaca street network. The model permits them to simulate the way trips are being made in the area being modeled. If the staff can replicate the flow patterns in the base year, they may be able to predict how travel patterns will respond in a future year to a change in the transportation network or the service provided on it. Figure 4.2 is the result of such a travel demand modeling process. The proposed change in the network is the construction of a bypass route for SR361 that includes a third bridge across the river. The proposed SR361 bypass is the new link labelled “38,500” in Figure 4.2, because the new bridge is expected to carry 38,500 vehicles per day. The AADT predictions in Figure 4.2 are for a specified horizon (forecast) year, if the SR361 bypass is built. The new route diverts traffic away from the old SR361 route. Compare the link AADTs in the southwest corner of Figure 4.1 with the AADTs on the same links in Figure 4.2. How did the MCPC staff build their travel demand model? How reliable is the model to use as a basis for deciding whether to invest millions of public dollars in the SR361 bypass project? These questions will be considered in this chapter.

THINK ABOUT IT Notice the horizon year AADT values on the two "old" bridges in Figure 4.2. Compare these values with the base year AADT values for the same two bridges in Figure 4.1. Develop an explanation for why the AADT values do not change much. Does this observation support an argument for the SR361 bypass project, or against it?

The MCPC travel demand model's primary output is the amount of traffic that is expected to be each link in the network in some horizon year, given certain assumptions about such inputs as using population, employment, land use patterns, and network structure in that year. In order to conduct an analysis of travel patterns, the transportation planner must consider what causes trips to be made and what decisions are made by a tripmaker. The reader is invited to think about these issues as they relate to trips that he or she makes.

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Chapter 4 Modeling Trnsportation Demand and Supply

+t PES EE S36 :

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FIGURE 4.2 AADT and LOS on Links in Forecast Year Urban Network [APC 2001, p. 71] The standard trave! demand modeling methods currently in use are based on several concepts. First, that most trips are not made for the sake of traveling, but to do something at the destination — work, shop, study, play, etc. This is known as the derived demand for transportation. Second, that travel patterns are influenced greatly by land use patterns. The nature of the activity on a given plot of land will determine the amount of travel to and from that location. Finally, that the various elements of individual decision-making regarding trips may be made subconsciously, more or less simultaneously, based on either careful thought or very little rational analysis, out of habit, and may be subject to change during the trip. Nevertheless, most practicing travel demand modelers follow a 4-step procedure that assumes a tripmaker considers the following four questions in the following sequence:

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Chapter 4 Modeling Transportation Demand and Supply

Edition, 6" Printing

Should I make a trip? What should be my destination? What mode of transportation should I use?

What route or path should I take?

Vi

~

~

THINK ABOUT IT Think back to the last 4 or 5 trips you made. Did you ask yourself any or all of the four questions above?

A

If so, in what order did you consider the questions?

Obviously, most individuals do not think about trips in this sequential structure. But remember: travel demand modeler is seeking to describe (and explain) the travel decisions of hundreds even --

thousands

--

of tripmakers. To keep the analysis — and the collection of data to support it manageable, --

most travel demand modelers have adopted the standard method that is based on the four questions listed above. As each of the four steps in the process is introduced in the lessons that follow, each question above will be restated in a way that recognizes that many persons may be making the decision implied by the question.

4.1.2 Land Use and Tripmaking

A 500-acre undeveloped site lies adjacent to State Highway 361 at the edge of Mythaca. The land is

suitable for either residential or industrial development. The Mythaca County land use planners are concerned about the patterns of land use and how they will affect the quality of life in the area, The

transportation planners want to be sure that the area’s transportation system roadway and public transit will be adequate to accommodate the new tripmaking associated with the new development. --

A person's tripmaking is the result of a decision to go somewhere and do something there.

Trip

making is a response to landowners’ decisions as to how to use their land. Transportation facilities and services are also a response to land use, either in anticipation of the traffic that will result or in response to the tripmaking that is already taking place. The relationship also works in reverse that is, land use decisions are affected by existing and promised transportation facilities and services — but it is not as strong, A decision to build a factory at a particular site, for example, may depend on several factors in addition to transportation, such as --

¢ ©

©

~ Vé

the availability of skilled or trainable employees, tax abatements or other concessions from the local and state governments, the suitability of the soil at the site for the intended development.



THINK ABOUT IT Make a list of the factors that influenced your choice of housing for the current semester.

Will these factors be different when you choose your first permanent

residence after getting your degree(s)?

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Chapter 4 Modeling Transportation Demand and Supply

The asymmetric nature of the land use-transportation relationship makes land use forecasting more difficult than transportation forecasting, but transportation forecasting is difficult enough. To see how land use can be translated into trips, a few specific examples will be helpful.

of People make trips in order to engage in some activity at the destination. The amount At one extreme of tripmaking to a plot of land is due in large part to the intensity of use at that location. attract it will or lack of very few trips. land use intensity is a vacant lot. Such a “land use” normally If neighborhood children use the vacant lot as a playground, their trips to the lot will typically be made by walking or by bicycle, not by motor vehicle. An example of an intense use of land is a fast food It restaurant, to which a large number of vehicle trips will be made, especially at typical mealtimes. would be very helpful to a transportation planner to be able to predict how many trips will be made to a particular type of land use at a particular location. --

--

Example 4.1 Undeveloped 500-acre site Consider the 500-acre undeveloped site mentioned at the start of this section. The transportation planners at the MCPC want to predict how many trips will be made to and from this site if the development is (a) residential or (b) industrial in nature.

Solution for Example 4.1.

way to estimate the number of trips that will be made to the 500-acre site would be to base that estimate on the nature and intensity of land use on the site. Fortunately, tripmaking data of that sort have been collected and published by the Institute of Transportation Engineers in its Trip Generation done by consultants, government report. [ITE 1997] The report is a compilation of trip generation studies

A reasonable

agencies, and ITE student chapters across the US.

If the 500-acre site is developed as a subdivision with single-family housing on lots of one-third

acre each, and ten percent of the total land area is devoted to streets and other public space, as many as 1350 homes will occupy the remaining land. Using the average trip rate of 9.57 vehicle trips per dwelling unit per weekday found under “Average Rate” in Figure 4.4(a), the transportation planner can estimate that the new subdivision will cause 1350*9.57=12,920 vehicle trips per weekday to be “generated”. Using the “Fitted Curve Equation” at the bottom of Figure 4.4(a) leads to an alternative calculation:

= = La(T) = 0.920 Ln(1350) + 2.707 = (0.920*7.20786) + 2.707 6.631 + 2.707 9.338 T = exp(9.338) = 11,364 vehicle trips per weekday Even though the two estimates (12,920 and 11,364) are fairly close, the planners would be wise to cities recognize that these values are estimates based on data collected in 348 studies conducted in other in unspecified years. Using Figures 4.4(b-d) to corroborate these estimates should be considered.

FYI

=

Do not let the label of the vertical axis in Figure 4.4(a) confuse you. It says "T Average Vehicle Trip Ends". The word "Average" applies to each point in the figure's scatter plot, because each point may be the result of several observations at that location. A better label might be "Average Total Vehicle Trip Ends" at a site for the

time period being studied

Fricker & Whitford

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in this case, Weekday.

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Modeling Transportation Demand and Supply

Single-Famlly Detached Housing (210)

Average Vehicle Trip Ends ve: Dwelling Units Ona: Weekday

Number of Studies: 348 Avg. Number of Dwelling Units: 198 Directional Distribution: 50% entering, 50% extting

inp weneration per DweilingUnit Average Fate

Range of Rates

Standard Deviation

FIGT and Equation

X%

x

Data Pointe

= Number Dwelling Units of

|

Fitted Curve Equation:

Average Rate

Ln(T)

=

0.920

L(x) + 2.707

Trip Generation, 6th Edition

263

°

R? s 0.98

Inatitute

of Transportation Engineers

FIGURE 4.4(2) ITE Trip Generation data page for Single-Family Detached Housing. Source: Trip Generation, 6th Edition, 1997, p. 263. © 1997 Institute of Transportation Engineers. Used by permission.

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Chapter 4 Modeling Transportation Demand and Supply

Single-Family Detached Housing :

(210)

Average Vehicle Trip Ends ve: ‘Persons One: Weekday

Number of Studies: 185 Average Number of Persons: 557 Directional Distribution: 50% entering,.50% exiting

Trip Generation per Person

Range of Rates

Average Rate

Standard .Deviation

1,69:

Vata PICT ang Equation 10,000

9,000 ~ 8,000 =

7,000

-

6,000

6,000

+4

x Fitted Curve Equation:

a

%

*

pncttsserecs

Trip Generation, 6th Edition

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1

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FIGURE 4.4(b) ITE Trip Generation data page for Single-Family Detached Housing. Generation, 6th Edition, 1997, p. 272.

©

Source: Trip Used 1997 Institute of Transportation Engineers. by

permission.

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Chapter 4 Modeling Transportation Demand and Supply

6" Printing

Single-Family Detached Housing ~

(210)

Average Vehicle Trip Enda ve: Vehicies Ona: Weekday

Number of Studies: 120 Average Number of Vehicles: 257 Directional Distribution: 50% entering,50%

exiting

Trip Generation per Vehicle.

Range of Rates

Standard Deviation

9.38

2.77

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400

500

800

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2

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FUNDAMENTALS OF TRANSPORTATION ENGINEERING Chapter 4 Modeling Transportation Demand and Supply

Single-Famlly Detached Housing (210)

Average Vehicle Trip Ende ve: Acree Gna: Weekday

Number of Studies: 144 Average Number of Acres: 70 Directional Distribution: 50% entering, 50% exiting

Trip Generation

Acre

Range of Rates

a

Average Rate

S.t7__-

28.04

,

84,94

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14,000

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-

13,000 12,000

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10,000 7

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3

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x.

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100.00

.

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Number of Acres.

Data Points

Fitted Curve

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mH

Trip Ganeration, 6th Edition

inatitute ot Tranaportation Engineers

FIGURE 4.4(d) STE Trip Generation data page for Single-Family Detached Housing. Trip Generation, 6th Edition, 1997, p. 290.

Source:

© 1997 Institute of Transportation Engineers. Used by

permission.

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Modeling Transportation Demand and Supply

Solution for Example 4.1, continued. In contrast to a proposed residential subdivision, if the 500 acres were to be devoted to a manufacturing facility, Figure 4.5(e) from the ITE Zrip Generation report could be used:

Average trip rate:

T = 38.88 * 500 acres = 19,440 vehicle trips per weekday

A Fitted Curve Equation for Land Use 140 in Figure 4.5(a) is not given, because its R? value is too low. If

it is known that the proposed manufacturing facility will have 2.5 million

Figure 4.5(b) could be used to estimate vehicle trips per weekday: Average trip rate:

T = 3.82 *

square feet of floor space,

2.5108 sqft = 9550 vehicle trips per weekday 1000sqift

Fitted Curve Equation:

T = 3.881

*

#106

oleae S

- 20.702 = 9682 vehicle trips per

:

weekday.

If the number of employees was predicted to be 3000, Figure 4,5(c) could be used: Average trip rate:

T = 2.10 * 3000 = 6300 vehicle trips per weekday

Fitted Curve Equation:

T = (1.740 * 3000) + 229.975 = 5450 vehicle trips per weekday.

The results of these calculations for manufacturing use of the land are summarized in this table:

Average trip rate Fitted curve equation T = 19,440 No curve

Variable

X = 500 acres

given

X =2.5 million square feet T=9550

T=9682

X = 3000 employees

T=5450

T=+6300

np ~

17

~

THINK ABOUT IT Which of the five T values computed in Example 4.1 for the Manufacturing land use would you adopt? Why?

The large range of T values— from 5450 to 19,440 — that were computed in Example 4.1 using Figures 4,5(a-c) is not unusual. (In fact, the input for the manufacturing land use in this example comes from an actual facility.) After all calculations are done using the ITE method, the planner must decide which single value or range of values is most appropriate. The ITE Trip Generation Handbook [ITE 2012] offers guidance in making this decision, but it also depends heavily on the judgment and

experience of the planner.

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FUNDAMENTALS OF TRANSPORTATION ENGINEERING Chapter 4 Modeling Transportation Demand and Supply

anufacturing (140) Average Vehicle Trip Ends va: Acres Ona: Weekday

Number of Studies: Average Number cf Acres: Directional Distribution:

a

Generation

i

56 35 50% entering, 50% exiting

Acre Range of Rates

Average Raie

Standard Deviation

41,93

__2.64.__- 386.00

38.85

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8.000+

5,0007

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2,000

x. P



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Inatitute of Tranaportation Engineers



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1

1 4

Generation, 6th Edition, 1997, p. 179.

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Fricker

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anufacturing (140) .

Average Vehicle Trip Ende ve: 1000 Sq. Feet Gross Floor Area Ona: Weekday

Number of Studies: 62 Average 1000 Sq. Feet GFA: 349 Diractional Distribution: 50% entering, 50% exiting

Trip Generation

per

1000 Sq.. Feet Gross Fic

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Range of Rates

3.82

-

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=

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|

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52,05

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x nN

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%

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x

Trip Ganeration, 6th Edition

1000 Gq. Fost Gross Floor Area

Fitted Curve

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T = 3.881(%) - 20.702

5

Mgr

170

Institute of Transportation Engineers

FIGURE 4.5(b) ITE Trip Generation data page for Manufacturing land use. 6th Edition, 1997, p. 170.

0.87

Source: Trip Generation,

© 1997 Institute of Transportation Engineers. Used by permission.

hae

Fricker & Whitford L

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&

8

146

Ch 4 Travel Demand Models

FUNDAMENTALS OF TRANSPORTATION ENGINEERING

2™ Edition,

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Chapter 4 Modeling Transportation Demand and Supply

NMianufacturing

(140)

Average Vehicle Trip Ende va:

Employees.

Ona: Weekday

Number of Studies: 61 Avg. Nurnber of Employees: 641 Directional Distribution: 50% entering, 50% exiting

a

Generation

i

Average Rate

of Rates

Standard Daviation 1.65

vata PIOT and Equation 11,000

10,000~ 9,000 =

a

gente

%

~

\

eee

.,

'™~

*,

7

x

dgeness tee ww .

x

gee en ege ens

*

X =

Number of Employees Average Rate

Fitted Curve Equation:

T = 1.740(X) + 220.075

Fi? = 0.04

161

Trip Generation, 6th Edition

Institute of Tranaportation Engineers

:

emnapeeceqenscceeccomeee ty

1000

FIGURE 4.5(c) ITE Trip Generation data page for Manufacturing land use. 6th Edition, 1997, p. 161. seneceenet

Fricker & Whitford

©

Source: Trip Generation, Used 1997 Institute of Transportation Engineers. by permission.

4,14

Chapter 4.1

.

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FUNDAMENTALS OF TRANSPORTATION ENGINEERING Chapter

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Modeling Transportation Demand and Supply

1

- Jon D. Fricker and Robert K. Whitford

2™

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The ITE procedures can be applied to any land use for which data are available.

A common use

of this procedure is to predict the impact of a new land use on nearby streets, from something as small as

a fast food restaurant or convenience store to a development as large as a regional shopping center or an automotive assembly plant. However, transportation planners often must deal with an entire metropolitan area. It would be extremely tedious to attempt to model tripmaking for even a small town on a

site-by-

site basis. Instead, transportation planners break up a study area into traffic analysis zones (TAZs). It is with this zonal basis that we will proceed with the standard 4-step travel demand modeling methodology in the sections that follow.

THINK ABOUT IT Begin to design a site-by-site analysis of any urban area you choose by dealing first only with one land use type, say, restaurants. How many restaurants are there in that urban area? How do you determine how many there are? Describe the steps you would have to take in order to estimate the number of trips made to and from all restaurants in that urban area, using data from the ITE Trip Generation report. Is this an efficient way to do Trip Generation in an urban area?

4.2

TRIP GENERATION

To anticipate the future transportation needs in Mythaca County, the Mythaca County Planning Commission staff is asked to predict how many vehicle trips will be generated by residents and visitors as they go about their daily activities. The MCPC staff needs to identify and adopt a method that can replicate current tripmaking levels and make reliable forecests of future tripmaking. For example, how many trips are made on a typical day to a large discount store? Without a satisfactory Trip Generation procedure, the rest of the four-step travel demand modeling process cannot be successful. 4.2.1

Trip Generation Concepts

How many trips will begin or end in each traffic analysis zone? Instead of attempting to study tripmaking on the level of detail of individual persons or specific origins and destinations, travel demand modelers normally assign the location of each end trip (origin and to a traffic zone In destination) analysis (TAZ). densely populated neighborhoods, a TAZ may consist of only a few city blocks. In more rural areas, a TAZ may cover more than one square mile. A TAZ’s boundaries are usually set to coincide with the edges of census tracts or census blocks.

When grouping or aggregating tripmaking by TAZs, the first question in the four-question sequence described earlier in this chapter is converted from the individual’s “Should I make a trip?” to the collective “How many trips are made from (or to) this zone?” A common preliminary step is to recognize that each trip is made for a particular purpose. Standard trip purposes are work, shopping, school, and recreation. Another important assumption in the modeling process is that the amount of tripmaking from a given zone is a function of certain measurable characteristics of the zone or of the people who live in it. For example, it is generally accepted that a family or household will make more vehicle trips per weekday if it has:

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Ch 4 Travel Demand Models

FUNDAMENTALS OF TRANSPORTATION ENGINEERING

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Chapter 4 Modeling Transportation Demand and Supply

of driving age,

e

more members

*

more people with jobs,

=

higher income, more vehicles to use.

e

4.2.2 Regression Models for Trip Generation Based on a list of household characteristics that could be expected to influence tripmaking, a planner could collect data on an adequate sample of households in each zone for these variables and build a linear regression model of the form (4.1) T=ap +a; Xi tag X2+... + an Xn where X; is a factor (usually demographic) that explains the level of tripmaking and a; is a coefficient or constant that converts these factors into number of trips T.

Example 4.2 Household-based Regression for Trip Generation

TABLE 4.1

Data for Example 4.2 Household Travel Survey Data

Whenever a new subdivision is proposed in

Mythaca County, the Mythaca County Planning Commission staff is asked to predict how many (1) Persons/HH vehicle trips will be generated by the development. 1 One MCPC staff member proposes an alternative to

ITE method based on certain household characteristics. Among the characteristics that might influence the number of trips is the number of persons in the household. Census data and surveys

(2) Veh-

(3) T (model)

Trips/day 3

5.4

5.4 6.8 6.8 6.8 6.8 6.8 8.3

the

1

2 3

of a sample of households from recently completed subdivisions have been compiled. A part of that

2 2 2 2 2

dataset is shown in Table 4.1. The data in the table

3

7 6

are sorted by household size (persons per household in column 1). Column 2 contains the number of trips reported by each household when the head of

3

10

8.3

3

12

3

11

8.3 8.3

household was asked about the previous day’s travel activity. Is it possible to develop a “model” from these data that will help the MCPC staff predict tripmaking levels from similar land uses, i.e., new

4

11

4

14

4

10

9.7

5

12

11.1

residential subdivisions?

6

18

12.5

8

12

15.3

8

16

15.3

9

15

16.8

10

16

18.2

Fricker & Whitford

4.16

5

10 1

9.7 9.7

Chapter 4.2

Fundamentals of Transportation Engineering - Volume

1

- Jon D. Fricker and Robert K. Whitford

h_. Chapter

L



,

.

Modeling Transportation Demand and Supply

Solution to Example 4,2

2™

Edition, 6” Printing

A glance at the data in columns 1! and 2 of Table 4,1 reveals that, in general, larger households make more trips. This relationship is expected. Can it provide the basis for a good forecasting tool? By entering columns 1 and 2 into a spreadsheet, we can use a feature like “Tools/Data Analysis/Regression” in Excel =

7

4

Vehicle Trips per Day

FUNDAMENTALS OF TRANSPORTATION ENGINEERING

k

to produce the best straight-line fit to the data. The resulting line is = 4.0126 + 1.4168x with an y adjusted r” value of 0.575. Using this equation, the expected number of vehicle-trips per day for each household size can be computed. These expected values are shown in the “T (model)” column in Table 4.1. The plots of the original data and the fitted regression line are shown in 4.7.

Figure

‘—

20



1

18

i2

e !

y= 1ATGBs #0428

6

|

*

4

*

,

2]

'

@

,

‘-

9

i

0

*

2

6

4

10

8

12

Number of Persons in Household @ |

Suneydata

=

Regresaion line ——Linear (Regression line)

FIGURE 4.7 Linear Fit of Household Vehicle Trip Data

*

a .

~ —

.

Vi



THINK ABOUT IT In Example 4.2, the relationship between tripmaking and household size was considered. Think of at least two other factors that might help explain levels of household tripmaking.

Examples of trip generation models built using linear regression are [FHWA 1967]

Trips produced in a zone = 36.03 + (5.09

cars/zone)

Trips produced per household = 0.69 + (1.39 * persons/HH) +

(4.2) (1.94

*

cars/HH)

(4.3)

Shopping trips produced in a zone =

y we

*

30.98

+ 1.03 (HHs/zone) + 2.20 (cars/100 HHs) - 5.39 (cars/100 persons)

(4.4)

For most trip types, trips are produced at the origin and attracted to the destination. When one end of the trip is at home, however, that end is always the production end and the other end must be the attraction

te mer

Fricker

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Ch 4 Travel Demand Models

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Chapter 4 Modeling Transportation Demand and Supply end. This means that home-based-work (HBW) trips could have a production equation like Equation 4.2 above for the traveler’s home zone and an attraction equation for the employment zone such as

[NCHRP365 1998]

HBW attractions =

1.45 * Total Employment

(4.5)

4.2.3 Cross-Classification Models for Trip Generation While regression models are computationally convenient, their use of zonal totals or zonal averages can

mask important variations between households within a zone. An alternative to using zone location to put households into groups is to use important characteristics such as household size and auto availability. This approach assumes that a household with three members and one car has tripmaking characteristics similar to other 3-member, 1-car households, whether or not they are located in the same zone. Table 4.2 is the result of collecting data on the tripmaking frequency of households for all reasonable combinations

of household characteristics.

TABLE 4.2

Average Daily Person Trips by Household Size and Autos Owned Urbanized Area Population: 50,000-200,000 Persons per Household 1

2

3

4

5+

Weighted Avg.

Zero

2.6

4.8

74

9.2

112

3.9

One

4.0

6.7

9.2

11.5

13.7

6.3

Two

4.0

8.1

10.6

13.3

16.7

10.6

Three Plus

4.0

8.4

11.9

15.1

18.0

13.2

Weighted Avg.

3.7

7.6

10.6

13.6

16.6

9,2

Autos Owned

Source: NCHRP 365, 1998

Table 4.2 is called a cross-classification table. If forecasts can be made of the number of each household type in each zone for some future year, the cross-classification table can be used to compute the total trip not vehicle productions for each zone. Note, however, that the entries in Table 4.2 are for person trips, modes. travel non-motorized transit or by trips. The entries may include trips by public

~ Ni « :

THINK ABOUT IT Look at the trends in the trip rates shown in Table 4.2, as the values of the household characteristics increase or decrease. Do these trends make sense?

—-9-— — 9 Example 4.3 Trip Generation by cross-classification Based on recent surveys, the Mytheca County Planning Commission (MCPC) staff has estimated the number of households in Mythaca that fall in each household size/vehicle ownership category. These estimates are shown in Table 4.3. The MCPC does not have the resources (money, personnel, or time) to use the develop its own cross-classification trip rate table like Table 4.2, so the MCPC staff decides to rates in Table 4.2 until better trip rate information can be obtained.

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Chapter 4.2

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Chapter 4 Modeling Transportation Demand and Supply

TABLE 4.3

- Jon D. Fricker and Robert K. Whitford

6" Printing

Numbers of Households, each Household Category Persons per Household

Autos Owned

1

2

3

4

5+

Row Total

0

1005

403

213

114

105

1840

1

2909

2038

875

526

369

6717

2

408

3915

1802

1425

1406

8956

3+

111

1075

1375

1383

860

4804

Column Total

4433

7431

4265

3448

2740

22317

A. How many person-trips per day will be produced by a five-person household that owns two vehicles? B. Using the cross-classification trip generation method, calculate the total number of person-trips per day that will be produced by Mythaca households, if the data in Table 4.2 and the “Number of Households” Table 4.3 are reliable.

C. If94 percent of the person-trips calculated in Part B used private automobiles (not public transportation) and the average auto occupancy is 1.96, how many vehicle trips were produced by Mythaca households in Part B?

Example 4.3 Solutions

A. According to the MCPC staff, there are 1406 households in Mythaca that have five or more persons and own two vehicles. This total includes households with exactly five members and two vehicles. In Table 4.2, each of these households produces an average of 16.7 person-trips per weekday.

B, Begin with the first cell in the cross-classification tables, i.e. the household category for one member and no auto owned. There are 1005 such HHs, each of which generates an average of 2.6 person trips per day. To find the number of trips produced by all such HHs, multiply 1005 by 2.6 to get 2613 person-trips per weekday. To compute the number of person-trips for all households, simply repeat this calculation for all cells in the “Number of Households” Table 4.3. Multiply the value in each such cell by the trip rate in the corresponding cell in Table 4.2, then add the products.

(1005*2.6) + (2909*4.0) + ...

+ (1406*16.7) + (860*18.0) = 209,871 person-trips per day

The cell-by-cell calculations were performed with a spreadsheet, as shown below.

TABLE 4.4

Total trips per weekday, each household category Persons per Household

Autos Owned

1

2

3

4

5+

Row Total

0

2613

1934

1576

1049

1176

8348

1

11636

13655

8050

6049

5055

44445

2

1632

31712

19101

18953

23480

94877

3+

444

9030

16363

20883

15480

62200

16325

56331

45090

46934

45192

209871

Column Total

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Chapter 4 Modeling Transportation Demand and Supply

C. Of the 209,871 person-trips calculated in Part B, 94 percent use private vehicles: 0.94 * 209,871 = 197,279 person-trips by private vehicle

If the average private vehicle carries

1.96 persons, the number of vehicle-trips produced by Mythaca

households on an average day is

197,279 person ‘trips 1.96 persons/vehicle —

_ 100,653 vehicle-trips.

4.2.4 Beginning the Middleville Case Study Middleville is a small but fast-growing city between Mythaca and Shoridan. Its current population is estimated to be 5000. To anticipate and plan for the transportation impacts of future growth in the Middleville area, the MCPC has begun to apply travel demand modeling techniques to the area. The MCPC staff has identified four sections of Middleville, each of which is devoted exclusively to a particular activity. These sections will be calied traffic analysis zones Zone 1 is manufacturing zone, zone 2 is a retail zone, and zones 3 and 4 are residential. (See Figure 4.8.) a

.

Zone

Zone 2

|

Retail

Manufacturing

Zone 4 Residential

Zone 3

Residential

FIGURE 4.8 Middleville’s Four-Zone Study Area The data that describe the amount of activity in each zone are summarized in Table 4.5.

TABLE 4.5 TAZ pop

Middleville T/G data

HH

vehs_

6 0 1400 1600 3000

i

0

0

2

0

0

3

3000 2000 5000

1100

4 Totals

Fricker & Whitford

900

2000

empl 1000 1500 0

0 2500

4.20

TAZ =

traffic analysis zone

= pop population in zone

HH = households in zone vehs = vehicles owned by HHs in zone

empl=employment

=jobs in zone

Chapter 4.2

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1

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Example 4.4 Trip Generation in Middleville Because the MCPC staff does not have the time or resources to develop its own trip generation model, it chooses to borrow a model developed for cities similar to Middleville, with the hope that it is suitable for Middleville. The borrowed model consists of two equations:

P = 93 + (4*vehs) + (0.1*HH) + (0.7*empl)

Trip productions:

Trip attractions:A = 327 + (2.2*empl) + (1.3*HH) According to the borrowed equations, how many trips per day will be produced and attracted by each

TAZ?

Solution to Example 4.4

Applying the borrowed equations to each zone i results in the productions P(i) and attractions AG) shown in Table 4.6. For example, P(1) = 93 + (4*0) + (0.1*0) + (0.71000) = 793 and A(2) = 327 + (2.21500) + (1.3°0) = 3627. This is the first step in the four-step travel demand modeling process that will be applied to Middleville in this chapter,

TABLE 4.6

Middleville T/G results

TAZi

P(i)

A(i)

!

793

2527 3627

2

1143

3

4

5803 6583

1497

Total

14322

9408

1757

In practice, both cross-classification and regression are used to compute zonal trip productions, depending on modeler preference, computer software capabilities, and data availability. Trip attractions for each zone are almost always calculated using regression equations.

Two words used in the previous paragraph deserve further mention

data and software. A large part of the effort involved in travel demand modeling is the collection and analysis of data. These data must be based on a representative sample of the tripmakers being studied. The analysis of these data must be statistically valid and suitable for travel demand modeling purposes. Over the years, many computer packages have been developed to help the transportation planner carry out the calculations involved in the modeling process. While most software packages are designed to implement the standard four-step methodology, many of them have capabilities and limitations that influence what specific data and modeling techniques a planner can employ.

~ Vi

(?



--

THINK ABOUT IT In Example 4.4, the total daily productions (14,322) in Middleville do not equal the total daily attractions (9408). Is this a problem? If so, what are the possible causes?

What options does the MCPC staff have?

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Balancing Ps and As In Example 4.4, EP = 14,322 and ZA = 9,408, Because each trip has a Production end and an Attraction the Ps and As must be balanced. Because the MCPC end, it must be true that = EA. In other words, equations thanin their attraction equations, they decided to planners have more faithin their production balance the Ps and As that came out of Example 4.4 by multiplying each A; value by ZP/ZA = values are The Ao=3627*1.522=5521, 14322/9408 1,522. Aj=2527* 1.522=3847, resulting A; = Ag=1757* 1.522=2675, and Ag=1497*1,522=2279, so that ZA=ZP=14,322. Now that both trip ends are

accounted for, the planners can attempt to build a trip matrix.

4.3

TRIP DISTRIBUTION

(1) EcanelyT.

At=

49099

There are four cities in the region that includes

Mythaca: (1) Econoly, (2) Mythaca, (3) Shoridan, (4) Middleville. Each city has an increasing number of retail stores. Residents of Mythaca now have many more shopping opportunities competing for their dollars. Each resident must make a choice as to the shopping locations he/she will choose as his/her

Spondan

4)

destination. For shopping trips, work trips, and any other trip type, a planner must be able to estimate the number of travelers at any given origin location (such as in zone 2 in Figure 4.9) who will choose any particular destination (from among zones 1-4in Figure

4.9).

4.3.1

‘\%

@)-Mythace

P2 =801T

A2=

FIGURE 4.9 Schematic diagram of shopping trips in the Mythaca region

Trip Distribution Concepts

How many trips that begin at a given origin will end at a given destination? Each trip made has two ends — an origin and a destination. In the Trip Generation step, only the number of trip ends in each zone was calculated. In the Trip Distribution step, trip ends are connected to form trip interchanges Ty, which represents the number of trips produced in zone i and attracted to zone j. Once the production end and attraction end of each trip have been determined, a trip matrix can be established. zone. The i™ row and j* column of the matrix A trip matrix has one row and one column for each for a contains the number oftrips that are produced in zone i and are attracted to zone j. Another name trip matrix is trip table.

Table 4.7 summarizes the peak hour shopping trips made between the four communities in or near Mythaca County, according to data collected by the Mythaca County Planning Commission (MCPC). Because Econoly is the largest city in the region and has the most stores, it is likely to attract a lot of shopping trips from the other three cities. However, shoppers tend to favor their own town, if there are enough shopping opportunities to satisfy their needs, because it saves travel time. The MCPC wants to know how many shoppers make trips to cities other than their own during the peak hour.

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TABLE 4.7

- Jon D. Fricker and Robert K, Whitford

2™ Edition,

Chapter 4 Modeling Transportation Demand and Supply ‘

1

6" Printing

Productions and Attractions for Shopping Trips in Mythaca Region

(1) Econoly

(2) Mythaca

(3) Shoridan

(4) Middleville

Productions

4724

901

193

108

Attractions

4909

774

174

69

Cities

The standard procedure for converting zone-by-zone production and attraction totals into trip interchanges T; is called the Gravity Model. The Gravity Model builds upon two principal

assumptions:

likely to be attracted to an attraction zone that has a higher

e

A

«

A trip produced in zone { is more likely to be attracted to an attraction zone that is closer to zone

trip produced in zone i is more number of attractions.

i.

The Gravity Model is an analog of Newton's Law of Gravity. The gravitational force between two bodies with masses m, and mz is _™m,*m,

(4.6)

where dj2 is the distance between those bodies. In the 1920s, the Swedish investigator Pallin used a form of Equation 4.6 to determine traffic flows between cities. [BPR 1963] He used City 1's productions in

place of m; and City 2's attractions in place of mz. Since then, the travel demand modeling form of Equation 4.6 has become

T, =B

AGA DAE

(4.7)

Tg is the number of trips that go from zone i to zone J. Fy is a function of the separation between zones i and j, and is usually called the traveltimefactor or thefriction factor. Normally, the separation between

zones is measured in terms of travel time ty. The most common form of Fy is 1

-

Fyj=a*—=a*ty?

(4.8)

with a= 1,0,

Example 4.5 Gravity Model: Trips Produced in Zone 2

To illustrate the relationships contained in the two principal Gravity Model assumptions stated above, consider the regional shopping trips summarized in Table 4.7. How well does the Gravity Model explain the way those trips distribute themselves from each production zone to the aveilable attraction zones? Begin with the 901 shopping trips that are produced in Mythaca (Zone 2 in Table 4.7). How many of the

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FUNDAMENTALS OF TRANSPORTATION ENGINEERING Chapter 4 Modeling Transportation Demand and Supply

shopping trips that start in Mythaca will be attracted to stores in Econoly, Mythaca, Shoridan, and Middleville? The average travel times in the region are summarized in Table 4.8. Note that intrazonal travel times ta are not zero. The diagonal entries are the average travel times for vehicle trips that stay within the same zone.

TABLE 4.8

Average travel times in the Mythaca region (minutes) Destination Cities

(1) Econoly

(2) Mythaca

(3) Shoridan

(4) Middleville

(1) Econoly

7

35

45

40

(2) Mythaca

35

5

20

12

(3) Shoridan

45

20

3

(4) Middleville

40

12

8

Origin Cities

2

Solution to Example 4.5

We can use Equation 4.7 to find Ta1, Tz, Ts, and Tz. First use Equation 4.8 to convert travel times tz, toz, tes, and ty into friction factors F21, F22, F2s, and F4: F,, =35* =0.000816, F,,

=5

= 0.0400, F,,

=20

= 0.0025,

F,,

=12°

= 0.006944.

Because it is a bit awkward to deal with numbers so small, scale up each Fy by a factor of 1000: Fy;

~

= 0.816, F22 = 40.00, Fas = 2.5, and Fas = 6.944.

w THINK ABOUT IT

What is it about the structure of Equation 4.7 that allows us to simply multiply each value by an arbitrary scalar and not affect the T; values that result from Equation 4.7?

The A; values for this problem are the trip attraction totals for each city in Figure 4.9:

Ai = 4909, A2 = 774, Az

=

174, and Aq = 69,

Now calculate T2: using Equation 4.7:

Ty =?,

AF) _ P,

DAE k

A,B

AiFn + AgFi2 + Agkyy + AgFag 4909 * 0.816

=101. * * (4909 0.816) + (774 40.0) +(174*2.5) + (69* 6.944) This result tells us that only 101 of Mythaca's 901 shopping trips (produced in Zone 2) will be attracted to — Econoly (Zone 1). Despite the high number of shopping trip attractions in Econoly which is an destinations. The closer indication of many shopping opportunities there most Mythaca shoppers prefer calculations for T21, T22, Tz3, and Tz can be made easier by using a spreadsheet such as that shown in Ty 1 =901

--

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Chapter 4.3

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- Jon D. Fricker and Robert K. Whitford

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FUNDAMENTALS OF TRANSPORTATION ENGINEERING Chapter 4 Modeling Transportation Demand and Supply

Table 4.9. In this table, parameter a is the scalar applied to Equation 4.8 to get the column 4 values, columns 5 and 6 contain the intemediate steps in Equation 4.7, and column 7 shows the results for T2i, T22, Tas, and T2s,

TABLE 4.9

Gravity Model Calculations for Example 4.5 from Zone 2

P=

901

a=

1000

b=

(1) Zonej

(2) AG)

1

2

(3)

2,00 (4)

(3)

(6)

{7)

_—t{2j)

F(2j)_

AQ)F(2j),

T(2j)

4909 774

35

4007.3

3

174

20

0.816 40.000 2.500

4

69

12

AFG@/sum(AF) 0.112 0.863 0.012 0.013 1.000

901

5

6.944

5926

30960.0 435.0

479,2 35881.5

101

777 11

12

—-— —-} The form of Equation 4.8 seems to make sense when auto travel between cities is involved. Short trips are more likely to made by auto than long trips. Example 4.6 illustrates.

—-}—

+







Example 4.6 Changing “b” in the Friction Factor What does the friction factor of Equation 4.8 look like when b in Equation 4.8 takes on values between 0.5 and -2.0?7

Solution for Example 4.6 Figure 4.10 shows that the value of b controls how quickly F; diminishes as ty increases. The lowest of the three curves plotted in Figure 4.10 is Equation 4.8 with b = -2.0. If the Ty values calculated using Equation 4.8 with b = -2.0 clearly overstate (or understate) the number of short trips, adjusting the value of b should be considered.

pee

|

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tw,

Te



“tee

tresses VG

‘Travel time Uy

FIGURE 4.10 Friction Factor plots as parameter b varies, with c = 0

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THINK ABOUT IT Ifthe results in Example 4.5 understate the number of peak hour shopping trips from Mythaca to Econoly, while overstating the number that stay in Mythaca, what should be done with the value of b in Equation 4.87

There may be cases in which short trips are not the most common trip lengths in the travel data being analyzed. Consider, for example, the study area in Example 4.7.

—-4-—

4





Example 4.7 Distributing 100 Trip Productions Consider a small town that has only four zones. (See Figure 4.11.) In this study area, 100 trips are produced in Zone 1. How many of those trips will find destinations in Zones 1, 2, 3, and 4?

Pi

=

Zone

1

100,

A;

Zone2 =

A2= 200

50

Zone 3

Zone4

A3 =75

Aa=675

FIGURE 4.11 Four-Zone Study Area Solution to Example 4.7 In column 3 of Table 4.10, the travel time from Zone 1 to each zone in the study area is given. If travel time did not matter, most of Zone 1’s 100 trips would go to Zone 4, because it has by far the most attractions. If travel time is the most important consideration, most trips produced in Zone 1 will not go to zones other than Zone 1. If the parameter values a = 500 and b = -2 are used in Equation 4.8, the

friction factor function is F, =500t;*. Table 4,10, which has the same structure as Table 4.9, summarizes the Gravity Model calculations for the 4-zone town.

TABLE 4.10 P=

100

Gravity Model Calculations for 4-zone town from Zone 1

b=

a=

500

(1) Zonej

AG)

lj)

1

50

2

2 3

200 75

10

4

67515

2)

=) «5

-2.00

(4) ~=—SF(Aj)_

125.000 20.000 5.000

2.222

1000

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(5)

(6) AFGYsum(AF)

(7) T(1j)

6250.0 4000.0 375.0 1500.0

0.515

52

0.330

33

12125.0

= AGF (Ij)

0.031

3

0.124

12

1.000

100

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The results of Example 4.7 are cause for concern. In Table 4.10, T1: > Ai, but it is not possible to have more trip interchanges than trip attractions for any zone. Assuming the P andA totals in Figure 4.11 are correct, the Gravity Model must be overestimating short trips and underestimating long trips. One recourse is to adjust the b parameter in Equation 4.8, using lessons from Figure 4.10, but short trips would still be favored, only to a lesser degree.

THINK ABOUT IT Whiat is the shape of the expected trip length distribution for trips made by automobile? Are very short trips (a few blocks) more common than trips of about 1-2 miles? Are PERCENT TOTAL TRIPS

trips of more than 5 miles more common than trips of about 3 miles in an urban area? Make a rough sketch of a trip length frequency distribution for an urban area, using the format of a probability density function.

4.3.2 Other Forms of the Trip Length Distribution

It has long been known that very short trips are normally not the most frequent vehicle trips. See Figure 4,12.

VOTAL TRIPS

9728

TRIP LENGTH

TRAVELTHIE (MINUTES)

FIGURE 4,12 Trip length frequency distribution for an urban area. A friction factor function

Source:

BPR 1963

of the form

Fj =atpe™,

(4.9)

can create a trip length distribution like that shown in Figure 4.12. Parameters a, b, and c are used to fit the model’s trip table (or trip length distribution) to the one observed for the study area. Equation 4.9

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offers the analyst much more flexibility than Equation 4.8 in matching the Gravity Model to travel patterns observed in a study area. Because of J.C. Tanner's [1961] work on this subject, Equation 4.9 is often called the Tanner Function. —

+

Example 4,8 Changing Both Friction Factor Parameters What does the friction factor of Equation 4.9 look like when a = -1.00 and -0.507

1,

b

=

+2, and takes on values between ¢

Solutions for Example 4.8 Figure 4.13 shows how a proper combination of b and c values can replace the monotonically decreasing function in Figure 4.10 with a function that increases as tj increases from very low values, then decreases as ty gets large.

v Va

= THINK ABOUT IT

A special form of Equation 4.9, in which a = 1, = -2 and c = 0, is actually Equation Friction factor F(i)

160

4.8.

b

In Figure 4.13, the plot marked by diamond-shaped points represents Equation 4.8. The other two plots in the figure show how the frequency of short trips and long trips can be reduced, with trips of medium length being the most common. —0—b =-2.0,¢ =0.0

—®—b=20, c =-1.0

—H—b

=2.0,c=-0.5

2500 2.000

5

1.500

4

1.0007



0.006Travel time (minutes)

FIGURE 4.13 Friction Factor plots for Equation 4.9

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—-i—



—-



Example 4.9 Using the Tanner Function In Table 4.10, the Gravity Model results for Example 4.7 with b = -2.0 indicated that more than half the 100 Zone 1 productions would stay within that zone. As Figure 4.12 shows, it is often the case that the shortest trips are not as common as slightly longer trips. Based on Figure 4.13, use the Tanner Function

(Equation 4.9) with b =+2 and c = -0.5 in the Gravity Model to compute Ti; for results with those in Table 4.10.

j

=1

to 4. Compare the

Solutions for Example 4.9

The spreadsheet (or manual) calculations that led to Table 4.10 are modified to use Friction Factor Equation 4.9 instead of Equation 4.8. The results, shown below in Table 4.11, now send most trips to the second-closest zone. The number of trips to the two most distant zones does not change much. Most of Zone 2's new trips have been redistributed from Zone 1. Because Zone 4 has such a large number of attractions, it attracts the second most trips from Zone 1.

TABLE 4.11 100

P= =

10

Gravity Model Calculations for Example 4.9 from Zone 1 b= 2.00 c= 0.50

2)

(1) Zonej

(6)

(4) (5) (6) F(1j) AG)F(Ij) AFG@)sum{AF)

AG)

tt)

2

200

5

20.521

3

75

10

6.738

735.8 4104.2 505.3

4

675

15

1.244

840.0

14.715

1

6185.4

1000 —

}



(1) T(1j)

0.119

12

0.664 0.082 0.136 1.000

66 8 14

100





THINK ABOUT IT Another difference between Table 4.10 and Table 4.11 is the value of the a parameter. Will the friction factor values in Column 4 or the trip interchange values in Column 7 change if the value of a is changed?

C

¢

If reliable data are available on the frequency distribution of trip lengths in a study area, the Tanner Function can be adjusted to reflect the travel patterns. Statistical methods exist for estimating the best values for b and ec. As in Example 4.5, a is just a scalar. The Tanner Function offers the analyst an opportunity to build a Trip Distribution model that matches trip length travel data. Sometimes, imtrazonal trips Ta (trips that have both ends inside the same TAZ) do not fit the tripmaking behavior that the Gravity Model attempts to explain. If intrazonal trips cannot be properly included in a single application of the Gravity Model, the intrazonal trips can be

treated separately. The Gravity Model can be applied for interzonal trips only, leaving each Ty = 0 until a separate intrazonal analysis can be carried out.

Wet

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Regardless of the form of the friction factor and whether intrazonal trips are included, the Trip Distribution step continues until trips have been distributed from each production zone. In Examples 4.7 and 4.9, the distribution of trips from production zones other than zone | still needs to be done. The result will be a trip matrix (or trip table) that summarizes all T, trip interchange values. The intrazonal trips Tj that would fill the diagonal cells in the matrix could be done by a separate process, could be included in the Gravity Model calculations, or could be left out of the Trip Distribution step entirely, depending on the objectives

of the modeling task.

4.3.3 The Middleville Case Study, Continued

Example 4.10 Trip Distribution for Middleville The MCPC planners decide to use Equation 4.8 with the traditional parameter value b=-2.0 to compute each interzonal T; trip interchange value. Intrazonal trips T, will be treated in a separate analysis. (This assumes that the P; and A; values listed in Table 4.6 are for interzonal trips only.) The average auto travel times ty between the zones in Middleville have been estimated and are shown in the upper left quadrant of Table 4.12. What will the resulting interzonal trip matrix look like?

TABLE 4.12 -2.00 = friction factor exponent

100

1

2

3

4

1

17.36

083

41.49

on

5.5

2

0.83

22.68

183

3.31

99 23

3

149

183

865

1.02

4

2.30

3.31

1.02

tsa

1

2

3

4

|

24

#110

82

66

2}

110

210740 74

82 66

3]

AG@FGj)

0

55

34 99

15597

233

552

1143

1831

0

744

29813

1950

0 3227 4030

358

18129

603

0|

5803 6583

4014

7521

1190

1598

14322

sum

13773

4884 0 2729

7534 2325 0

3179

0

5721

10083

4)

8831

18253

793

229

4 5232

3!

Tot.P

3

263

3 «3978

2|

4 ~@#©6301

2

0

2

4563

1

= friction factor multiplier

Fj)

autot(ij)

44

Calculations for Example 4.10

Td

Tot

1

Note: In Table 4.12, row labels (1-4) indicate origin zones; column labels (1-4) indicate destination zones, For example, the average auto travel time from zone 2 to zone 4 is 5.5 minutes.

Solution for Example 4.10

With b = -2.0 and a = 100, Equation 4,8 becomes F, =100*t;*°. For trips produced in zone

1

and

=100*t3° =100*(11.0)*° =0.83. For trips produced in zone 4 and attracted in zone 2, F,, =100*t3° =100*(5.5)*° = 3.31. Although average interzonal travel times are not always = symmetric, that is, tj tj, they are symmetric here. Consequently the friction factors are also symmetric - Fj = Fj in the upper right quadrant of the Table 4.12. In the lower left quadrant of Table 4.12, the intermediate calculations for AjFj are stored. For example, AgF32 = 5521 * 1.83 = 10,083. In the attracted in zone 2, F.,

--

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Chapter 4 Modeling Transportation Demand and Supply denominator of Equation 4.7,

DAF appears. This is simply the row sum of the AjFj values. In row 2 k

of Table 4.12's lower left quadrant, we see that

3179

+ 0 + 4884 + 7534 = 15,597. Note that each

diagonal entry A(i)F(i,i) is set to zero, because only interzonal trips are being considered. Finally, each

Ty value can be calculated using Equation 4.7: 7,,

=P,

As > AFu



6583 « 5831 29813

_ 1950.

The lower

k=1,4

right quadrant of Table 4.12 shows the results for all the interzonal Tj calculations. This is the interzonal trip matrix (or trip table) for the Middleville study area.

—-b— —-+

>

-4-—

THINK ABOUT IT Although the travel time and friction factor portions of Table 4,12 are symmetric, the resulting trip matrix is not. Why is that?

An experienced transportation planner would not be satisfied with the trip matrix produced in Example 4.10. He or she would notice that we started with zonal attraction totals A1=3847, A2=5521, As=2675, As=2279 and ended up with A;=4014, A2=7521, As=1190, Ac=1598. The Gravity Model used in Example 4.10 has changed the zonal attraction totals for zones 2, 3, and 4 quite a lot. The remedies most likely to help are: ©

»

e

Adjust the Friction Factor exponent in Equation 4.8 if trip lengths are not being represented correctly. Use the Friction Factor Equation 4.9, instead of Equation 4.8, if the actual trip length distribution is not monotonically decreasing. Look for another variable besides travel time to explain how travelers choose between multiple

destination zones. These are topics more suitable for coverage in a separate course in transportation planning.

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MODE CHOICE

4.4.1 Mode Choice and Utility How many travelers will choose each mode oftransportation? Nationwide, the percentages of urban commuting trips made by the various modes in 2009 were [ACS 2011]: ®

76.1% alone in privately operated vehicles

*

«

10.0% carpool

#

5.0% by bus and rail transit

e

2.9% walking

«

4.3% work at home

#

1.7% by bicycle, taxi, other modes

FIGURE 4.14 Typicel commuter mode options

When it comes to predicting which mode will be chosen for particular trips, several factors come into play. For example, many persons ride public transit because they have to. They may be too young or too old to operate a motor vehicle. They may not be financially able to own and operate a motor vehicle, or they may not be physically able to do so. These persons are called captive transit riders, to distinguish them for modeling purposes from choice riders. Choice riders use transit because they have compared the attributes

of all available travel modes, and have decided that public transit is the best alternative for their

trips. This decision to use public transit is most likely to occur in large cities, where traffic congestion and parking costs make using a private vehicle sufficiently unpleasant and expensive, and where public transit service is available and of adequate quality. Although this chapter will continue to use examples

applicable to an urban context, the reader should note that models similar to those to be introduced here could be applied to choices of travel modes (air, bus, private vehicle, rail) for intercity trips.

The current state ofthe practice in mode choice modeling is the multinomial logit QMNL) model. The MNL model incorporates the notion that a traveler with a choice tends to choose the travel mode that has the greatest usility to him/her, but it also recognizes that (a) the utility may be difficult for the modeler to measure and (b) individual travelers may perceive the same mode choice alternatives in different ways. The result is a utility function of the form Un = 25m + Ayn Xm treet 8,

mXa,m



(4.10)

The utility function includes measurable variables x; that help explain the likelihood that a traveler in ._, category i would choose mode m. Common examples of xim are the travel time and out-of-pocket cost for each mode. The ainXim terms in Equation 4.10 comprise the measurable utility Vm. The random variable ¢ accounts for factors that may influence a tripmaker’s mode choice decision, but that are not easily measured or observed. For instance, two otherwise identical individuals with the same available

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travel mode alternatives may place a different value on the ability to work online while commuting. As a result of these variations, each mode’s utility to a particular individual will often be higher or lower than represented by the equation.

THINK ABOUT IT Identify at least two other personal factors (like wanting to be able to work online) that might influence your choice of travel mode, but does not directly involve mode attributes such as travel time or cost. Would your personal factors be observable and measurable?

The values of the coefficients a;,. in Equation 4.10 are the result of a statistical analysis based on surveys taken of individuals as they consider real or hypothetical mode choices. The choices made by the for the available alternatives are fed persons surveyed and the values of the measurable variables into a statistical analysis. The software that carries out this analysis normally employs maximum likelihood estimation techniques. Research has indicated that treating « in Equation 4,10 as a random variable with a Gumbel distribution and an expected value of zero leads to the easy-to-use logit equation:

P

e”"

(4.11)

“+3 jalk

where P,, = the probability that an individual will choose mode m from a specified set of alternatives.

—-t



Example 4,11 Express Bus to New Office Park

e

Discouraged because only six percent of the workers at the new office park at the edge of Mythaca use the express bus service from a certain white-collar neighborhood, the Mythaca Bus Company (MBC) asks the Mythaca County Planning Commission to conduct a survey of persons who are commuting to the new development. The MCPC finds that two factors affect commuter mode choice the most: out-of-pocket cost (OPC) and total travel time (TTT). The MCPC computations for MNL model result in a utility function Vin = ao - (0.47*OPCy) - (0.22*TTTm), where 89,20 = 0.73, OPCius = $0.75, TI Tuo = 10.5 minutes and TT Tu = 18 minutes. All other values are zero. a

A. Does the MNL model developed by MCPC replicate the actual bus mode share? B. According to the MNL model, what would the bus mode share be if the MBC reduces the bus fare to zeTo?

Solution to Example 4.11 —_!

A. Entering the coefficient and variable values provided by MCPC into the measureable utility part of Equation 4.10 leads to

Veto = 0.73 - (0.47*0.00) - (0.22*10.5) = -1.58

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Vous

= 0.00 - (0.47*0.75) - (0.22*18.0) =-4.31

Note that all of the

an coefficients in this version of Equation 4.10 are negative, and that both utilities are negative. Entering these Vn values into Equation 4.11 produces

mm

auto

eVauto + @V%bus

Pos ~

e158,

0.2060 0.0134

91584431

0.2060+0.0134

=

gag

0.2060+0.0134

431

bus

=y—

gVauto ye%bus

5-431

____ 9.061

According to the MCPC model, about 94 percent of the commuters would choose auto and only 6 percent would choose bus. This matches the observed mode share, so the MCPC model seems to be correctly specified. Always check these mode share calculations. Find the sum of the P, values that are calculated using Equation 4.11. The sum should always be equal to 1.00.

B. IfMBC reduces its fares for this express service to zero, the auto utility equation remains unchanged, but the bus utility equation becomes Vous = 0.00 - (0.47*0.00) - (0.22*18.0) = -3.96. When the Pn calculations using Equation 4.11 are redone, the mode shares are now Vauto

Pup eVauto =z?

eMbus

4

__e

e584

4

gVbus

6396

0.2060

___

0.2060+40.0191

c3.96

ebus

Ps ~ gVauto

-1,58

g 1584 6598

_ pois

0.0134

0.206010.0191_

ogs

Even when no bus fare is charged, more than 91 percent of the commuters are expected to drive to the office park. Looking at Equation 4.10 to explain this strong preference for auto, only two reasons can be found. One is the 7.5-minute difference in Total Travel Time. This difference probably includes walking to the bus stop and waiting for the bus both activities that many people dislike. The other factor might be in the first term of Equation 4.10, the mode-specific constant aon. In this example = 0.00, but aoauo = 0.73. Unlike the ¢ term in 20,bus Equation 4.10, which attempts to explain --

individual variations around the measurable utility Vm, the aom term reflects a general degree of preference for mode m that is not measured by the other a, ,, terms in Equation 4.10. The

,x;

flexibility and/or comfort of driving one's own vehicle may give the auto mode an advantage that cannot otherwise be measured in the utility function, except in the mode-specific constant dom. If the MCPC mode share model is correct, introducing fare-free service to the office park will not have a major impact on bus mode share.

—-H

~

=

THINK ABOUT IT Notice that both utilities computed in Example 4.11 had negative values. Does it make sense for something to have negative utility? If so, offer an explanation.

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4.4.2 Logit Model Attributes

When only two choices are involved, the structure of the logit model is easy to see. Consider two mode choices, A and B, A and B can be any modes, not necessarily auto and bus. According to Equation 4.11, mode A's share of the travelers will be

P4

VA

Mode B's share will be Pg

VB

or

eVA +e¥B The can be rewritten both the numerator and the denominator of its Pg=1- Pa. Ps equation by dividing right-hand side by

eVA +¢¥B

eA to get 1

yyAn

1+e%B-VA

(4.12)

Note in Equation 4.12 that, when Va = Va, Pa= 0.50. This means that, when the utilities of two alternatives are equal, their mode shares are equal. In the case of an individual, he/she is equally likely to choose Alternative A or Alternative B. Figure 4.15 shows the relationship between V4-Vs on the horizontel axis and Pa on the vertical axis. When Va-Vs= 0, Pa = 0.50. If Va becomes larger than Va, then Va-Vs > 0 and Pa will become larger than 0.50. If Va is smaller than Vp, then Va-Vs < 0 and Pa

will be less than 0.50.

THINK ABOUT IT In Example 4.11A, the two modal utilities were -1.58 and -4.31. The difference in utilities was +/-2.73. Find the solution to Example 4.11A on the Logit plot in Figure 4.15. If the two modal utilities in Example 4.11A had instead been -!1.58 and -14.31, what would the mode shares have been? Find this point in the logit plot in Figure 4.15.

What have you discovered?

V(A}V(B)

FIGURE 4.15

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Plot of logit function for the two-alternative case

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Example 4.12 Reviving Off-Peak Bus Ridership The Mythaca Bus Company (MBC) is experiencing financial difficulties. Ridership is falling as operating costs continue to increase. Other travel modes drive alone auto and ridesharing are increasing their mode shares. Three strategies for off-peak service are under active consideration by --

--

MEC: A. Increase fares from 75 cents to $1.00, in hopes of increasing revenues. B. Decrease service frequency from four times per hour to twice per hour, to reduce operating costs. C. Increase service to six times per hour, in hopes of attracting more ridership and more revenue. Which of these alternate strategies would help MBC's financial situation the most? Using data from the last mode choice survey done by the Mythaca County Planning Commission, MBC has developed the MNL mode choice model shown here: Um = a - (0.41*OPCm) + (0.24*FREQn) - (0.68*TTTn). In this model, FREQ, = frequency per hour of service with mode m, and OPC and TTT have the same definitions as in Example 4.11. MBC wants to try the model in a corridor that is served by atoll road whose toll for drive-alone (DA) motorists is $0.50. Vehicles that have at least two occupants (ridesharing vehicles, RS) pay no toll. Buses operate in the toll road's median on an exclusive busway and pay no toll. In the MCPC mode choice model, ao.pa = 1.56, A0,x3 = 0.96, FREQpa = 12, FREQns = 6, TTTpa = TT Tas = 25.3 minutes and TTTtus = 21.8 minutes. The current bus mode share of the 545 off-peak travelers through the corridor in a typical off-peak hour is 0.206 (20.6 percent), which translates into 112 bus passengers. Use the MCPC model to evaluate the three strategies with respect to fare revenue changes.

Solution to Example 4,12 The corridor has three competing travel modes: drive-alone (DA) auto, ridesharing (RS), and express bus. This means that the utility equation must be applied three times:

Vpa = 1.56 - (0.41*0.50) + (0.24*12) - (0.68*25.3) = -12.969 Vas = 0.96 - (0.41*0.00) + (0.24*6) - (0.68*25.3) = -14.804 Vins = 0.00 - (0.41*0.75)

eve

Se pee pe

Pom

+ (0.24*4) - (0.68*21.8) =-14.172

etn

SMT

70 * 1 md = 0.206

34.08 ]97

The fare revenue from 0.206"545 = 112 passengers is 112*$0.75 = $84.00.

A. If bus fares rise to $1.00, Vius = 0.00 - (0.41*1.00) + (0.24*4) - (0.68*21.8) = -14.274 and

tei

pete

esa _6.32%107 Qita | OM 33 Ae IQ”

0,190

Bus ridership would drop to 0.190*545 = 104, which would produce 104*$1,00 = $104 in fare revenue. Despite the ridership drop, the fare revenue increases $104 - $84 = $20.

B. Ifbus service is reduced from four times in the hour to twice, the bus utility function changes to Vous

Fricker

= 0.00 - (0.41*0.75) + (0.24*2) - (0.68*21.8) =-14.65 and

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_

_

eVbus

e

_ 4334*107 =0.138

14-65

eVDA + eYRS + Vous

912969, .-14804 | 14.65 3) 444977 Bus ridership would decrease to 0.138"545 = 75, which would produce 75*$0.75 = $56.25 in fare revenue, Because the ridership drop is not accompanied by a fare increase, total fare revenues in the corridor will decrease.

C.

If>bus service is increased to

six times per hour, the bus utility function becomes

Vins = 0.00 - (0.41*1.00) + (0.246) - (0.68*21.8) = -13.69 and

Pus =

_1.13*10% =0.295

eVbus

eVDA

+e'RS + ¢ bus

e7 12.969

+e

14.804 +e

15.69

3.844*10°6

Bus ridership would increase to 0.295*545=161 passengers. The resulting fare revenue would be 161*$0.75= $120.75. This is $36.75 more than the original fare revenues. These revenue changes must be compared with the changesin operating costs that are associated with each strategy.

~

Vai

THINK ABOUT IT The coefficient for service frequency in the utility function in Example 4.12 had a positive sign. Why is that?

Example 4.13 Modes Crossing Murdoch Bay In recent years, Murdoch Bay has become a popular place for wealthy people to spend their weekends. In recent years, some less familiar travel modes (viz., helicopter and hovercraft in Figure 4.16) have attracted a surprisingly large number of vacationers who want to reach the far side of Murdoch Bay from Shoridan in a novel manner. Local transportation planners have collected data about these services. The MNL model they developed for irips across Murdoch Bay from Shoridan is shown in the equation below. Vm = am - 0.009 Cost - 0.057

IVTT - 0.061 OVTT

|

(®)

FIGURE 4.16 Less familiar passenger modes. (a) Helicopter. Photo courtesy of Lynden Alaska Hovercratft

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b) Photo by Jon D. Fricker. (b) Hovercraft.

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The modal attributes that are expected to be effective next summer are summarized in Table 4.13. What Will be the mode shares P,, for each mode m next summer?

TABLE 4,13 m

Modal attribute data for Example 4.13 am

Cost (S$)

IVIT

OVIT (minutes) 33 34

1

helicopter

0

85.40

Gninutes) 5.35

2

hovercraft

0.40

88.16

15.7

mode

Note:

IVTT = in-vehicle travel time; OVTT = out-of-vehicle travel time

Solution to Example 4.13 Substituting the appropriate values into Equation 4.10, we get Voeticapter

= 0 — (0.009*85.40) — (0.057*5.35) — (0.061 *33) = 0 - 0.7686 - 0.3050 - 2.0130 = -3.0866

Voovernt,

= 0.40 — (0.009*88. — (0.057"15.7) — (0.061434) = 0.40 - 0.7934 - 0.8949 - 2.0740 = -3.3623 16)

Equation 4.11 allows us to convert these measurable utilities into the probability that each mode will be chosen:

e

—3.0866

elem Pratcopte: = g3866

° 3.3623 930866, 3.3623

P

Note that

Pheticopter

0.0457

+

Phovercratt

_—_0,0457

= aro 0.0803 —-35630,0457+0.0347

0.0347

0.0457+0.0347

= 0.5685

_ 0.0347 _ aais 4

0.0803

= 0.5685 + 0.4315 = 1.0000, because these were the only two choices

analyzed. In theory, the logit equation can be applied to three modes, or to as many modes for which reliable data are available with which to estimate the coefficients in the utility equation.

ange



Before moving on to another example, look again at the table of input values in Example 4.13. Both modal alternatives use the same coefficients in computing utilities, but the hovercraft’s am value was 0.40, while the helicopter's an value was 0.00. The am term is called the mode-specific constant. It is produced by the same statistical software that estimates the best values of the coefficients for the variables Xim. The am term accounts for modal attributes (as perceived by the traveler) that are difficult or impossible to measure, such as comfort, convenience, and feelings of security.

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—-— Example 4.14 Adding a Hot Air Balloon Mode Consider the introduction of a third travel mode for trips across Murdoch Bay from Shoridan. To illustrate the strengths of the multinomial logit model, let the new mode be one that may appear to be frivolous — a hot air balloon. This new mode is used here to demonstrate that the MNL model only "cares" about the attributes of a mode, not its name or technology. If the attributes for the helicopter and hovercraft modes in Example 4.13 do not change, what will be the mode shares for the three modes now available to travelers?

TABLE 4.14

ees:

FIGURE 4.17 Hot Air Balloons.

Photo by Gary Tomlin, ABQ Photography; Courtesy of Albuquerque International Balloon Fiesta®.

Attributes of third mode in Example 4.14

Cost ($)



3

L

.

mode

Ga

hot air balloon

1.1

70.59

IVTT

OVTT

(minutes)

(minutes)

38.0

42

Solution to Example 4.14

Applying the MNL model begins with using the utility equation in Example 4.13:

= balloon - 9.009 Cost - 0.057 IVIT - 0.061 OVTT Voutloon = 1.1 - 0.009 (70.59) - 0.057 (38.0) - 0.061 (42) ‘Viatloon

Voatloon

= 1.1

- 0.635 - 2.166 - 2.562 = -4.263.

= ™ Nothing about the helicopter and hovercraft attributes has changed, 50 Vhelicopter -3.0866 and Vhoverorait 3.3623, as in Example 4.13. In the denominator of Equation 4.11,

>, 0M)

=e

3.0866 5. 93-3623

«4.263. 9.0457 + 0.0347 + 0.0141 = 0.0944.

j=,3

Using Equation 4.11, the predicted mode shares are Pheticopter

=

oe

0.484, Phavercratt =

nie

= 0,367, and Ppaticon =

an =

0.149.

The sum of the three mode shares is 1.000, so the calculations seem to be correct. More importantly, the mode with the highest (least negative) utility value has the highest mode share, and so on. As usual, it is

wise to check the calculations for reasonableness.

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Vai

THINK ABOUT IT

"What percent of the non-hot-air-balloon travel market is captured by the helicopter mode in Example 4.14? How does this compare with the helicopter mode share in

Example 4.13?

If a fourth mode were to be considered for trips across Murdoch Bay from Shoridan, the attributes of the three previously-existing modes (and their utilities) would remain as before. The attributes and utility of the fourth mode would be calculated, and Equation 4.11 would again be used to “divvy up” the customers. This ability to leave the prior modes’ attributes and utilities unchanged is called the independence of irrelevant alternatives (ILA) property of the MNL model. It holds as long as the competing modes are truly independent of —i.e., distinct from — each other. For example, if one set of transit buses ran on diesel, and another set of buses ran on an alternative fuel, but each bus type had identical service attributes, it would be better to combine the two bus types into one mode.

4.4.3 Middleville Case Study

As in most small and medium-sized cities, the automobile mode in Middleville is dominant. However, some people must rely on modes other than auto, and the Mythaca Bus Company provides reasonable transit service in this community. It would be helpful to the MBC if it had a mode choice model with

which to test some proposed changes in fares and service.

—Example 4.15 Mode Choice in Middleville The MCPC planners have assembled a simple MNL model that relies primarily on travel time as its basis. The utility function for trips between any pair of zones i andj is Vm = am — (0.22 * tj), where auto = 0.9 and anit = 0.0. Average auto travel times between zones were displayed in the upper left quadrant of Table 4.12 in the section on Trip Distribution. Average transit travel times between zones are displayed in the upper left quadrant of Table 4.15. What percent of trips between each zone pair will use the transit mode, if the only alternate mode is automobile? Solution for Example 4,15

Using the MNL model is a two-step process: compute utilities for each mode using Equation 4.10, then compute mode shares using Equation 4.11. This two-step process must be carried out for each zone pair for this example. For trips between zones 1 and 2, the utilities are Vi,2,aut0

= 0.9 — (0.22 * t12,auto) = 0.9 — (0.22 * 11.0) = 0.9 — 2.42 =-1.520 and = 0.0 — (0.22 * t1,2,transit) = 0.0 — (0.22 * 22.8) = 0.0 — 5.016 = -5.016.

V1, 2,Aeansit

The auto utilities for all zone pairs are stored in the lower left quadrant of Table 4.15; the transit utilities for all zone pairs are stored in the upper right quadrant of Table 4.15.

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TABLE 4.15 transit t(j) |

2

1

Data and calculations for Example 4.15 4

3

transit V(m) |

| 228 | 150 | 18.2 22.8 | 82 | 134 | 149 81

1

2

4

auto V(m) |

2

4

3

4

3

-1.782 | -5.016 | -3.300 | -4.004

2

-5.016 | -1.804 | -2.948 | -3.278

3

3.300 | -2.948

4

4.004

ptr)

1

| 134

1

2

I

| 7.5 | 132 182 | 149 | 132 | 71 15.0

3

__1

|

-1.650 | -2.904

|-3.278 |

-2.904 | -1.562

2

4

3

I

0.372 | -1.520 | -0.904 | -0.552

I

0.104 | 0.029 | 0.083

2

-1.520 | 0.438 | -0.728

0.310

2

0.029 | 0.096 | 0.098 | 0.049

3

0.904 | -0.728

|

0.152 | -1.278

3

0.083 | 0.098 | 0.142 | 0.164

4

0.552

| -—0.310 |

-1.278 | 0.394

4

0.031 | 0.049 | 0.164 | 0.124

|

|-0.031

Note: In Table 4.15, row labels (1-4) indicate origin zones; column labels (1-4) indicate destination zones. For example, the average transit travel time from zone 2 to zone 4 is 14.9 minutes.

The probability that transit will be used to make a trip from zone 4.11 again:

Pros =

5-016

5016 |

91520

1

0.006631

=

to zone 2 is found by using Equation

—_-0,006631 =

0.006631+4+0.218712

This probability appears in the p(tr) portion (the lower right quadrant) calculations were completed using a spreadsheet.

0.225343

= 0.029

of Table 4.15. The remaining p(tr)

Transforming the Model Output. Before we proceed to the fourth, and final step, of the travel demand modeling process, two other tasks must be performed. The first task is to convert mode shares into person trips made using each mode in Middleville. This is accomplished by simply multiplying the p(tr) transit mode share matrix in Table 4.15 by the T(i,j) trip interchange matrix in Table 4.12. For example, the number of persons using transit from zone 3 to zone | can be computed as follows: (1) Find ps:(tr) = 0.083 in Table 4.15 and T(3,1) = 1831 trips in Table 4.12. (2) Calculate psi(tr) * T(31) = 0.083 * 1831 = 152 transit users. The person-trips by auto from zone 3 to zone 1 is calculated as follows: (1- psi(tr)) * T(31) = (1 - 0.083) * 1831 = 1679. These values appear in the (3,1) locations in Table 4.16. [Because Table 4.16 is taken from a spreadsheet, the hand-calculated answers (152 and 1679) do not exactly match the spreadsheet computations (153 and 1678).] Using a spreadsheet, this first task of computing persontrips can be finished quickly.

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TABLE 4.16 lauto person trips TG)

Calculating interzonal 2}

3

4

O|

255]

210]

226

0]

323]

292 525 622 |

1|

person-trips

by each mode in Middleville

transit]

1]

2|

4

3,

T(ij) 1

2! 3]

1678, 2911,

0}

4]

3833]

504]

1890/

13270

1]

oO;

8}

19

9

2;

7

«Oj

35]

27

3]

153]

316;

0}

122

4)

60]

197/

99)

oO]

7052

Note: In Table 4.16, row labels (1-4) indicate origin zones; column labels (1-4) indicate destination zones. For example, the number of auto person trips from zone 2 to zone 4 is 525.

The second task involves converting person-trips by auto into vehicle-trips by auto. This recognizes that each automobile can carry more than one person. If the average vehicle occupancy is estimated by MCPC to be 1.29 persons per vehicle, dividing each person-trip entry in the auto half of Table 4.16 will produce the auto vehicle-trip values in Table 4.17.

TABLE 4.17

Auto vehicle trips Ty between Middleville zones

Origin Zones i

~

Vi

-

j

Destination zones 1 2 3 0

198

163

175

1301

0 2257

250 0

1465

2972|

390

226 407 482 10287,

THINK ABOUT IT What is an efficient way to estimate average vehicle occupancy? Do you think the value might vary by time of day and/or by zone pair?

Now that the Middleville travel data have been converted into vehicle trips by travel mode, we can turn our attention to how travelers choose routes to reach their desired destinations.

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TRIP ASSIGNMENT

Five or six times each autumn, crowds in excess of 50,000 people attempt to travel to Mythaca State University's football stadium to see a college football game. Under their normal configuration, the streets of Mythaca do not have the capacity to accommodate all the traffic that heads for the stadium. The

University asks the Mythaca County Planning Commission to use its computer models to test some ideas its Athletic Department staff has about rerouting and controlling traffic. That is certainly a better way to test traffic control strategies than "trial and error".

4.5.1

it

FIGURE 4.18

Football stadium on game day. Photo

courtesy of Purdue University Marketing Communications

Trip Assignment Concepts

What route or path will be taken by each tripmaker? After three steps of the four-step method, we have established T;* the number of trips that go from zone i to zone j by mode m. What remains to be determined for each T;" is which set of links in the

transportation network will be used to reach zones j from zone i. The assumption on which most route choice models are based is that travelers wii! choose the origin-destination path that has the shortest travel time. (Common variations on travel time are distance, out-of-pocket cost, number of traffic signals, or a

combination of such factors.) The simplest route choice model is called the A/ or Nothing (AON) assignment model. It assigns ail trips from origin zone i to destination zone j to the links along the path

thet has the shortest travel time. The AON method is simple, but is not very realistic. Quite often, there are several different reasonable paths from zone i to zone j. This is true for transit trips in very large

cities with well-developed transit service and for automobile trips in cities of even modest size. Furthermore, even when one path is clearly the fastest while traffic volumes are very low (free-flow conditions), if an increase in traffic causes this path to become congested, other routes may become attractive as alternatives. Accounting for increases in travel time as traffic flow increases is known as capacity restrained trip assignment.

THINK ABOUT IT Pretend that, as you read this, you suddenly remember that you had promised to meet a friend at across town. (Fill in the blank with a specific store, theatre, restaurant, or other location across town from where you are now.) You need to drive to that location as soon as possible. Write down the streets you would use to reach that

destination. Would everyone else take the same route as you would?

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At low traffic flow rates, travel time increases slowly. However, as traffic flow approaches the capacity of the links on the paths being used, travel time increases quickly. The most common function to represent the travel time effects of congestion is written as

t=to

ES (Ye)

(4.13) |

where t= travel time on link, to = free flow link travel time, C = capacity of link, V = current flow rate on link, and a and b are parameters. The functional form in Equation 4.13 is known as the BPR or

FHWA volume delay function (VDF), because it was published in 1964 by the Bureau of Public Roads (BPR) — a government agency whose responsibilities were later taken over by the Federal Highway Administration (FHWA). The 1964 BPR report used the values a=0.15 and b=4.0, and many transportation planners still use these parameter values in their models. In recent years, however, modelers have begun referring to VDFs as linkperformance functions (LPFs) and have begun to use

different values for the parameters a and b. One iden is to fit Equation 4.13 to the speed-flow curves in the Highway Capacity Manual [Feng and Gion 1995, Singh 1995], but an even better idea would be to fit the LPF parameters to the data observed in the study area being modeled. [Fricker 1989, Fricker and Moffett 1993}

The FHWA LPF in Equation 4.13 should be applied to each link in a network. The capacity term

“C” in the FHWA LPF is normally defined in terms of the upper limit of level-of-service (LOS) “C” and is called the “practical capacity”. The link’s LOS “E” (or “absolute”) capacity is commonly taken from

tables that provide default values for link types by functional class, location within the urban area, spacing of traffic signals, etc., but it could also be determined for each link more precisely by using techniques in the HCM. Although one could also determine the link’s LOS “C” capacity using the HCM, it is usually

sufficient to simply multiply the link’s LOS

“E” capacity by 0.75 to estimate the LOS “C” capacity.

Equation 4.13 can be rewritten as

t

b

faite (VY) |

(4.14)

Using the traditional values a = 0.15 and b = 4.0, the resulting LPF looks like the curve in Figure 4.19 that has diamond-shaped markers, A few variations on the standard LPF are also shown in the figure. Note that the form of Equation 4,13 allows travel times to be computed for capacity values that are greater than those physically possible. This is actually a desirable feature, because a route choice model’s initial “guess” may put too much traffic on some links. As long as the LPF penalizes a link with a very large travel time for having had more traffic assigned to it than is actually possible, further iterations of the model will correct for this.

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Multiples of free-flow travel time

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-

0 15,

a

15,

ae —

be

ee

€.6

4.00

2.00

1

6.86

0

0.2

0.4

0.6

0.8

1

12

14

1.6

Volume/Capacity ratio

FIGURE 4,19 Link Performance Functions as Parameters a and b vary —-$-—



4

Example 4.16 Capacity and LOS in Traffic Assignment

An urban principal arterial has an absolute capacity of 1400 vehicles per lane per hour and a length of 1.0 mile.

A. What is the LOS “C” capacity of the principal arterial? B. Ifthe link’s free flow speed is 45 mph and the standard values of a and b are used in Equation 4.13, what is the link travel time for traffic flow rates V=0, V=500, V=1000, and V=1500? Plot these points and the curve through them.

C. Research [Feng and Gion 1995] has suggested that a=0.76 and b=5.1 be used for an urban arterial. Repeat Part B with these values. How do the two LPFs differ? Solutions for Example 4.16

A. LOS “C” capacity = 0.75 * LOS “E” capacity = 0.75

*

1400 = 1050 vphpl

B. The link’s free flow travel time to is 1.0 mile/45 mph * 3600 sec/hr = 80.0 seconds. A spreadsheet was used to apply Equation 4.13 and produce the table of link travel times below for each of the flow

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Chapter 4 Modeling Transportation Demand and Supply rates of interest, for both this part and Part C. The values are summarized in Table 4.18 and plotted in

Figure 4.20.

Multiples of free-flow travel time

178

TABLE 4.18 Link travel time (seconds) as values of LPF parameters a and b V= 1000 V = 1500 b v=0 a V¥ =500 0.15

4.0

80.00

80.62

89.87

129,98

0.76

5.1

80.00

81.38

127.41

454.89

ee

18

eee

3.00

Zim

0

0.2

04

06

0.8

1

12

14

18

Volum a/Capacity ratio

FIGURE 4.20 Two LPFs for Example 4.16 C. The suggested revisions to parameters a and b make little difference at low flow rates, but they produce significantly larger travel times as flow rates approach practical capacity, i.e.,

Yer 1.0.

Beyond that capacity, the travel times increase much more rapidly than for the standard FHWA LPF.

—-$

\

4



# |

,



THINK ABOUT IT Does the general shape of the LPFs in Figures 4.19 and 4.20 remind you of a curve you have seen in Chapter 2 of this text that is representing similar phenomema? Which curve is it? Explain the similarities and differences.

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4.5.2 User Equilibrium Having established the role of the LPF, one more important concept in route choice modeling can be introduced: user equilibrium. To keep the first example of user equilibrium simple, let us consider a corridor with just two reasonable paths, each with a linear LPF: ta = 8.8

+ 0.4 Va;

ta

= 7.0 + 0.8 Va

(4.15)

In Equations 4.15, the units of flow are thousands of vehicles per hour. According to a minimum-time Toute choice model, the first driver (when flow V=1 vph) will choose path B because its free-flow travel time is 7.0 minutes, compared to 8.8 minutes on path A. In fact, all subsequent drivers will choose path

B, until ts = 8.8, which is path A’s free flow travel time. To determine the number of such drivers, find Vs in the equation ts = 7.0 + 0.8 Vs = 8.8. The solution, Vp = 2.25, means that the first 2250 drivers will choose path B as the shorter time path, but the 2251" driver will find that path B is no longer the shortest time path. Any subsequent driver {according to the route choice model) will choose the path that has the shorter travel time for the flow levels that prevail at the time of the decision. In other words, once both paths are in use, the user equilibrium condition states that the travel time on both paths will remain essentially equal.

Example 4.17 User Equilibrium with Two Paths In the two-path corridor described above, 3800 vehicles per hour are making the trip. What will be the values of V, and Vs, if the two paths are found to be in equilibrium? What are the corresponding travel times ta and ty?

Solutions for Example 4,17 Use Va = 3.8 - Vp in the LPF for path A, then set that LPF equal to path B’s. 8.8 + 0.4(3.8-Vs)=7.0+0.8

ta=8.8 + 0.4 Va = 8.8 + 0.4(1.033) = 9.21 ta

= 2.767; Va=3.8- 2.767 = 1.033

Va; Va= minutes

= 7.0 + 0.8 Vp = 7.0 + 0.8(2.767) = 9.21 minutes

The path time calculations for t, and ty not only verify that the path flow calculations were done correctly, they also verify that the two paths in the corridor are in equilibrium.

The graphic representation of what was analyzed in Example 4.17 is shown in Figure 4.21. Route B has a lower free-flow travel time (when V=0) than does Route A, but after Vp = 2.25, the travel time on Route B becomes greater than Route A's free-flow travel time. Normally, when two lines cross in a plot, it has special meaning. In Figure 4.21, all it means is that both routes have the same travel time and the same flow rate. For equilibrium to be in effect, all used routes must have the same travel time. In most cases, the flows on the routes in use will not be the same. See the results for Example 4.17 to verify this statement.

A dashed horizontal line at = 9.21 has been added to Figure 4.21 to illustrate what user

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Travel time units

180

equilibrium means. According to the principle of user equilibrium, travelers choose routes so that no change of routes will improve their travel times. The result is the same travel time on each used route. A vertical line drawn down from each point where the t= 9.21 horizontal line crosses an LPF will intersect the horizontal axis at a flow rate for a route. The sum of the flow rates found this way must equal the total flow using the routes.

[met—--RioutsA

die

Route B=

=

8129.21

13.0 12.0 11.0 10.0

8.0

To 6.0 4

3

2

1

i)

5

6

Vehicle fiow rate (1000s vph)

FIGURE 4,21

Seeking Equilibrium Traffic Assignment for Two Routes

An important concept in user equilibrium is whether a particular route is being used. In Example 4.17 and Figure 4.21, it is clear that Route A will not be used until the travel time on Route B reaches at least 8.8 time units. Computing the flow on Route B at which this situation occurs is not very difficult.

To this point, we have examined traffic assignment using linear LPFs. Sometimes it is possible to use a spreadsheet to help solve a problem where the travel time function is non-linear such as in Equation 4.13. What can be done is to set the LPFs up and find the traffic flow on each route, such that the travel times on all used routes are equal.

—-}—

9

Example 4.18 North and South Routes are shown in Figure 4.23. The northern route has a shorter distance, but it has less capacity. The link performance functions that govern the north and south routes are

Two possible routes from an origin

ty

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to a destination

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Chapter 4 Modeling Transportation Demand and Supply 5000 cars leave the origin O at the speed limits indicated in the figure. How many of the 5000 vehicles use the north route and how many use the south route, such that travel times on the north and south routes

will be equal? O-D distance 12 mi

imi

Gpead iimit 45

5080 care

per hr

mpheclty 2400

Origin

speed

Deatination

imit

60 moh

3200 0-D diatence 20 mi capecity

FIGURE 4.23 Trip assignment equilibrium with non-linear LPFs Solution to Example 4.18

The table at the right is the spreadsheet set up to solve by trial and error the flow on each route such the total O-D flow equals 5000 vehicles and the two route travel times match. A convenient alternative is to use the Solver feature in the spreadsheet. Both solution methods show that Vs = 2680 vehicles will choose the longer distance (but faster speed) southern route and 2320 cars will take the northern route. . The equilibrium travel time for either route is 26.26 minutes

=

Trial Vs 2000 3000 2700 2650 2670 2680

ts 21.44958 31.00779 26.49999 25.92002 26.14681 26.26279

ty 53.10938 20.88683 25.82916 26.94502 26.48714 26.26402

++ fr L

4.5.3 Traffic Assignment in Current Practice

CC cee

The traffic assignment examples given so far in this lesson are, of course, greatly simplified. For one thing, travelers probably use criteria besides travel time in choosing their routes, Even if travel time is the principal criterion, different travelers may perceive the same travel time differently. Although tolls and other factors can be combined to replace travel time with a generalized cost value, many analysts are satisfied that travel time gives a result that meets their requirements. The other complication is that any link in a street network is likely to have traffic on it that is coming from many different origins and going to many different destinations. The examples in this section implied that all travelers in the corridor had the same origin and destination, or that the origin and destination did not matter. Fortunately, efficient algorithms have been incorporated in standard travel demand modeling software that can implement user equilibrium traffic assignment for an entire transportation network.

The results of the traffic assignment step are critical for two reasons. (1) The link flows in the results for the existing network are usually the best indication of how well the travel demand model has replicated existing travel patterns. Traffic counts on links are much easier to collect and are more reliable than the data collected for trip generation and trip distribution. If there are major discrepancies, the

Fricker

&

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182

Ch 4 Travel Demand Model

FUNDAMENTALS OF TRANSPORTATION ENGINEERING

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Edition, 6” Printiog

Chapie4 Modeling Transportation Demand and Supply modeler must look diroughoul the four-step process For mpud and modeling eros. (2) The flow pattern prodeced by the model's forecasts uimally Ford the basis for public investinend involving Target anrounts of public funds [Pihe fortesst shows future demand far exceeding presen capacity in some portion of ihe bamsporiaton system, a decid regeuding: mayor iicreases in Capacity Gr measures Lo reduce iavel must be made. The LOS valuss in Figure 4.) were based on a Four-step process that enuded

with tradiie assiprunterit.

Trafie aseigument alan serves aé the basis

for other important analyses, as Exatople 4.19 will

illustrate. oe

Example

ee

ee

ee

ee

ee

ee

Middleville VAT and VMT

4.19

Carrying aut 4 Full-scale trafie aséigioment on the Middleville mad network 16 beyond the aoope of hie text. Lf bradfic assigointent had been completed For the Middleville study area, trovel dine and speeds could be ashmated fic mads that connect the zone pars. Table 4.19 shows such intereonal speeds. State abd federal agencies require that the MCPC provide tatrmates of the acount of travel that fakes place in the Wiiddleville study area. Tro ways to meaeure the arent of bravel are vefiele-fours af fave! (VHT) and veiiclesmifes of rravel (VMT) Calculate the VAT and VMT totals for mterponal trips in the Middleville study area.

TABLE 4.19

intéecoonal aute speeds

Average

tring)

Ongin Doris

Solethoms for

Deatinabon zones 3

4

1

2

I

13

15

2

34

15

36

27

3

42

24

2

4

20

28

7 2

17]

19

Exaniple 4.19

In the absence of congested inierzonal travel irae from a compleied traffic assignment, Ist us use Hie free-flow travel Gate in Table 4.12 and the wehidle tripe by auto Table 4.17. For ate

VHT estimaice:

i

inps fom zone 3 to cone 4, the free-flow travel Gm) 189.9 tinutes. There were 482 aula trips Bor 20ne 4 to zone 4.

Therefore, the ¥HT far this zone pair is

VMT estimates: The VAT

+422 —220"" vehicles 60 min hour

=

80 veb



hrs.

(3,4) one pair uses the 22 inph average speed Found in Table 4.19. The ¥VMT estimate for (3,4) 1s 30 velnele-hours * 22 oilea‘hour = 1740 veticle-omles traveled The total internonal VRIT for the ehody ares is 30,738 vehicle-tules. The total VHT 1s 1217 vehoclehowe. Set Table 4.20 fora sucntnary of the VHT and YVMMIT caleulations.

Fricker& Whitford

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450

Chapter 4.5

Fundamentela of Trane portation Engineerdng - len O. Fricker and Robart

FUNDAMENTALS OF TRANSPORTATION ENGINEERING Chapier4+ Madeling Transportation Demand and Supply

a

=

2™

K Whiter

Edition, 6% Printing

THINK ABODT [T What is the avenge travel speed for all interzonal trips in the network?

TABLE 4.20 VAT and VMT caleulations Interzonal

VHT using

Interzonal

auld tea) I 1

0}

for Middleville zone pairs

VRIT amg auto bi)

and apeedldig)

2]

#

4

46)

23)

35

I

37 80

2}

32]

fy

Sl)

3)

ITB)

278)

oO}

1

2

3

4

0}

68S)

S78,

423

2)

id

a)

Illi)

107

3)

S690)

Geko

O}

1750

4)

3234)

7082)

1739

ol

30738

1217

ee

ee

eee

ee

es

ee

ee

ee

4.3.4 Beyond the Curreat Practice

Aaving ben intedeced bo

the siundard four-siep travel demand modeling process, the reader is aéked bo

comaider again the nation that 4 typical person (even subconsciously) takes travel decisions in euch a eequential manner Some mesearchers, bothered by thas dirastie simplifitaiion acd aoded by inproved

comiputabonal power, have locked

iba nea

approaches.

One innovation im tavel demand modeling stems from the recagmitien that tary Grips aut Teo from Point A to Point B and back to Point A. A person’s inpe during the course of a day tend is ectoply fotin tours. A comoron example the personal eoand, auch as stopping at a store on the way hen fom

i

work, This person's Home-Work-Shop-Hooe trip tour would be treated as three separade inps under the standard four-step meihodalogy. In theory, each trip in the chain would involve a fresh look al ihe teode chaise question, wheress in réadity, the mode used by the traveler on the nent top would be encmncuély dependent on the mode used in dhe previous fink in dhe tap tour. This approach bo the travel decision problem is called 4enwey-Bared Modeling [Kitamura 1988]. Alihough Activity-Based Models are being ined in some locabons, ihe four-step process wall be the standard for the fortsecable future. Applied vik ackequate dada, dhl, and judgment, it will continud to bet a reaconable basis for sound tank portation planning.

CHAPTER 4 SUMMARY The transportation demand modeling proces attempis to replicate the tapmaking deciioné made by individuals under ok¢envable corcumstances, in dhe hope that a fortcasing bool Gan be developed If certain inpuls periticung bo present bapodking can be coneerted inte dhe Gravel patterns that are taking: place today, perhaps those same relalionships can be weed Lo prédict how Folut condition: can affect the

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183

184

Ch 4 Travel Demand Models

FUNDAMENTALS OF TRANSPORTATION ENGINEERING

2™ Rdition,

6” Printing

Chapter 4 Modeling Transportation Demand and Supply

travel patterns of the future. The “future” can be very short-term, in the case of “What happens if that bridge is closed next week?” More often the future is on the distant horizon, as in “Where will congestion be the worst in twenty-five years if current growth continues and no transportation projects are undertaken?” Having reliable travel models gives decision-makers the ability to see — at least approximately — the consequences of major public investments. This ability helps them decide between competing projects. It also can illustrate the consequences of not taking certain action. Travel demand modeling is an important element of the transportation planning process, but it is not the only component. A broader view of transportation planning is presented in the next chapter.

ABBREVIATIONS AND NOTATION FOR CHAPTER 4 49m OF &n

im

A AADT

mode-specific constant in MNL utility equation coefficients in MNL utility function

Trip attractions annual average daily traffic

AON BPR

All or Nothing Trip Assignment

DOT

Department of Transportation The random variable in the total utility function that accounts for factors that may influence a tripmaker’s mode choice decision, but that are not easily measured or

g

Bureau of Public Roads

observed

empl

FHWA Fy

G/M

HBW

= employment jobs in zone Federal Highway Administration Friction Factor Function for Gravity Model Gravity Model

TIA

home-based-work trips households in zone Independence of Irrelevant Alternatives

ITE

Institute

HH

IVIT LOS LPF MBC MLE MNL MCPC M/S

o-D OPC

OVTT P

Pm

of Transportation Engineers

In-Vehicle Travel Time Level of Service link performance function Mythaca Bus Company Maximum Likelihood Estimation multinomial logit model

Mythaca County Planning Commission Modal Split or Mode Choice Origin-Destination out-of-pocket cost Out-of-Vehicle Travel Time

Trip productions Probability that mode m would be chosen; proportion of travelers who would choose mode m.

pop

population in zone

Fricker & Whitford

4.52

Chapter 4 End Materials

Li Fundamentals of Transportation Engineering - Volume

FUNDAMENTALS OF TRANSPORTATION ENGINEERING Chapter

T

4

1 ~

Jon D. Fricker and Robert K. Whitford

2™

Edition, 6" Printing

Modeling Transportation Demand and Supply

to

trip ends per specified time unit (weekday, site peak hour, etc.) at a particular land use free-flow travel time

TA

TAZ

Traffic Assignment or Trip Assignment Traffic Analysis Zone

T/D TIG

Trip Distribution Trip Generation

Ti

Intrazonal trips

Ty

Trip Interchanges 4

}

The number of trips that

go from zone

TMIP

Travel time from zone i to zone j Travel Model Improvement Program Total travel time

Un

total utility of mode m

VDF vebs

VHT

Volume-Delay Function vehicles owned by HHs in zone vehicle-hours of travel

Van

measurable utility of mode m

ty

TIT

VMT xX

X-E X-I Xi Xia

X-X

i

to zone j by mode m

vehicle-miles of travel independent variable in ITE Trip Generation equations External-Internal External-Internal a factor (usually demographic) that explains the level of tripmaking Measurable independent variables that help explain the likelihood that a traveler in category i would choose mode m. External-External

GLOSSARY FOR CHAPTER 4 e

e

e

e e

e

e

e

Base year: The year used as the starting point for travel demand forecasts; usually a recent year for which data are available, Capacity restrained traffic assignment: Accounting for increases in travel time as traffic flow increases Cross Classification: A trip generation method that organizes household trip rates in accordance with certain household characteristics Derived demand: The recognition that a trip is made because of the activities to be undertaken at the end of the trip. Free-flow travel time: The time that an average driver would take to traverse a link or path if no other

vehicles were present. Friction Factor: A means of converting travel times or other measures of separation between a trip's origin and possible destinations for use in the Gravity Model. Gravity Model: A Trip Distribution method that is based on the relative spatial separation of traffic analysis zones and the relative amount of activity in the destination zones. Horizon year: The specified year for which a forecast is made; usually 5, 10, or 20 years into the future.

Fricker & Whitford

4.53

Chapter 4 End Materials

185

186

Ch 4 Treaval Demand hiodal

FUNDAMENTALS OF TRANSPORTATION ENGINEERING Chapier4+ Modeling Transpoctation Demand and Supply «

Link performance function: A function that ont

®

©

« «

« ©

that

lnk varies.

eshimates how haved

2™

tito

Edition,

lik

on a

6 Printing

will vary

ad the

flow

Multinomial logit model: A mode choise model that wes the utility of competing tudes bo estimate the share of tripmakers thal cach mode will eam. Traffic Analysis Aone: A ptographic cubstt ofa atody area. Traffic Assignment A procedure by which taveler route choice in a sired or highway network siriulaled. to mcludé Transit Assiprionett iF ihe Trip Assignment: The genene form oF Traffic trang network offers more than one maecnable way to adh a destined. Trip Chsin bution: A procedure to desonbe and explam how travelers choose their destinations. Trip Generation: A procedurt to eshmate how many bps are ads bo and fom cerain locations, such 2s bouseholds, individual sites, orTAZs Trip Interchanges: The nuniber of tripe that jo Foon zone i bo zon| Trip Matia: A mathx that sucumarizes the number of tips thal 2o between sone i (represented by the row of the matrix} and zonej (represented by dhe J" row of the matnx). Trip Table: Another name fora Top Maina. User tquilibrinm: Travelers choose mutes 60 thatno cheng oF utes will chee ave times. function: The older tenn for Link Performance Function. Volume-delay

Assign,

1 «

ono

INDEX FOR CHAFTER 4 Aghvity-Based Wfodels, 50 altrachon, 18,22, 24, 2% Balancing Ps and As, 24 base year,

7,3

BPR LPF, 43

napacily resiramned trip

8] pcm, 42

Gravity Model, 25, 24, 77 honzon year, 3

independence of relevent altermaiives, 41 Inetitute of Transportation.

Engincers, 6 interzonal inips, 34)

taphive transl nders, 32 choice transit riders, 32 ortee-classi fication, 19, 22

Cross-Classification Model, 18

onisé-tlassi Gestion able, LE derived demand, 4 equilibrium, 4

FHWA LPF, 43

free-flow, 42, 44 friechon factor, 23, 25, 28, 31 Foeton Factor, 26

inp, 3) ITE Tnp Generation, intrazcial

12, 14

link perfomance Functions, 43

Link Perforroaice Functions, 4d Measurable utility, 32 mode-specific conslant, 34 Trultimomial logit needed, 3.2,

40

dul-oF pocket Goat, 33 petson

tips,

privtuction, 18,22, 24, 23 reoression model, 16 Tanner Function, 25 tours, 4h traffic analysis zone, 16 traffic analysis zoidé, 20 traffic aaaigrmenl, 47, 48,49 trip assignonenil, 42 trip distibuiron, 49 trip generation, 6, 16, 17, 22,

45

trip trip trip trip

interchange, 24 maina, 24

purposes, 16 table, 74 peer equclibriuin, 46, 47, 43 vehicle tape, 18 Holuone delay Function, 43

18

REFERENCES FOR CHAPTER 4 *

ACS (000.

Commuting in the United Safes: 2009. American Community Survey Reports,

15, i&uwed Sapicmber 2011. Baettievdd 7 Jartoary 2014

fron

ls.po

ACS-

prod 20D pubatees-

15.paf.

Fricker & Whitfird

44

Chapter 4 End Materials

Fundamantola of Traneportetion Engineering

FUNDAMENTALS OF TRANSPORTATION ENGINEERING Chapter4 Modeling Transpottation Detianid and Supply

-Jon 0. Fricker end

2™

Robert

Edition, 6" Printiog

+

Area Planning Commnnssion, Tippecance County, Indiana, Tronspertation Pian for 2025, Greater Fofoyette drea Transportation and Development Study, Mery 2K]

+

BPR (1963). Burtau of Public Roads, 0.5. Cepartent of Comunecot, Cofthrating & Testing a Size Urban Area, Gravity Model for day July. BPR (1964). Bureau of Public Roads, 0.5. Department of Commerce, Tragic Assignment Manual,

*

K Whittord

Jume. #

©

* *

®

*

#

#

Bhs goon publicadons an OS Bureau of Transportation Stabsties, Transportation Statetes Annual Report 2000, Chapter 4 - Motility and Access to Transportation, Table 1 - Mode of Travel to Work: 1959, bitpe a6 viewed 27 Gelober 2002. yew. bis. pow‘ ane

BTS 20K

pubhcabons A,

God (1995), “Traffic Assigament: BPR bo HCH (Part 2) — Devers Feng Li-Yang Application", Compendia of Papers, Fifth Nottone! Conference on Troneportation Planning Methods Application: — Fofume f, p 3-5 to 3-14, Apal. Transportabon Research Board. FHWA C1967) Geidelines for Trip Generation Anofysis, Federal Highway Adommsination, US DOT. 1973. Reprinted Apo] Fricker, Jon B. (19S). “Two Procedures to Calibraic Traffic Assigament Models", Proceedings, Second Conference on Liser’s Guide and Handbook

Inatitute

of Transporation Engineers, Washington, 00. *

Kilarnura, B. (1988). “An Evaluation of Acivity-Hastd Travel Analysis”, Transportation, Vial. 15, Nos. 1-2, p. 9-4.

#

NMCHREIOT (1976). Traskportarion Planningfor Sal! Urbon Areas, National Cooperalive Bighway Reatanch Program Repod 167, Transportation Research Board, p. F-4.

#

NCHRES65 (1998), Transportation Estimation Techniques for Urban Planning, National

#

Coopemtyve Highway Research Program Report 365, Transpartabon Research Board. Singh, Rupinder (1994), “Beyond the BPR Curve: Lipdating the Speed-Flow and Speed-Capacity

Relationships in Traffic Assignment”, Compendium of Papers, Fifth Nationa! Conference on Transportation Fiaaning Afethods

1198 pereon-

F. Multiple Regression

inpa per HH per day

4.3

Trip Distribotion

Gravity Model Caltubition wih mew 4b", Example 4.5 used the Friction (or Travel tine} Funchon in Equation 4.6, which wed b= -2.0. Repeat the Example, this time using b=-228. Your work rnuast be prtgenbed in the sace format wedi Table 4.9. Show 2 manual caleulation of Fi4).

4.130

4.14.00

Trip Lengthe and Firtetios Factors.

inp length in the nesulting: inp matrix te

Fricker& Whitford

Ef

the use

be too fnigh,

458

of Equation 4.6 with b = -2.0 causes the average

shold

the value of b be inertaned or decreased?

Chapter 4

Ete Materials

Fundamenta of

- Jon 0. Fricker and Robart

Trane portation Engineering

FUNDAMENTALS OF TRANSPORTATION ENGINEERING Chaplet Madeling Transportation Demand and Supply

2™

K Vhittord

Editon, 6° Brintiag

Trip Ddstribetios — Agia plant le Middleville. An automobile company 16 planning te build a

4.15.

1.8 million square foot Factory in Zone Fin Middlewille. In anticipation of the new factory, Middleville recedes funding from the state for an expresaway that mms between Zones | and 3. The new enpresaway reduces auto bravel time between Zones and 3 to 6.1 minutes. Use the Gravity Made] with Fy =

7,

|

Ge (riiirtes), to allocate the S804 tips produced in Zone are m SXpIeSsway operation Use A(=8T70, A s970, A(S F580, and AG t=

where

auto Gavel

3 after dhe Fectory and

2980 for this problem Ose the tabular format shown in Table 4.9. Starting values for antomotile travel Gomes in Middleville are given in Table 4.12. Note: Do not include T(3,3) in your calculations; assume T(3,

3).

Trip Téistribetion for MATS by ihe Gravity Model. Using acceptable Top Generation procddures, the cent Middleville Arta Transporiabon Study (MATS) has produced the horinon-year (hyt) prddiection aid attraction totals for tach zoned, 48 shoved in Tale A below. BATS has also determined thal Pj = LO "4. The h-year ty values aré given in Table &. (04 = infinity) Using dhe new Fy equation and the format of Table 4.9, calculate the predicted values of Tz, Tas, and Ta. Table A. MATS b-year Producto Talle B. hh-year Interzonal Travel 4.16.

Times (rrunutes)

aod

Zone P;

14

Ay

4.17.

fiat)

z 30) |

L

|

4

4

3

ih

I

2

3

4

1

a

1a

Is

13

2

13

=

13

1k

4

Ig

1a

e



4

3

16

cm

Ti

| 1000 1500

Gravity Model Caleulation with Taoner Fumction. Example 4.3 used the Fiction (or Travel Function in Equation 4.8, which wies b = -2.0. Repeat the Example, this ome using Equation 4.9

witha = A.

10,

b

=

2.00, and

¢

=

-.25.

(15 ponte) Show your seluion im the eames format at Table 4.9. Supeestioo: (1) Build a apreadshecet bo replicate Table 4.9. (2) Change the formulas in column 4 te apply Equation 4.9 (3) Copy and paste your néw spreadsheet into the materials you subrut. B. (3 pots) Show a hand calculation for F(2,4}.

Alterowihves

10

b=-2.0 in the Gravity Model The Gravity Model calculations in Table 4.9

“predicted” wher

the O01 shopping inps from Zone 2 would go iPb—2.0. However, the MCPS has dala thal indicate the actual tip interchange values for shoppite tips Bom Zone 2. acquired aurvey

These “laget values” are:

T2367, TER

Ti,

27, The MCRC wanis to adjusts Gravity Model to match the survey cate A. Build 4 spreadahect thal duplicates the structure shown in Table 4.9, atl add the T(27) eorvey lata as atitw column &. bnstead of “-2" in Equation 4.8, try diffensit valued of b until the values in Column 7 maich the values im Column &. (Note: In real lift, you would never be able to match aumvey dala exactly, but dhe is HW problem) What value of b allows you fo match the dere values? B. What dees thos recult say abou the tip length disiibution (TLD) of shopping tips from Zone 2 based on the sutwney data, as opposed to the anginal TLD iw Coluton T of Table 49? Explain how Changing b made the maich posable, making reference to Figure 4.10. a

Fricker& Whitford

459

Chapter 4 Eted Materials

121

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Ch 4 Travel Bamend hodel

FUNDAMENTALS OF TRANSPORTATION ENOINEERING Chapter4 Modeling Transportation Demand and Supply

2™

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4.4 Mode Choice 4.19.)

Mode



express bus Jane. Ad express bus lane

15

introduced on the tw

expreceway

betudten Zones 3 and |, make the boreal traeit travel tie only 7.) tinued, instead of 15.0 minutes. Estimate the tranait and auto mode shares betacen Zones 3 and 1 after the exprissway and saprece bus

Berrios are inopecabion. Ose the MNL model and ihe aute and bus utility functions that were used in Exarnple 4.15.

420. eq

Multinomlsl Logit Mode Choice Model A calibration effort resulted m the following utility

Lato

Dn = arm - 920285 3) - 0.032 3: - 0.015 Xy - 002 wher 7) = Agcess plus Boress Tite in momutes

2a = Waiting Time

i

XX,

minutes

= Line-Haul Time it minutes My = Ohl oF Pocket Coss in cente Mg

The trip diatibudron forecast for 4 particular interchange was a horinen year volume of Ty = 5000 person pet day. the honzon year, inp makers bebeeen zones andj woll have a chodoe betyeen modes A and B, with the following hon2on year att buts:

inps

1

Attribube: | XT Aiode A | 5

Bode B

ld

|

)

XP

PAS

|

a

20)

|

14

740

|

A

1th 450

calibrated mode-cpecrtic constants are ay= 0.12 and ap = 0.56, apply the Multinomal Logit model to estimate py and pa for the horizon year, then ootvertto the boil

A. Assuming thal the

nutiber of tops Ghat wall otcor between zones and) by each mode. 1

mode

= B. Did both modes need fo have a non-zero pec lic Gomstant? What ifa,.= 0.44 and ag O00? Would the results found in Part A of this problem change? Explain. Modal Split for Express Commuter Bus. The red cruiser bus line presenithy 3) eprece busts from a suburban community (capacily 45 passengers per bus) that 14 £0 percent loaded cunng the rush hour. Htadways ant 2 minutes, Le, average wart tone ig 1 rronute. The buses go to the CAD 10

421.

wher they digcharees the pasictnpers at a cingle bus tecminal, Thos means that an individual walks on the average of 4 minutes to his‘her destination. The buses operaie on a reverse Flow passenger portion of the expressucy (limited to buses) without tolls, which reduces the line-haul portion of their inp fom the auto inp time of AO minutes to 13 mom. The pick- op time, however, increases the in-vehicle time for tie bos oder an average of 7 runules, whertas the automobile bre to reach the enprecaway 16 4 Hotiutes. We bos rider has to walk mort than 3 minutes from home, The average tine from the expressway io parking for an auton dhe CAD invelves 4 min PYTT) The average walk from the parking: garage bo the place of work 1 3 minutes GYTT. The bus fare is $100 per trip. The auto 1 subjected to a $4.00 per day parking charges. Other out of pocket coats For auto ane $1.00 for gas and oil and $1.20 for bolls per aute tip. A survey has inchcated that die mdivddual chovee wolity 1s detercondd by Holes away,

IVTT,,-4"OVTT,,- 0.15*OPTC,,

Uy,

IVTT

GVTT

ALTO

MIN

MIN

BUS

MIN

MON

Mode

Fricker& Whitford

460

OPTC in §

Chapter 4 End Material

Fundamantela of Traneporhetion Engineering - Jen

FUNDAMENTALS OF TRANSPORTATION ENGINEERING Chapter4 Modeling Transportation Demand and Supply

2™

O:.

Fricker and Robert

K Alter

Edition, 6" Printing

Because it ié a mayor urban arta, he averige autocnobile has 18 persons riding. AL What ié the mode spit durmg the tosh hour?

B. Based

on ihe bos odership,

how many automobiles come

From. thie connnmnaniby?

MAL Mode Choice Madel for Teachers, A proup of teachers in the Wlythaca Selon! District hove agreed to stop comming by motor vehicle. Inciead, each of these teacher will choose each monn brbwecn wallonge and brtycling £0 school, depending on the weather. The utility functions for

422.

the

tye non-motorized modes for diese teachers art:

bn - ta We Uwe: = +7.9-05 tan Unwe

where W is weather.

a

weatherrelated

A. Wirtn the

weather

16

= 0-05

variable travel and ti6

aod, what

&

Gime

inies. Woe)in

in

good weather: We]

i bed

lie probability that a "noo-teotonzed” teacher with a choece

bebwten a 15-minute walk and a Goimnute bike ade wall choose the bicyole node? B. At what value ofthe weather coefficient ¢3 will the teacher in Part A be equally likely to choose

walk and Hieyole in bad weather? 4.23. Mode Chotce to Work. The Muliinommal Logit Choice Model deteromnes the trode shares. conultant 6 using the following ubility tnodel to prechet the tock: shares between Zonté 3 and 4: Via = Br - 0.05 TT - 0.25 coate, Bae is the mode-specific constant, TT. 1 travel tine, The tnodal altributes are:

where

Mode

Bs | TTe

Auto(Al)

[21

| lécmn

[12

[2lomim

[Carpaul*®

A. What ie he B.

anid

Coste 1 the iivel coal

per

A

perso.

Cotte,

| $2.50 | $0.80

Transit{T} [0.0 [30min | $0.75 *AsguTied an average of 3.2 persone per carpool mode ehart for autos, carpools and buses between Zones 3 and 47

effort te use parlone space more efficiently, the industries thal altract tips milo Zone4 propose a program that eicouniges carpe) aud trandt uit. Exmyployess who ener a cotipany lot

nat

with fewer than thre otcupauits will have to pay a packing fee of $3.00 per day per car. Canoes with three or mone occupants will be given fee parang. Those who oe transit will be alle bo ride the buses fret, because the companies will buy transit pacees Bor ther etoployess. Whal mew mode shares are predieted by the MAIL nadel?

4.4

Trip Askigoment Equilitwhom Tratflk Assignment. There are two travel pate if ie between towns A and 5.

424,

8

has a link performance fimchon t = 14+ 2), while Pah 2's LPF is t: = 3.7 + 0.3 20, where t= travel dime (minutes) aid x = flaw (1000s way. Ifthe total flow rae between A and B is 3184 vph, what

Path

1

art the équilibnuc flows and oravel times on Paths

425

Route Choice with

o pew

expressway.

|

and 27

A new expresiway has an LPF t{X) =

6.1

+ 3.5

Vit},

where YOR) is in 1000s of vehicles per hour ina given direction. The old arterial streets between Zones 3 = 82 + 17.0 ViA). aed J are still available, with a LPF of

A)

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Chapter 4 Modeling Transportation Demand and Supply

A. Ifall drivers from Zone 3 to Zone 1 want to minimize their individual travel times, at what flow rate V(X) will drivers begin to divert back to the arterial route? Take care to clearly state your units of flow. B. If T(3,1) = 2265 vph during the peak hour, find the equilibrium travel time from Zone 3 to Zone and calculate V(X) and V(A) for the peak hour.

1

Trip Assignment from Rural Area. There are two routes froma rural origin to the CBD destination. The most direct route A is 21 miles with an average free flow speed of 45 mph and a capacity of 2000 cars per hour. The alternate route B is 30 miles with an average free flow speed of 60 mph and a capacity of 4000 cars per hour. As traffic increases, the time to traverse the routes is given by 4.26.

the following functions:

t,

=tA a

—|__ _V

(-¥%)

and ty =

1

8

2

-(¥6)']

How would you anticipate that 3000 cars wo longer distance (but faster speed) southern route and 2320 cars will uld divide themselves between routes A and B?

Traffic Assignment Fundamentals. A. Do you think that route choices in your local urban area are made such that the user equilibrium

4.27.

condition exists in the area's road network? Support your answer by citing examples. B. Is free-flow speed defined as the fastest speed at which one can drive on a given highway? 4.28.

Link Performance Functions and Delay Estimates.

It is 9:40 PM as the Airport Shuttle van is

taking you on SB US281 to your downtown San Antonio hotel. Up ahead, you see a flashing blue light. It turns out to be a police car blocking the left lane of three lanes, because of a collision. You are alert enough to * determine the current vehicle density # convert the density to a vehicle flow rate V (2700 vph)} ® remember the standard LPF for a one-mile segment of freeway with a design speed of 70 mph:

tyeg

= 51.4

Vv

14(Z)

$4

seconds al

where C = 1800 vph per lane times the number of lanes.

Using the data and the LPF above, how much delay can be expected if SB US281 is restricted from three lanes to two lanes for one mile? Show your calculations to 0.1 second.

Highway link flows. Three inbound lanes of an urban interstate (I-28) have a LOS “E” capacity of 1800 vehicles per hour per lane. It has been determined that the following link travel time equation (using the LOS “C” definition of capacity) describes the congestion effects along a particular 1-mile segment of I-28:

4.29.

4

t=t,

r+0ss() | Cc

A. During the morning peak hour, it takes traffic an average of 1.75*t, minutes to travel that 1-mile segment of 1-28. What is the peak-hour volume (vph/lane) on this segment? Fricker & Whitford

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B, Assume that the current 3-lane volume on this segment is 4800 vph and that t. = 1 minute. If one of the three lanes were to be converted to a High-Occupancy Vehicle (HOV) lane and 25 percent of the current vehicles would be eligible to use it, what would be the travel time in the HOV lane over the one-mile segment? What would be the travel time in the two remaining lanes? 4.30.

Trip Assignment with Five Routes. One of the big events in Mythaca County each year is the

Murdock Bay Regatta, which takes place in and around Shoridan. Immediately after the last Regatta event, however, thousands of vehicles leave Shoridan and head inland to (and through) Mythaca. There are five possible routes from Shoridan to Mythaca. The link performance functions for these five routes are: = t1=18+4.5 x1; 12=21 + 7.0 x2; t3 =264+4.9 x95 te =29 + 3.4 x4; ts 34+ 0.3 xs t in where is minutes and x is in 10° vph. A. It is expected that 8300 vehicles will be making the Shoridan-Mythaca trip in the maximum-flow hour after the Regatta. Will all five routes be used? B. A Mythace County planner has tried to convert the expected total flow and the LPFs above into route flows. His solution includes x:= 3.50; x2.= 2.82; xs = 1.58. Do these values seem correct to you?

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PLANNING AND EVALUATION FOR DECISION-MAKING

nOL

5

SCENARIO In the Scenario for Chapter 4, the Mythaca County Planning Commission (MCPC) staff was asked to study the perceived congestion on SR361 as that highway runs through the City of Mythaca. As the MCPC staff collected data and began to apply the four-step travel demand model to the SR361 corridor, several citizen groups were proposing solutions to the congestion.

A. Developers advocate the relocation of SR361 to an alignment that bypasses the city entirely. This alternative would involve the construction of a bridge across the river, acquisition of prime farmland as right-of-way west of the

city, and modifications to the roads at the north end of the new bridge.

B. Downtown merchants urge the State DOT to expand 2-lane SR361 to four lanes in the city. This alternative would require that some homes, trees, and commercial property along the urban sepments

of SR361

be taken and

demolished. C. Environmental interests want increased

FIGURE 5.1 SR361 passes through a residential neighborhood. Photo: Jon D. Fricker

transit service offered along the existing SR361 — in the form of elevated monorail from South Mythaca, through downtown, and across the river to the university campus. Some taking of land would be necessary, but far less than for Alternatives A and B.

D. Taxpayer watchdog groups and neighborhood preservationists favor the “do nothing” approach. These people say that increasing road capacity only encourages more driving, and investment in expensive transit technology is never justified. It is almost certain that other projects will be proposed. Eventually, someone will have to decide which course of action to take,

CHAPTER OBJECTIVES By the end of this chapter, the student will be able to ... Explain how the transportation planning process is used to help make public investment decisions. Use economic analysis to determine if a proposed project’s benefits justify its costs. 3. Use economic analysis to select the best alternative to meet a specified objective. 4. Rank alternatives using multiple criteria, including non-economic factors. 1.

2.

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INTRODUCTION The travel demand modeling and forecasting procedures covered in Chapter 4 are not done in a vacuum. As the Scenario for this chapter indicates, there is more involved in transportation planning than applying a travel demand model, and computing VHT and VMT values. Each of the four alternatives in the Scenario — even the “do nothing” alternative — will affect different people in different ways. Each alternative will confer benefits on some groups and cause some groups to bear costs. Some of these benefits and costs will be measurable or quantifiable; some will be impossible to assess in economic terms. Ideally, the choice of alternative should be based on an objective and rational assessment of each alternative. This chapter describes processes and techniques that can be used to develop a recommended course of action.

~ vi

«»

THINK ABOUTIT For each altemative in the Scenario, name at least one benefit and one cost that results. Identify the groups that will receive the benefit and bear the cost.

5.1

THE TRANSPORTATION PLANNING PROCESS

Transportation planning is a continuous process, as the cyclic nature of Figure 5.2 indicates.

\

Goals

|

mo

Monitoring

FProtiem & Operation

cient An Ww

FIGURE 5.2

OT ipl)

a

Good Long-Range Planning Practice. (FH WA/FTA undated)

If the process is not based on

list of 2a community vision, the result may be nothing more than a The vision that drives a include phrases like “a disjointed projects. community’s transportation plan may balanced multimodal transportation system”, “reliable mobility choices”, and “efficient state and nationwide connections for people and freight.” (DRCOG 2009) A good example of a goal statement is “Provide safe, environmentally sensitive, and efficient mobility choices for people and goods; and integrate with and support the social, economic, and physical land use development of the region and

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state.” (DRCOG 2009) The four alternatives in the Chapter’s Scenario should be evaluated in the context of the community’s vision and goals. Goals are general statements. Objectives offer ways to measure implementation of the transportation plan using measures of effectiveness (MOEs) or performance measures. Examples of objectives and their MOEs are (SMATS 2007): 1.

Relieve traffic congestion and minimize travel times. MOE = Reduced congestion on major corridors.

2.

Provide for safer travel by all transportation modes. MOE = Reduction in fatalities and serious crashes.

3.

Maximize access to the transportation system by underserved and disadvantaged persons. MOE

= Increased availability of transit service to target populations. 4.

Encourage measures to reduce vehicle emissions. MOE = Changes in air quality measures.

5.

Improve intermodal connectivity for freight. MOE = time and cost involved in freight movement.

6.

7.

Encourage land development patterns that promote transportation efficiency. MOE = change in trip lengths and use of walking, bicycling, and transit. Incorporate new technologies as appropriate to maximize the use system. MOE = changes in travel time and travel costs.

of the existing transportation

The congestion in the Chapter Scenario is an example of Problem Identification. Four alternatives (including “do nothing”) are described. Methods for the Analysis and Evaluation of alternatives are demonstrated in this chapter. They rely upon the results of models such as the travel demand models described in Chapter 4. Once the preferred alternative for each proposed project in a community has been chosen by local decision-makers and gotten approval by state and federal officials, the projects are ranked. The projects that do not exceed the expected funding are added to a multi-year list called the Transportation Improvement Program (TIP). This is the Plan Approval phase of the transportation planning process. Program Development is one name for the scheduling of the projects in the TIP, so that adequate funds are available during each year of the TIP. Initiative Development and Operation is the place where the operational elements of a completed project are implemented. For example, what is the best way to provide service if the transit alternative in the Chapter Scenario is chosen. Continuous monitoring (measurement) of the transportation system’s performance and condition is important to other elements of the overall transportation planning process, especially Problem Identification. The community vision is subject to periodic or continuous review, and updating the vision need not wait for the completion of the cycle. The process is continuous.

5.1.1

A typical framework

The transportation planning process needs a context or a framework. The process can react to transportation problems as they arise. Preferably, the process can anticipate problems, prevent them, or implement a long-range vision for the future of the community. In reality, some of each — react,

anticipate, prevent, implement — is part of the planning process. In most situations, a variety of actions are possible. Choosing what is best for a community may depend on the viewpoints of those making those choices. The decision process must also take into account considerations such as land use policy and economic development objectives.

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§.1,2 Involving the Stakeholders The transportation planning process is ultimately a public process. To be successful, it must involve a variety of stakeholders, each of whom has his/her own interests. A stakeholder is a person, a group of persons, a company or an organization that has a stake in the decisions being made. Transportation investment decisions, such as building a new road, improving port facilities, or.extending an airport runway, can have a widespread and varied effect. These impacts can be positive to some groups, but harmful to others. A person who owns (or works in) a convenience store that relies on pass-by traffic to stay in business may be irreparably harmed by a project that diverts that traffic to another route. The store’s neighbors may be glad to see the traffic go elsewhere, but they may also regret the loss of the store and its jobs. A person handling baggage at an airport may welcome the job security from the increased air traffic that a runway extension will make possible, but the airport’s neighbors will object to the noise associated with larger aircraft and their more frequent takeoffs and landings. An effective early planning strategy is to identify (and notify) all possible “stakeholders”. Including stakeholders in the planning and development of the project is not only a requirement in most cases, it usually leads to a better result. Even where community consensus cannot be reached, a sufficient level of consent to a particular solution means that a satisfactory outcome has been obtained.

i-—





+ ——-

Example 5.1 List at least six stakeholders who need to be involved in the planning process for the SR361 project described in this chapter’s Scenario. What might their concerns be? Solution to Example 5.1 Table 5.1 contains a list of potential stakeholders and the issues that might concern each. Some stakeholders may participate simply as observers. Other stakeholders may not accept an invitation to be involved. If the consent of any stakeholders is likely to be critical, these stakeholders should be required to participate, rather than risk having them assert their opposition at the end of the process.

TABLE 5.1

Stakeholders for Example 5.1

Local Community — Public Agencies Mayor’s office/City Council County Council and boards Taxation agencies (federal, state, city) Visitor information bureau

Overall Project Overall Project

--

--

Effect on community Effect on community, Taxation

Funding plan, bond issues, tax implications, taxation plan Project information and timeline, public information program

Utilities

Routing and temporary power/water

Emergency Services Coordinator

Fire/ambulance/police routes during construction Traffic control during construction and requirements for

Local police

future enforcement

City Engineer, design engineer,

All aspects of physical design

consultants

Transit agencies Regulatory agencies (environmental, sconomic, zoning)

Airport officials

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Effects on bus system, changes in bus routes Establish and manage control systems Changes in access to the airport

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Local Community — Citizen Groups Chamber of Commerce

Effect on business in the community, valuation of land, attraction of new industry

Environmentalist groups

Local neighborhood groups Employees and local union(s) Community Improvement Sports stadium convention facility

Land use, impact on wetlands, noise How project will affect their neighborhoods Employment practices How project affects the group’s mission Potential impact on events

operators

Local Businesses and Individuals Affected Business owners along existing SR361

Access to their businesses during construction, loss of customers afterwards

Construction companies

Banks and developers Materials suppliers Drivers who use SR361 daily Truckers using SR361 Real estate investor

Construction design, bidding process Financing, land acquisition, zoning/land use Specifications and availability of construction products Duration of construction; alternate routes; project benefits Duration of construction; alternate routing; project benefits Changes in property values; commercial investment demands

Persons who live or own land along the

ROWs

Impacts on property values and quality of life during project implementation and after completion.

THINK ABOUT IT Which of the stakeholders on the above list are likely to be the most powerful and influential? Which of the stakeholders on the above list are likely to have the “Jeast clout”, and therefore need some assistance in getting their concerns heard?

As was demonstrated in this chapter’s Scenario, ideas for projects can be advanced by any individual or group. The alternatives are formalized by transportation professionals for analysis. In cases where complex network-wide impacts are being assessed, the transportation planning staff will conduct a computer-based study of proposed alternatives and report the results to a technical committee. This

of representatives of the various jurisdictions in the area — city, county, law enforcement, public transit, airport, and citizens. The comments and recommendations of the technical committee are sent to the planning commission, which is usually made up of elected officials and citizens. committee typically consists

5.2

BRIEF REVIEW OF ENGINEERING ECONOMICS

This section covers only those aspects of Engineering Economics that the transportation engineer needs to rate and rank specific projects that are being planned or evaluated. For coverage of related topics, such as depreciation, taxes, and inflation, the reader is encouraged to consult one of the many textbooks on the subject of engineering economics.

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5.2.1

What isEngineering Economics?

Engineering economics is a particular way of looking at the economic (or financial) side of engineering decisions, Engineering economics can be applied in both the private and the public sectors of the economy. An economic analysis determines a proposed project’s benefits and the costs that must be expended to achieve those benefits over the life of the project. A life-cycle analysis is often done for several possible alternative public projects, to determine which one has the most worth (value).

5.2.2 Time-Oriented Value of Money Project costs that will occur five years from now are worth less in terms of today’s dollar. The rate at which the value of a dollar amount diminishes with time is called the discount rate. (Note: We are not talking about inflation when comparing projects, but rather the cost of money. Inflation rates can be factored in later, if necessary.) Conversely, the discount rate can be used in a cash flow analysis to

of future cash flows. In evaluating a project, it is usually helpful to draw a cash flow diagram that shows the “stream” of costs and benefits. In Figure 5.3, each upward arrow By indicates a benefit in (or at the end of) Year k and each downward arrow C;, indicates a cost in (or at the end of) Year k. The project is shown to have an expected life of N years. determine the present value

Siitltl ry I,

| i,

om

|

FIGURE 5.3

Stream

of Costs and Benefits for an N-year Project

Using a discount rate d, the present value (PV) of a stream of costs Co, Ci, Ca, Cs, ....Cy is Cy + C; + + Cc, =Cy + C, +

f

PV,Cone

(ld)

8"

(+a?

(14a)?

Likewise, thePV of the Benefits is PV,Benefits =

+

i+d (14d)

Ba

+e

NPW

=-Cy

+

21-91

I+d

(5.2)

(1+4)"

The Net Present Worth (NP'W) of a project is PV ienetts

—P'Vcosu, OF

, B24 (+d)

(5.1)

(1+d)"

Ba

Sn

(1+d)"

(5.3)

Any problem can be solved using the simple relationships in Equations 5.1 to 5.3. Spreadsheets are ideal to use when the annual values are not all equal. Special relationships also exist when the values of C., C2,

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Cs,.... Cyare identical or increase or decrease in either a geometric or an arithmetic manner. Figure 5.4 shows the terms and equations used for the most common cash flow problems in engineering economics. Factor and formula

Type

Cash Flow Diagram

Relation



F=P* [FIP,dn]

Single | [FIP,d,n] =(1+d}"

__t

Amount

[PF,dn]=



P=F*pRda] | ,

(1+4)"

Pada] _ (+d)-1

‘ |

_ [PIAdn] P=A*

i

=

[AP,dnj =

20+a)"

=

(1+d)"-1

.

Uniform

Series

[F|A.d,n]

Al 3 [A|F,d,n]

=

A=P* [APA]

(l+d)" -1

_

d

(edo

A=F

PGdal- _ (i+d)"-dn-1

= *[AIF,d,n]

P=

¢

Geometric

[AIG 4,0) dn]

n

1

Gsd"-1

d

el 8

PuAuden]=|—S*2/_|

'

[PelAvdg.n) =

|

\" '

poet...

igen

2

eo

si en] [Pel PIA

maton

| Py

(5) ifg-d FIGURE 5.4

Fricker & Whitford

{

AOeow'

I

Gradient

A

G* [PIG,d,n]

= . A=G*[A|G,dn]

——-

4

4a

-LLLL

Arithmetic Gradient

|

‘|

F=A*[FA,dn]

~——*— d

| |

Cash Flow Relationships

5.7

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r

where Cy is

Decision-Making

When C1=C,=C;=C,=C:, Equation 5.1 simplifies to PV com = Co + Cy n

the constant (or uniform) cost for each year k. The sum of the series

> kal

>

5

k=l ( (1+

!

(1+ d)

; is often denoted as

= [P|A,d,n], a factor that converts the uniform annual (or periodic) A values (here, A C,) into the present worth of the uniform series. P

PVoosts

=

Cy *[P Asd.n] |

=C,

*

(ird)

-1

(5.4)

d(1+d}

As before, d is the discount rate and n the number of years. The notation “P|A” stands for the Present Value, given the uniform Annual Amount. The factor “A|P” means the uniform Annual Amount, given the Present Worth. It is the reciprocal of “P|A”. When the annual benefits are uniform throughout the project and the annual costs are also uniform, then the Net Present Worth becomes

NPW = -Cy + (B-C)*|[P/A,d,n] 5.2.3

(5.5)

Discount Rate

When dealing with life cycle costs, the discount rate reflects the time value of money. How does a 20year Project A, which has a low initial investment (e.g., $2000) and costs $700 per year to operate, compare to Project B, whose initial investment is $5000 but costs $450 per year to operate? For Project A with d=5%, Equation 5.4 produces the present value of the annual costs: PV costs = $700*[P| A, 0.05, 20] = $700

(1+0.05)° -1

| 0.05(1+0.05)" ls

$700*[12.4622] = $8724

Adding that value to the initial investment of $2000 leads to the $10,724 entry in Table 5.2.

TABLE 5.2 Project

A B

Investment 2000 5000

Comparison of two projects with various discount rates Present Value of Costs

Annual Cost

d=0%

d=5%

10%

700 400

16,000

10,724 10,610

7,960 8,830

14,000

In Table 5.2, Project A has a higher PVcoss value than does Project B until the discount rate is increased. At a 5% discount rate, the projects have almost the same Present Value. At 10%, Project A becomes better. A higher discount rate gives less weight to benefits and costs in the more distant future. As a result, Project A’s extra $300 per year in operating costs will not offset its lower purchase price, if the discount rate is high enough. Varying the length of the analysis can also affect the outcome. In Table 5.3, the PVcoss values for Projects A and B using a 5% discount rate were computed for project lifetimes of 10, 20, and 30 years. As might be expected, the higher annual value of Project A begins to dominate when the project lasts

longer.

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TABLE 5.3

Net Present Value for different project lifetimes with d = 5% Present Value

A

Investment 2000

Annual Cost

B

5000

400

Project

Edition, 6" Printing

N=10

700

years

7,405 8,090

of Costs

N=20 years

N=30 years

10,724 10,610

12,760 11,150

In a comparative economic analysis, all values must be discounted with the same discount rate. Applying another discount factor may alter the selection, depending on the makeup of the costs and benefits. Repeating the analysis with other reasonable values of the discount rate is a good way to determine how sensitive the results are to the choice of discount rate. This is one example of sensitivity

analysis. =

Example 5.2 Choosing Technologies

A proposed project can be accomplished using either of two possible technologies.

Version “A” is

accomplished by investing $8 million. The annual operations and maintenance (O&M) costs are estimated to be $860,000, until the project reaches its lifetime of 20 years with no salvage value. Version “B” involves investing in a much higher quality system at $14 million and sustaining much lower O&M costs of $100,000 per year. Version B will have a residual (salvage) value of $3 million at the end of twenty years. If the discount rate used is 10%, which Version should be chosen? Note: Salvage value is not treated as an added benefit, but rather as a reduced cost in cash flow analysis.

Solution to Example 5.2

The present value of costs for Version “A” is

PVA, = $8,000,000 +]

$860,000

1+d)*-

(+d) 1 d(1+d")

= $8,000,000 +| $860,000 *

1.1)? -1

oy 0.1(1.179)

= $8,000,000 + ($860,000*8.51) = $15,320,000. The present value of costs for Version “B” is PV.ost

=

000 +

($100,000 *[P

|

A,0.10,20)— ($3,000,000 [P| F,0.10,20]).

PVia1 = $14,000,000 + ($100,000 * 8.51) — ($3,000, 000*[1.10-7°}) = $14,457,000. Version B has the lower present value of costs, but other factors may enter into the choice of technologies. Because public sector budgets are usually so limited, and because the public sector is influenced by the time to the next election, choosing Version A with its lower initial cost may be preferred by elected officials, given that lifetime costs for the two alternatives are so close.

5.2.4

Nominal and Effective Discount Rates

In the previous sections, the discount rate was given as if the rate were applied only at the end of each year. Often, discount rates are applied at more frequent intervals, such as quarterly, monthly, or even daily. Consider these two definitions [Newnan 1980]:

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Decision-Making

©

Anominal discount rate is the annual discount rate without considering the effect of any

©

The effective discount rate is the annual discount rate, taking into account the effect of

compounding.

compounding during the year.

If a bank or lending institution states an annual percentage rate, this usually means the nominal interest rate, but the customer should check. —



Example 5.3 Bonds earning interest Potential investors have the option of buying bonds promising interest at nominal rates from 5 percent to 20 percent, which reflects characteristics of the bonds, such as risk and tax liability. How much (in — percent) will a bond at each rate earn, depending on the frequency at which the interest is compounded quarterly, monthly, or daily?

Solution to Example 5.3 Use a variation of the [F|P,d,n] = (1+d)" formula in Figure 5.4, in which d is replaced by d/n andn is the number of interest periods per year. For quarterly compounding at 5 percent nominal interest, n =4 and d/n = 0.05/4 = 0.0125. For monthly compounding at 5 percent nominal interest, n =12 and d/n = 0.05/12. For daily compounding at 5 percent nominal interest, =365 and d/n = 0.05/365. The revised formulas n

are: a

[FIP,d,n]

= [FIP,.dn]

= [FIP,d,n]

=

n (1 +S)

(

+

a

4

=(1 0125)*= 1.0509, which is an effective rate of 5.09 percent

12

n

n (1+2) -(1+235)

=

(1.004167)!2= 1.0512, which is an effective rate of 5.12 percent

365

n

= =(1 000137)" 1.0513, which is an effective rate of 5.13 percent (1 Results of similar calculations of effective interest rates for nominal interest rates of 10, 15, and 20 percent are shown in the table below.

( +S)

=

+

208 |

Effective Rate

Nominal !

|

|

Rate 5% 10%

Quarterly Monthly 5.09% 5.12% 10.38% 10.47%

15%

15.87%

20%

21.55%

Daily 5.13% 10.52%

16.08%

16.18%

21.94%

22.13%

Example 5.4 Return to Table 5.2 Recalculate the present value of the annual operating costs for Projects A and B for use in Table 5.2, if the specified discount rates are nominal and compounding is done monthly, instead of annually.

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Solution to Example 5.4

= [P|A,d,n] formula in Figure 5.4, but use A $700/yr = * = $58.33/month, d= 0.05/12, and n= 12 months/yr 20 years 240 months to compute the present value if the $700 annual costs: For Project A at

20 PV coun = 12

5 percent nominal rate, use the

‘lp

2% 12

= $58,334| 240|

0.004167)" (1+ oui67) 1 __ = ,0041

240

$58.33*[151.53]

= $8839,

0.004167(1+0.004167)

This is slightly larger than the $8724 calculated just above Table 5.2. The present value of the $400 annual costs for Project B in Table 5.2 was $10,610 - $5000 = $5610. With a 5 percent discount rate compounded monthly, the present value becomes:

PVcos =

0.05

(1+-0.004167)

=———*| P| A,———,240

12 450.

12

J-soror| 0.004167(1+

240

= $37.50*[151.53] = $5682.

-1

163

The PV of all costs for Project A is now $2000 + $8839 = $10,839. The PV of all costs for Project B is now $5000 + $5682 = $10,682.

Projects with Gradients Often, a cost or a benefit is not uniform, but changes with time in a predictable manner, Constant Arithmetic Growth or Decline. Figure 5.5 shows the case in which costs change each year by a constant value G. There are several ways in which the present value with constant gradient G can be computed:

PVC =Cy

C,;

C,+G C,+2G

C,+(n-1)G ,

+ +d + (l+d)* + (+d)

(l+d)"

where

C=C;

= C2

=...=C,

or PVC =Cy +(C*[P}A,d,n])+(G*[P|G,d,N]) 0

1

2

8

&

C+20

C+

&

|

C+48

C+fhi-18

FIGURE 5.5

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Cash Flow Diapram for Uniform Arithmetic Gradient

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Chapter 5 Planning and Evaluation for Decision-Making

Example 5.5 The Mythaca County Highwey Engineer wants to buy a new software package to track and analyze pavement maintenance costs. The software has a price tag of $5000. Other county engineers who have been using the same software like it, but they warn their Mythaca colleague to set aside an additional $600 the first year for technical support. This extra cost drops to about $400 the second year, $200 the third year, and nothing after that. What is the present value of the cost of the software, including technical support? Use a discount rate of 5.2 percent.

Solution to Example 5.5 the technical support stayed at $600 per year for three years, the present value of that uniform series would be (using Equation 5.4)

Hf

3

PV costs

“CFA

sn)

=o

(1.052)

=1

0.052(1.052)

1643

=

cone] 0.052 "1.1643

$600*[2.7131]

= $1627.84

However, the cost decreases $200 each year over the second and third year. Using the Po|G equation for = an arithmetic gradient in Figure 5.4 with d = 0.052, 3, and G -$200,

n=

n

a

*

—(d*n)-1 _

[PG] = +d) *(1+d)" d°

and Pg =

*

[PgiG] = -200

(1

3

1.1643-0.1560-1 _ 0.008253 -(0.052 * 3)—1 ~_ =2.6214 * 0.002704*1.1643 0.003148 (0.052)? (1.052)? 1.052)"

2.6214= -$524.28.

*

Combining the uniform component and the negative = gradient component, the present value of the 3-year technical support costs is P $1627.84 + (-$524.28) = $1103.56. Add that to the “Year zero” purchase price of the software, and the total present value of the G

software cost is $5000 + $1103.56 = $6103.56.

Constant annual percentage growth. When the growthis a geometric gradient g, and the discount rate is d, the following cash flow relationship occurs. 2

NPV=

If

C;

-

C2

l+d

+c

—C3—... —C,—C, then the [P|A,d,g,n]

of Section 5.3 will use this relationship.

5.2.5

n-1

0t8 ... +c, ate) 148.0, (1+d) (i+d)" (1+d)

equation in Figure 5.4 applies.

An example at

the end

Equivalent Uniform Annual Costs

Frequently, the choice among alternatives is made on the basis of the lowest Equivalent Uniform Annual Cost (EUAC). The EUAC is the initial cost (investment), minus discounted salvege, if any, multiplied by the [AJP] Factor. For the two projects in Example 5.2, [A|P] is calculated as follows: + $860, 000 = $1,800,000 per year

EUAC, and

$14,000,000

EUACs=

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[scone +$100,000 = $1,693,000 per year

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The EUAC method allows the comparison of alternative projects that have different expected lifetimes. The primary assumption is that each alternative project being evaluated will be replaced at the end of its useful life with another project just like it. If that assumption can be made, the project with the smallest EUAC value has the lowest cost.

Example 5.6 In Example 5,5, if the County can spread the cost of the software over three years at a discount rate of 5.2 percent, what amount should the County set aside each of the three years to pay for the software and

technical support?

Solution to Example 5.6 There are two reasonable ways to find the Equivalent Uniform Annual Cost (EUAC) of the software. One way is to compute $5000*[A|P] + $600 + (-§200*[A|G]), which is $5000*[0.3686] +$600 -$200*[0.9662] = $1842.93 + $600 - $193.24 = $2249.68. Because we have already calculated the present value of all the software costs in Example 5.5, why not simply convert that value into its uniform annual equivalent?

_ 0.0605 = = d(i+d)" _ 0.0529(1.052)? = AIP, d=0.052, Al n= 3 yrs] vr (i+d)"-1 (1.052)7-1 0.1643 A=P

5.3

*

[A[P] = $6103.86

*

0.3686

0.3686 = $2249.80.

ECONOMIC EVALUATION OF TRANSPORTATION ALTERNATIVES

5.3.1

Introduction

The responsible engineer is obligated to search for the best solution(s) to specified transportation problems. The solution must explicitly meet the system specifications, demands or needs for the system. (See Chapter 1.) Sometimes this is not an easy task. Many times, it is possible to make a recommendation regarding competing transportation systems or options based purely on cost or net benefits (benefits minus cost), using the principles of engineering economics. Each candidate project should be evaluated over its entire expected life. This brings the time-value of money into the problem.

There are three types of projects that could be considered. 1. Aproject needs to be done. Which alternative has the lowest “life-cycle” cost? 2. Several alternatives that have equal quantified benefits. Which alternative has the lowest cost? 3. The candidate alternatives have different quantifiable benefits and costs. How can the benefits and costs be compared in some rational way? Because of the large number of public concerns in transportation (e.g., safety, pollution, equity), the project to be evaluated is frequently a project where the major funding comes from government. In these types

of projects, the benefits usually accrue to the users of the system, although sometimes the

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Chapter 5 Planning and Evaluation for Decision-Making operator also benefits. The costs, on the other hand, will usually be costs paid from public funds, such as taxes, an existing trust fund, or 2 bond issue. In most cases, taxpayers fund these systems, whether they

use them or not. (One exception for automobiles is a toll road.)

Example 5.7 Bridge Repainting The State DOT wants to repaint some highway bridges that pass over I-46. To do this, they must close one or more lanes of traffic, causing delays during peak periods of travel. The DOT has two choices:

A. Do the bridge repainting only during normal daylight work hours. This requires that the job site be set up and torn down each day. The normal bridge repainting job done this way takes three days. B. Work continuously on the bridge repainting job until it is finished. Working into the night means that the job can be completed within 24 hours, but local work rules require that nighttime labor be paid at

arate 1.5 times the standard daytime rate. What are the advantages and disadvantages of each option, and who is affected?

Solution to Example 5.7 Under Option A, at least three days of peak period traffic must endure the delays resulting from one or more lanes being closed. Under Option B, two cycles of setup and teardown are eliminated, but nighttime work is not as productive or safe as working with daylight. Option B will probably be much more expensive to the State DOT than Option A, but who will receive the benefits from those increased costs? The drivers on I-46 who will experience much less delay! If the DOT routinely adopts the more expensive Option B, it will be able to paint fewer bridges with its annual paint budget. Option B is an example of one party paying more, so that another party can realize the benefits. In some cases, it may be the best thing to do!

—-+ 5.3.2



—- ——-

— —

4

— —

Evaluation Process Using Engineering Economics

As illustrated in the previous section, engineering economics includes the time value ofmoney. The decision to spend money eliminates the possibility of investing it instead. Therefore, the value of money is discounted over time. (Figure 5.4 shows a summary of the most common cash flow relationships.) This is not "inflation", which is measure of the rise in prices over time. The time value of money accounts for the effects of using money over time, rather than investing it in a bank or in an activity that promises a teturn of the investment. Projects are then judged on the basis of some economic criterion, a

such as their net present worth or their net benefits, including all the costs and benefits that exist. The evaluation process begins by establishing specifications for the system(s) being evaluated, defining each particular alternative, and then performing an alternative preliminary design on each. (Note: One alternative is frequently the "do nothing" alternative.) With the design options in mind, costs

of the alternative approaches to design can be estimated. Options frequently evaluated are: e The approximate or exact location of a new road e

The number of new lanes to be added

«

The technologies to use

*

Additional safety features that may be required

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Operating strategies to be employed

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Traffic control methods to adopt

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The comparison of alternatives is always based on a comparison of measures ofeffectiveness (MOEs). In this section, we are concerned with those comparisons for which cost is the only MOE. The MOESs are based on the choice of criteria to be used to distinguish alternatives. These criteria are discussed in the next section. 5.3.3.

Criteria for Comparing Alternatives

The criteria most often used in the evaluation of transportation projects are (1) net present worth, (2) benefit-cost ratio, and (3) equivalent uniform annual cost. It is often helpful to apply more than one of the criteria before making the project selection. e

Select the project that has the highest net present worth (NPW). Determine and compare the net present value or net present worth or net present benefits. This is calculated by determining the benefits accrued over the life cycle of the project and subtracting the investment plus the annual costs, less any anticipated salvage value over the life of the project. The life-cycle costs are usually discounted using a rate d. es

NPW =-Cy-

-

C,

> z+ k=l + d)

B,

z+

s

e

(5.6)

-

(1+d) (1 +d) where C, = amount of cost in time period k, B, = amount of benefit in time period k, d k=l (1

rate, and S = salvage value. Select the project that has the highest bene/fit/cost ratio

=

discount

(BCR). The benefit/cost ratio is calculated by determining the benefits over the life cycle of the project and dividing by the costs (investment plus annual costs, less any anticipated salvage) determined over the life of the

project. The life-cycle costs are usually discounted by a discount rate of d. Assuming the annual benefits and costs do not vary from year to year, the benefit/cost ratio is shown in Equation 5.7.

Benefit Cost

_

where P = present value;

B*[P|A,d,n]

Cy+(C*[P|A,d,n] —(S*[P|F,d,n]) A = annual value ; F = future value;

(5.7)

[PiA, d, n] is the Present Worth Factor, given the uniform annual amount A over n years at an annual discount rate d. (See Figure 5.4.) [P|F, d, n] is the Present Worth Factor, at an annual discount rate d, of an amount F that occurs n years into the future. (See Figure 5.4.) e

Select the project with the lowest equivalent uniform annual cost (EUAC) or highest equivalent uniform annual benefit (EUAB). In this method, the present values are transformed into the equivalent uniform annual cost or benefit. In the case of costs,

EUAC = PV cent * [AIP,d,n] =

PVeost

(5.8)

[P| A,d,n]

This method is especially helpful when comparing projects that have different lifetimes. It also helps with projects whose costs are made up of several distinct pieces.

Total BUAC = EUAC, + EUAC, + EUACs+

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EUAC,

(5.9) Chapter 5.3

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Chapter 5 Planning and Evaluation for Decision-Making

Example 5.8 Projects with Different Lifetimes Compare projects X, percent.

Y, and Z, each with a different lifetime, using discount rates of Annual Cost

Annual Benefit

nei ($10)

Life Ors) 20 30

100

30

700

Y

$3.0 $5.0

200

100

1,000

Z

$10.0

15

300

2,000

1,500

Project

x

soon,

10008)

5

percent and 10

EVAB-EUAC “atd=5% std=10%

0008)

$360,000 $476,000 $329,000

$348,000 $270,000 -$52,000

Solution to Example 5.8

The best way to handle the discrepancy between natural project lifetimes is to convert benefits to equivalent uniform annual benefits (EUAB) and costs to equivalent uniform annual cost (EUAC). In the equations that follow, the annual benefit is the first term and the annual cost is the last term. In the numerator of the middle term, the present value of the salvage value is subtracted from initial investment cost, the result of which is the present worth of the net cost. The denominator of the middle term is the equation for [P|A,d,n]. As seen in Equation 5.8, dividing by [P|A,d,n] is equivalent to multiplying by [AJP,d,n]. This means that the middle term represents the uniform annual equivalent of the present value found in the numerator. .

Project Xsu

EAB-RUAC =700,000-

3,000, 000 —-20-000. 20 1.05)"

(1.05)? -1 *

100,000

(1.05)

= 700,000 — (240,000 + 100,000) = $360,000 Project Ys%

5000, 000

- 100.000

05 290, 000 ata -BUAC=1,000,000- —____.05—__ -1 1.05°°

|

0.05% (1.05)°

= 1,000,000 — (324,000 +200,000) = $476,000 Project Zex,

10,000,000 2,000,000

EBUAB-EUAC=1,500,000-—-.05""__ ‘ 300,, 000 (1.05)"5

-1

0.05*(1.05)!°

= 1,500,00 — (871,000 + 300,000) = $329,000 When the discount rate is increased to 10%, the answers are: = — Project Xiox EUAB EUAC $248,000 = — Project Yiox EUAB EUAC $270,000 = — Project Zio, EUAB EUAC -$52,000

The results are shown in the shaded area of the table above. Project

Y

is the best at both discount rates.



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Example 5.9 Transit AVL

An automated vehicle location (AVL) system for transit has an initial cost of $1 million, with annual costs of $100,000 and no salvage value at the end of a 15-year lifetime. If the benefits are $260,000 per year and the discount rate is 7 percent, determine Ratio. (C) Is the AVL project worth pursuing?

(A) the Net Present Worth and (B) the Benefit-to-Cost

Solution to Example 5.9

A. Bring the value of the annual benefits and costs back to their equivalent present values. Net Present Worth = Bamua*[P|A,0.07,15] - Co - Cynnun[P|A,0.07,15] 1§

[P|

A,0.07,15]=

(1.07)"=1 =9.1 0.07(1.07)'5

NPW= Benefits - Costs = ($260,000*9.1) - $1,000,000 — ($100,000*9.1) = $456,000 B. The Benefit/Cost ratio is also based on the present worth of benefits and costs. $260,000*9.1 PW(Benefits) _ = 1.24 ° PW(Costs) — $1,000,000+($100,000* 9. 1) C. For the project to be worthy of further consideration, the necessary conditions ate NPW > 0 and B/C ratio > 1.0. The closer to zero the NPW is, and the closer to one the B/C ratio is, the more likely the decision will be based on other criteria, if no other projects are competing for available funds. Based on its NPW and BCR values calculated above, the AVL project is worthwhile for implementation, or it can continue to be considered in comparison to any other proposed projects.

4+

Example 5.10 Railroad section

A section of railroad is made up of the elements listed in the table below.

Because the elements do not have the same expected lives, but can be expected to be renewed or replaced indefinitely, Equivalent Uniform Annual Cost is the method to use to combine the cost components on a common basis. Determine the EUAC for each element when a 10 percent discount rate is used.

Element

Investment

Land Grading Railbed Track Signals Total

500,000 65,000 180,000

200,000 40,000

Salvage Value

|PjA,i0%n]

EUAC

1,200 0

100

500,000

50

20%

12,000

30

20

40% 5%

9.999 9.915 9.427

10

0

51,200 6,544 30,656 23,317 11,510 123,227

Annual Cost

5,000

Life(yrs)

8.514 6.145

Solution to Example 5.10

The Land element of the railroad section has three components, each of which needs to be converted to its Equivalent Uniform Annual Cost, (1) Use [A|P,0.10,100) =

aa

100 1

= 0,1000007 to convert the |

Initial Investment of $500,000 to its 100 annual amounts: Call the first Land component Al. Al = = = $500,000*0. 1000007 $50,003. 63. (2,3) The Annual Cost, A2 $1200, is already on an annual basis,

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FUNDAMENTALS OF TRANSPORTATION ENGINEERING 50 move on to the Salvage

1

Value A3, which can be “annualized” by using [A|F,0.10,100] =

= 0.000007. A3 = $500,000*0.000007 = $3.63. EUAC for Land = Al +A2 - A3 = |

$50,003. 63 + $1200 - $3.63 = $51,200. Note that A3 is subtracted from the EUAC sum, because Salvage Value is deducted from the other costs. If you don’t like to work with numbers like 0.1000007, instead of .

$500, 000

$500,000*[A|P,0.10,100], J, you can use [Al

Te TA,0.10,100]

meme

$500,000

=

| a.10)%—1

=

|

$500,000 = >

[9.999274]

0.10(1.10)'™ $50,003.63. In the shaded column of the table above (and in the solutions below), [P/A,0.10,n] is used. [P|A,0.10,n]

=

1

, 80 either factor can be used.

[A|P,0.10,n]

For the Grading element, the EUAC cost components are

Al _

_

___—*$65,000_—_— $65,000

$65,000

[P| A,0.10,50]

(.10)-1 |

[|

[9.915]

_ $6,556; A2=0;

0.10(1.10)

|

_

= 0.20*$65,000

==

[F|A,0.10,50] |

$13,500

(1.10) -1

= $13,500

_ $11.60.

[1163.91]

0.10

EUAC for Grading = Al + A2 - A3 = $6556 + $0 - $11.60 = $6544. For the Railbed and other elements, the computations are similar: EUAC

gaithed

*

=

2,000

rear" 0.10(1.10)°

EUACtract =

$200,000 10)

_

gq

=

i000-1 (1.10)

= $180,000 9:40" _ $19 094 + $12,000 $438 $30,656. (1.10)°° -1 0.10 |

* 000 _ - 9.057200,

55

492

+ $0 - $174.60 = $23,317.

10) 0.10

0.10(1.10)7° EVACsignas



+-$5000-$0=

$6510 + $5000 - $0 = $11,510.

0.10(1.10)'° The EUAC values eppear in the rightmost column of the table above. The EUAC method allows project elements with different lifetimes to be compared on a common basis.

—-b-—

« Vi “ ,

THINK ABOUT IT The standard way to treat Salvage Value in a Cash Flow Analysis as reduced cost, not as increased benefit. Does this rule make a difference in comparing alternatives when using NPW? When using BCR? When using EUAC?

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5.3.4 Projects with Multiple Quantifiable Benefits The same methods of benefit-cost comparison that were applied in the previous sections are applicable to problems where there are benefits from different sources (e.g., fuel use and safety) that are quantifiable in monetary terms. The benefits need to be determined separately and then combined as shown in Example 5.11.

Example 5.11 Road Widening

A $3.5 million road widening project over a ten-mile stretch of highway is proposed.

The project will not induce any increase in the 3-hour peak period traffic volume (currently 5000 vehicles). Use 250 as the number of days in a year having peak period traffic. The average peak period speed of the existing traffic

will increase from 35 mph to 45 mph. Fuel use will improve from an average of 23 mpg to 24.5 mpg.

The average annual cost to maintain the highway segment is $123,000. If time is worth $12 per hour and gasoline costs $3.25 per gallon, determine the project’s net present worth and benefit/cost ratio with a design life of 20 years and a discount rate of 8 percent. Solution to Example 5.11 Calculate [P|A, 0.08, 20] =

(1.08)? -1 0.08(1.08)

= 9,82. The NPW of the project's life cycle cost is then

20

|

NPWicc = $3,500,000 + $123,000*[P{A,0.08,20] = $4,707,860 The NPW of each component of the benefits is calculated as follows. e Time saved per day. 10 mi/35 mph

=



10 mi/45 mph = 0.286 hr — 0.222 hr = 0.0635 hr saved per vehicle per day.

Annual value of time saved. 5000 veh/day * 250 commuting days per yr * 0.0635 hr/veh * $12 per hr. = $952,500 per yr Energy cost reduction. Gallons saved per day. 10 mile/23 mpg — 10 mi/24.5 mpg = 0.4348 gal - 0.4082 gal = 0.0266 gal per veh Annual value of gallons ‘saved (250 days of commuting) = 5000 veh * 250 days * 0.0266 gal/veh *$3.25/gal

= $108,141

per

yr

The annual benefit beginning in Year

1

= Time savings + Energy savings = $952,500 + $108,141=

$1,060,641 (assumes no “inflation”.

To find the discounted present value of uniform annual benefits of 20 years, again use [P|A, 0.08, 20] = 9.82: $1,060,641 * 9.82 = $10,415,495

-

The Net Present Worth of the project is NPW(benefits) NPW(costs) = $10,415,495— $4,707,860= $5,707,635.

The benefit/cost ratio is NPW(benefits) NPW(cost)

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$4,707,860

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Chapter 5 Planning and Evaluation for Decision-Making

Example 5.12 Traffic grows on the widened road. Assume that the traffic grows at the rate of 2 percent per year on the roadway widened in Example 5.11. Recalculate the new net present worth and benefit/cost ratio for the project.

Solution to Example 5.12 Because traffic grows at g = 2% per year, the annual benefit will grow according to the Geometric Gradient in Figure 5.4. The discount rate in Example 5.11 was d= 0.08. Because g + i, use the first [PalA] equation in Figure 5.4. [Ps|A,0.08,20]

=

1.02" _(itey" 1.087 | 11.353; Aid) i= |_| 0080.02_|_ 11959

$2,060,642 Pa= $1,060,641

py

*[11.353]

=

*[11.353]

=

$12,041,457 $12,041,457.

This is larger than the $10,415,495 found in Example 5.11 under the assumption of no traffic growth. The Net Present Worth of the project becomes $12,041,457— $4,707,860= $7,333,597 and the benefit/cost ratio becomes $12,041,457/$4,707,860

5.4

= 2.56.

a

RANKING TRANSPORTATION ALTERNATIVES

5.4.1 Introduction

C

Some citizens of Mythaca County have questioned how the County Highway Engineer has been spending the county’s limited road maintenance budget. The citizens group claims that more roads are in bad shape than ever before, and its members suspect that the engineer makes his maintenance decisions on a political basis. The engineer points out that he has only $365,000 per year with which to maintain more than 1000 miles of county roads. He admits that he does not use a formal system to decide which roads should be patched or resurfaced in any given year. Instead, he uses his judgment. After meeting with the a

¢

citizens group, the engineer agrees to ask for advice from the state’s Local Technical Assistance Program (LTAP) at Mythaca State University. The LTAP offers technical assistance to local public agencies (cities, towns, and counties) in the state on matters related to transportation.

Have you ever had to make an important decision, but the choice between two or more options was not an easy one? The County Engineer remembers looking for an apartment many years ago, as he was about to begin graduate school in a city new to him. After visiting several apartments, he had narrowed down his choices to

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FIGURE 5.8 Gravel County Road. Photo: Jon D. Fricker

Chapter 5.4

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FUNDAMENTALS OF TRANSPORTATION ENGINEERING Chapter 5 Planning and Evaluation for Decision-Making

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two — one in the Bloomfield neighborhood, the other in East Liberty. Having been trained to think systematically, the engineering student made a list of the attributes favoring each apartment.

THINK ABOUT IT

*.

Y

“What attributes are you likely to consider in choosing a place to live?

Once you have

made your initial list, try to rank your attributes from most important to least important.

When the engineer-to-be saw his lists of attributes, arranged in two columns, guess what he saw? He saw two columns of almost exactly the same length. In this case, if the choice was so difficult, that the engineering student felt compelled to make a structured list, the result of having made such a list was likely to be inconclusive. Well, the future county engineer made a decision, and it was a decision with which he turned out to be very satisfied. As he looked back over this experience, what surprised the engineering student was that the attributes that made his choice so satisfying were not even on his original list! In the apartment choice example, the engineering student had identified only two alternatives as worthy of further, detailed evaluation: the apartments in Bloomfield and East Liberty. To keep the situation simple, let us say that only two attributes mattered to the student: rent and distance to campus. These factors have the advantage of being easily quantified, e.g., using units of dollars per month and miles (or kilometers) to campus. The quantities used to assess factors are often called measures of

effectiveness (MOE). If the two factors are not equally important to the student, he might choose to apply weights to their values. Normally, weights are assigned such that their sum equals 100 percent or 1.00. In the apartment case, rent might be given a weight of 60% or 0.60, and distance a weight of 40% or 0.40.

These values are summarized in Table 5.4.

TABLE 5.4

Apartment choice problem Measure of Effectiveness

Factor

Weight

Bloomfield

East Liberty

Rent per month Distance to campus

0.60 0.40

$270 2.1 miles

$180 3.9 miles

THINK ABOUT IT If rent and distance to campus really were the only factors that matter, which apartment in Table 5.4 would you have chosen? Why? How much higher would the rent have to have been for the apartment you chose before you would choose the other

apartment? Suppose one apartment appealed to you more than the other, how might you measure and weight appeal?

The apartment choice case described a personal decision. It was likely to have significant impacts only on the landlord, the renter, and perhaps the renter’s neighbors. In the public sector, the situation is likely to be much different. As custodians of public budgets, public officials are entrusted

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with making decisions regarding programs or projects that could affect thousands of people. Because of this, public officials need to make decisions that are consistent and defensible. They need a system.

5.4.2

Multi-Criteria Decision Making

Because there may be numerous criteria or system attributes that are important in comparing one system alternative to another, a process called Multi-Criteria Decision Making (MCDM) is used.

Performance Measures or Measures of Effectiveness Performance measures must be developed to determine how well the alternative projects perform in relation to the objectives. Some factors, like air pollutants, energy use, and noise, can be measured directly. Such direct measurements can be used in lieu of dollar amounts to determine the factor’s impact. There may also be hard-to-quantify factors like aesthetics, public opinion, and equity. Ways to

include these factors in a rational ranking process must be established. Even if MOEs are quantifiable, of1 to 5 or 1 to 10. For their values will probably need to be transformed. MOEs can be rated on a scale example, if the cost MOE for one alternative is better (i.e., costs less) than the other alternative, then the better alternative might receive an MOE rating of 5, with the higher-cost alternative receiving a rating of 3 or 4. Care must be taken to be consistent in assigning ratings to the MOEs. Higher mobility and economic development MOE values should receive Aigher ratings; higher costs and higher pollution MOE values should receive ower ratings.

MOE Weights The weight given to each measure of effectiveness is usually subjective, but it should be defensible. Sometimes it is inherent in the reason for the project. For example, “We need to improve access to the new sports stadium.” If limited funding makes cost very important, travel time important, and safety and pollution less important, then the weights could be 40% on investment cost, 30% on travel time and 15% on each of the other two. The sum of the weights will always be 100%. In some cases, the selection of weights should be endorsed by the stakeholders. It may also help to vary the weights and determine whether (and how) the rankings change.

—-§-— Example 5.13 Congestion and pollution from a six-lane freeway

A six-lane freeway corridor connects a major residential area with the industrial/commercial section of a city. It has become extremely congested and is harming air quality in the 12-mile corridor. Four projects have been proposed as solutions:

e

Build a fourth lane in each direction for motor vehicle traffic. light rail transit (LRT) line in the median of the existing freeway. Convert the existing third lane in each direction into a lane for high-occupancy vehicles (HOVs)

e

Adda busway without altering the present freeway.

«

e

Put ina only.

The criteria and weights for evaluating the effectiveness of each proposed project have been established in public meetings. They are given in the Table 5.5. Table 5.6 shows the ratings for each alternative project and MOE. Show how to combine this information into a multi-criteria ranking.

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TABLE 5.5 MOE

Measures

6" Printing

Weighting the MOEs

of Effectiveness

How Measured

Weight

A

Reduction in Congestion

Improved travel time

20

B.

Reduction of Air Pollution

Reduced Ozone and Particulates

35

Access

Ease of using the system

D.

Investment Cost

Dollars

20

E.

Operational Cost

Maintenance and Labor

10

F,

Community Economic

Land Use and Attractiveness to

10

Development

Investors

C.

~—s

TABLE 5.6 MOE

5

Rating the alternatives relative to their MOE performance (5 = best)

Measures of Effectiveness

Add Lane

LRT

HOV

_—

Busway

A

Reduction in congestion

3

5

B

Reduction of Air Pollution

2

5

3

3

Cc

Access

5

2

1

4

D

Investment Cost

1

3

5

4

E

Operational Cost

4

2

4

3

F

Community Economic development

1

4

1

2

3

Solution to Example 5.13

Apply the weights to the various performance ratings. Reduction of Air Pollution (MOE B) by LRT is computed as 35*5 = 175. Access (MOE C) by HOV is computed as 5*1 = 5. The weighted results are then summed and compared. In Table 5.7, the light rail transit alternative has the highest weighted sum. This suggests that the light rail line offers the best option for the corridor.

MOE #

TABLE 5.7 Applying the weights to the ratings Measures of Effectiveness Weight AddLane LRT HOV

A

Reduction in Congestion

20

B

Reduction of Air Pollution

Cc

Access

D

E F

Busway

100

40

60

35

60 70

175

105

105

5

25

10

5

20

Investment Cost

20

20

60

100

80

Operational Cost

10

40

20

40

30

Community Economic Development

10

10

40

10

20

225

405

300

315

TOTAL

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Chapter 5 Planning and Evaluation for Decision-Making

5.4.3 Ranking Alternatives with Transformed

MOE Values

At the start of this section, the citizens of Mythaca County wanted their Highway Engineer wanted to adopt a more systematic way to choose road segments for maintenance and repair. To test any proposed ranking system, a list of eleven road segments that are eligible for road maintenance activity in the next

fiscal year has been prepared. Three factors have been identified as the basis by which the “most = deserving” road segments must be selected: pavement condition (PSR 5.0 is best, or least deserving of = selection), daily traffic volumes (lower AADT is less deserving), and a hazard index (HAZ 0 is least deserving). The measures of effectiveness for each factor on each road segment are given in Table 5.9.

TABLE 5.9 Segment

PSR

A

1

B

3

Cc

2 2

D

E F

3

G H I

4 2

HAZ

Length

366

0

2.3

448 5704 106

0 0 2

2.5

AADT

5

3

J

1

K

Roadway Data for Priority Setting

2

Segment: Road identifier

1

263 359 278

0

125

i

1

119

0

672 98

0 0

HAZ:

$/mile

$79,000 $18,000

6.6

$61,000 $75,000 1.5 $31,000 2.6 $34,500 2.0 $11,000 1.9 $85,000 3.2 $20,000 1.2 $65,000 0.5 $60,000 Index of traffic safety hazards (0 = safest) 1,2

PSR: Pavement Condition (5 = best) Length: Segment length (miles) AADT: Annual Average Daily Traffic $/mile: Cost to remove deficiencies Source: Shaffer (1987)

Note that the units for each MOE are different. So are the ranges of values, between most deserving and least deserving. Note that Segment F has the best pavement condition (PSR=5), but it also is considered to have a safety problem (HAZ>1). Segments A and have bad pavements (PSR=1), but no apparent

J

safety problems (HAZ=0). Segment C has, by far, the most traffic and PSR=2, but no safety problems.

~

=

THINK ABOUT IT Using only your personal judgment, choose and rank the three road segments most deserving of funding in Table 5.9.

Ranking alternative projects using the Percentile Method. Most likely, you have taken an aptitude test. The Scholastic Aptitude Test (SAT) is an example. Along with your raw score (out of 800 on each section), you probably were informed of your relative standing among all individuals who took the SAT. This relative standing is expressed as a percentile score. If your raw SAT score put you in the 89* percentile, this means that your score was better than 89 percent

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of the scores recorded on the SAT. We can apply this normalization technique to the roadway data in Table 5.9.

By definition, the roadway segments with the worst PSR value (Segments A and J) are the most deserving roadways in terms of the pavement condition factor, and should be assigned percentile scores of 100. Likewise, Segment F bas PSR=5, which is the least deserving of the roadway segments and ought to have a percentile score of zéro. Unless they have factor values that are tied for first or last place, all other road segments will be assigned percentile scores between 0 and 100. In the case of Road Segment B (with PSR=3), there are six other segments with PSR values worse (more deserving) than Segment B's, and two other segments with PSR values better than (less deserving) than 366. This means that the PSR percentile score for Segment B in Table 5.9 is PSR Percentile (B) = where L = number of alternatives less

=*100 ==*100

=25.0

(5.12)

deserving than Segment B D = Total number of segments with factor values different from Segment B’s. Note that Segments E and I have the same PSR value as Segment B, so D=8, meaning that 8 segments have PSR values different from Segment B’s. The general form of Equation 5.12 will be

Factor percentile score (Alt. i) =

=*

100

(5.13)

for each alternative i, Equation 5.13 transforms the value of each factor to a 0-100 scale, which removes the problem of having factor value scales of 1-5, 98-5704, and 2-0 in Table 5.9.

The definition of “least deserving” may change from case to case, even for the same factor. If the objective is to identify pavements in the worst condition, Segment F in Table 5.9 is the least deserving. If the objective was to nominate a segment for a Best Pavement Condition competition, Segment F would be the most deserving segment in Table 5.9. Once the factor-specific percentile scores have been calculated for a segment, that segment's composite percentile index (CPI) can be computed: n

CPI(Alt.i)= }) w, *P, j=l

(5.14)

j

where w; is the weight assigned to the j" factor and P; is the segment's percentile score for the j" factor. Example 5.14 shows how to use Equation 5.14 in the Percentile Method.

Example 5.14 Ranking road projects using the Percentile Method.

If the weight of each factor in Table 5.9 is 1/3 and if the engineer had about $600,000 to allocate, use the Percentile Method to determine which of the 11 projects he should fund.

Solution to Example 5.14 Segment B's PSR percentile score has already been found to be 25.0. Using Equation 5.13, Segment B's AADT percentile score would be:

AADT percentile score (8)=

Fricker & Whitford.

=*100

5.25

=80.0

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Decision-Making

because 8 segments have lower AADT values than Segment B. Segment B's HAZ percentile score is

:*

100=0.0. Ifthe three factors in Table 5.9 have equal weights, Segment B's CPI will be:

CPI(B) = (1/3X(25.0) + (1/3)(80.0) + (1/3X(0.0) = 8.33 +26.67 + 0.0 = 35.00. After all the CPI values for all segments have been computed using Equation 5.14, they are entered into Table 5.10 in descending order of their CPI values.

TABLE 5.10 Segment

J

Priority ranking of highway segments by Percentile Method

PSR AADT

HAZ

CPI

Dollars($)

63.3

78,000

714

90.0 30.0

0.0

H D

87.5

161,500

71.4

10.0

100.0

63.0 60.5

Cc

714

1000

100.0

0.0 0.0

A E F

100.0

K

25.0 0.0 25.0 71.4

G

10.0

70.0 40.0 60.0 80.0 0.0 50.0

I

25.0

200

B

87.5 87.5 90.0

0.0 0.0

0.0

57.1

56.7 50.8 49.2 35.0 23.8 20.0 15.0

90,000 402,600 181,700 46,500 89,700 45,000 30,000

22,000 64,000

Cumulative ($) 78,000 239,500 329,500 732,100 913,800 960,300 1,050,000 1,095,000 1,125,000 1,147,000 1,211,000

The limited county road budget can be allocated to the most deserving road segments. Segments J, H, and D receive the three highest CPI scores. Together, those three road projects would cost $329,500. Adding the fourth most deserving project (Segment C) would exceed the $600,000 budget specified in the problem. The Percentile Method is one ranking method (among many) that the County Highway Engineer might adopt as a rational system that can be replicated by anyone having the same road segment data.

—-t-— =}

¢

Ranking alternative projects using the Range Index Method. Note that, in Table 5.9, the busiest road (Segment C) had an ADT value much greater than that of the second busiest road (Segment J). In Table 5.10, however, Segment C’s percentile value for ADT was only a little higher than Segment J’s. If the cardinal values of factors are just as important as their ordinal values, an alternative to the Percentile Method to consider is the Range Index Method (Shaffer and Fricker 1987). The Range Index (RI) normalizes the raw factor values using this equation:

Factor RI(Alt, where

i) = ~L—!L-#199

fy —f.

(5.15)

{= raw factor value for Alternative i

fi. = raw factor value of least deserving alternative fy = raw factor value of most deserving alternative

Figure 5.11 helps explain Equation 5.15. For a given factor, the values for each alternative are ranked from most deserving to least deserving, defined according to the intent of the ranking process. In Table 5.9, Segment C has the highest AADT value, making it the "most deserving" segment in terms of traffic

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f=

volume in the competition for funding. Therefore, 5704. The best (least needy) AADT value in Table 5.9 is 98 for Segment K, so {=98. In Equation 5.15, the

Range



fm



f1—5704 98

fy “I*

Most deserving factor value

> 100

5606. For the factor

AADT and Segment J, fi- fi. = 672 - 98 = 574 and

AADT RI(J) = >4.*100=10.24. The segment with

5606 the second highest AADT in Table 5.9 has an RI value of only 10.24. Applying Equation 5.15 to Segment J's other factor values, PSR RI(B) =

HAZ RI(B) =

Ll 1-5

f,

fi

“Pg

Factor

value specitied alternative for

Least deserving factor value

>0

100 =100.00 and

FIGURE 5.11 The Range Index Method.

100 = 0.00.

Source: Shaffer and Fricker 1987

As was done with the Percentile scores, the Range Indices for Segment J can be combined into a Composite Range Index (CRI), using appropriate weights: CRI(AIt.i) =

wj*RI,

(5.16)

For segment BJ, CRI(B) = (1/3)(100.00) + (1/3)(10.24) + (1/3)(0.00) = 36.74.

Example 5.15 Ranking road projects using the Range Index method. Repeat Example 5.14, but this time use the Range Index method.

Solution to Example 5.15

After all the CRI values for all segments have been computed using Equation 5.16, the segments can be ranked in order of need, with the highest CRI as the neediest. The results are shown in Table 5.11.

TABLE 5.11 Segment

D Cc

H

J

75.0 75.0 75.0 100.0 100.0

E

50.0 75.0 50.0

B

F

&

PSR AADT

A

K

Fricker

Priority ranking of highway segments by Range Index Method

I

0.0 50.0

G

250

Whitford

0.1

HAZ 100.0

100.0

0.0

0.5

50.0 0.0

102

48 29

4.7

04 32

00 00

62

Dollars (S) 90,000

41.8

161,500

36.7

00 349 50.0 0.0 0.0 50.0

0.0

CPI 584 583

5.27

343 25.0

187 182 168

94

402,600 78,000 181,700

46,500 30,000 45,000 89,700

64,000 22,000

Cumulative ($) 90,000 492,600 654,100 732,100 913,800 960,300 990,300 1,035,300 1,125,000 1,189,000 1,211,000

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Decision-Making

THINK ABOUT IT

7

Based on what you have seen so far about the Percentile and Range Index methods of normalizing factor values, what are the pros and cons of each method? Which method do you prefer? Why?

5.4.4 Comments on Multi-Criteria Decision-Making (MCDM) Methods

Comparing the methods The MCDM method introduced in Section 5.4.2 used integer ratings on a 1-5 scale, The ratings for the quantifiable factors could have instead been based on values transformed by methods such as the Percentile or Range Index methods. The remaining hard-to-quantify factor ratings could be based on the collective (and subjective) judgment of a group of qualified individuals.

Don’t make the weights too heavy. common tendency to give the most important factor a weight that is too high with respect to the less important factors. Under most ranking or priority setting schemes, assigning weights such that the highest weight is more than three times the lowest weight causes a preemptive situation. This means that the higher-weighted factor so dominates the low-weighted factor, that the low-weighted factor has little or no influence on the outcome of the ranking procedure. If this is the case, why even bother collecting data

There is

a

for the low-weighted factor? This is one reason why the methods presented in this lesson call for allocating factor weights such that their sum is 1.00 or 100 percent. It tends to be much easier to assign weights like “5” and “1”, than to assign weights like “83” and “17”. In any case, try to keep the ratio of highest factor weight to lowest factor weight smaller than 3.0. MOESs that are unpleasant or nearly impossible to quantify.

We return to the problem of placing a value on human life. As we asked you to consider earlier in this chapter, a great many elements could go into arriving at such a figure. The effort would be immense, controversial, and even emotional. The result would eventually be a number to put into an analysis such as those described earlier in this chapter. One strategy that may avoid much of this difficulty is to estimate the values for all the other (presumably less controversial) factors, then determine the value of human life that would just barely justify the project being undertaken. In many cases, the “breakeven” value will be so low or so high as to make the decision obvious (or nearly so). Even in cases where the “breakeven” value is in the “gray area”, where well-intentioned analysts will disagree, the dispute has been reduced to a decision about a single number: Is the “breakeven” value of human life high enough? Yes or no?

CHAPTER 5 SUMMARY The provision of transportation involves much more than designing and building a facility or service. The needs and preferences of the community must be determined. This may be difficult, because of the different viewpoints held by various stakeholders in the community. Once problems and needs have been identified, alternative solutions are generated and evaluated. The evaluation of each alternative involves an assessment of benefits and costs. Whenever possible, the benefits and costs are expressed in monetary

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terms, and appropriate economic analysis tools can be applied. However, some criteria are difficult or impossible to convert to dollars. This chapter covers both cases, and presents standard procedures by which competing projects can be ranked with respect to specified criteria.

The transportation planning process is a public one. Members of the public must be involved in the process. The process is also greatly influenced by government entities, whose regulatory, funding, and administrative activities help determine which transportation projects become reality. Project evaluation, ranking, and selection is a difficult, but necessary process, especially for transportation engineers who have limited budgets funded by tax revenues. Whatever method is used, it must be consistent and reflect appropriate factors and their measures of effectiveness

ABBREVIATIONS AND NOTATION AADT BCR

Annual average daily traffic

CPI

Composite Percentile Index

CRI EUAC

Composite Range Index

HAZ

Hazard Index for roadwey section

MCDM

Multi-Criteria Decision Making

MOE

Measure of Effectiveness

NPV

Net Present Value

NPW PSR

Net Present Worth

TIP

Transportation Improvement Program

Benefit-Cost Ratio

Equivalent Uniform Annual Cost

Pavement serviceability rating

GLOSSARY e *

e e e

Discount rate: The rate at which the value of a dollar amount diminishes with time. Effective discount rate: the annual discount rate, taking into account the effect of compounding during the year. Goals: A general statement of the direction a program should go. Hazard Index: A measure of the safety conditions on a roadway segment. HAZ = 0 is best. Life Cycle Cost Analysis: An analysis that includes all costs and benefits that are expected during the complete life of a project, including salvage value.

e

Multi-Criteria Decision Making: using more than one factor to distinguish, evaluate, and rank

»

Net Present Value: the discounted value of a series of cash benefits or costs in a future year, brought back to “Year Zero”. Nominal discount rate: the annual discount rate without considering the effect of any compounding. Objectives: A more specific list of activities designed to meet goals. Objectives should be measurable or otherwise permit a clear appraisal of the extent to which they have been achieved.

competing alternatives

e +

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Chapter 5 Planning and Evaluation for Decision-Making Pavement serviceability rating: a rating of pavement condition on a 1-5 scale. PSR = 5 is best. Salvage value: The expected value of an asset at the end of its useful life. Treated as a reduced cost, not as an added benefit.

Sensitivity analysis: Varying inputs to see how much the outputs vary. In this way, the sensitivity of a process to the variability of certain inputs can be ascertained. Sunk cost: An expenditure that is committed to, and therefore will not affect the cost analysis. Transportation Improvement Program: a published schedule of all transportation projects for an urban area or state.

INDEX annual percentage rate, 10 benefit/cost ratio, 15, 20

composite percentile index, 26 composite range index, 28

discount rate, 6, 8, 9 effective discount rate, 10 equivalent uniform annual

cost, 13, 16 goal, 2

hazard index, 25 life cycle, 8, 15, 19 measure

of effectiveness, 3,

15, 21

Multi-Criteria Decision Making, 22, 29 net present value, 15

net present worth, 6, 15 nominal discount rate, 10 objectives, 3, 22

pavement condition, 25 present value, 6

salvage value, 9, 15, 16, 18, 19

sensitivity analysis, 9 stakeholder, 4 Transportation Improvement Program, 3

REFERENCES DRCOG 2009. 2035 Metro Vision Regional Transportation Plan, Denver Regional Council of Governments, adopted December 2007, amended January 20, 2009. http://drcog.ore/documents/2035%20MVRTP_revisedMarch09_TableofContents Cht_Ch2.pdf, retrieved 9 October 2014. FHWA/FTA undated. Metropolitan Transportation Planning: Executive Seminar. http://www.planning.dot.gov/Documents/MetroPlanning/metroTrans.htm, retrieved 8 October 2014.

Newnan, Donald G. Engineering Economic Analysis. Engineering Press, Inc., 1980 Shaffer, Joseph L., "A Methodology for Determining and Prioritizing County Highway Network Needs", MSCE thesis, School of Civil Engineering, Purdue University, May 1986. SMATS 2007. Saginaw Metropolitan Area Transportation Study, Chapter 3: Transportation Planning Goals and Objectives. Revised Draft June 2007. Saginaw Metropolitan Planning hapter_3_goais. 5 8 Organization, ocs/Plannin: http:/;

(

¢

3.

retrieved 9 October 2014. Shaffer, Joseph L. and Jon D. Fricker, “Simplified Procedures for Determining County Road Project Priorities", Transportation Research Record 1124, Transportation Research Board, 1987, p. 8-16.

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EXERCISES FOR CHAPTER 5: PLANNING AND EVALUATION FOR DECISION-MAKING 5.1 The Transportation Planning Process 5.1. Metropolitan Planning Organizations. Planning function in urban areas are carried out by Metropolitan Planning Organizations (MPOs). Do you live in a place that is within an MPO’s jurisdiction? If so, answer the questions below. If not, answer the questions for an urban area of interest to you. The information should be available online. .

What is the MPO’s official name? How are the cities and counties within its jurisdiction represented on the MPO’s governing body? What is the current horizon year for the MPO's long-range transportation plan? Does the MPO have responsibility for anything besides transportation planning and land use in its jurisdiction?

5.2, Stakeholders — Apex Industries. Apex Industries, a major employer in the Eastern Mythaca area, is threatening to move its operations to a city in another state. Apex cites deteriorating transportation infrastructure and services as a major factor in the decision to leave Mythaca. Its business depends heavily on the port facilities at Mazurka and, without a bypass highway, they have to use the very heavily traveled roadways through the city. A meeting of major stakeholders in Mythaca was convened. The result was a decision to hire you as a consultant to document the nature and extent of the transportation problems in the Mythaca area. A. Name five major stakeholders other than Apex and describe why they are key "players". B. List five kinds of data that you would want to collect in order to document the nature and extent of the transportation problems that plague Apex so much that its management seeks to relocate. 5.3. Stakeholders — New Interstate near Shoridan. Because of the Governor’s desire to provide more recreational opportunities for the state’s residents, the state is proposing to build an interstate highway connecting Mythaca County to New Cyberon, a large city to the north. The proposed route will pass within three miles of the Shoridan Central Business District. (A description and map of Shoridan is given in Chapter 1.) Because of its undeveloped resort potential, Shoridan’s City Council cannot reach consensus on whether to favor having an Interstate highway so close to their small town. There

would be significantly improved access to the community, but that is not viewed as a good thing by some individuals and groups. Use your knowledge and judgment regarding communities and the forces that are at work as the local and state governments consider this "better access" question. List at least five stakeholders (local banks and environmentalists would be two). For each stakeholder, indicate which side of the issue you would expect them to be on and write a short statement that outlines the arguments they would present at a public meeting to validate their position on the proposed location of the Interstate. 5.4. Stakeholders — Airport Relocation, There are a number of pilots who fly smal] single-engine aircraft into Shoridan’s airport regularly. However, the 2200-foot gravel airstrip limits the number and kind of aircraft that can safely land and takeoff at Shoridan. There is an air taxi company that would like to fly regular daily service from Shoridan to the nearest major city in a 9-passenger aircraft that requires a 3700-foot paved runway and improved lighting. Doing this would mean a whole new airport, whose location would be about a mile from the existing one. The proposed airport relocation

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would involve building a runway across some wetlands. Also, a radio tower would need to be moved to provide the required safe approach angle, Developa list of three stakeholders most likely to be in favor of the new airport and a list of three stakeholders most likely to be opposed. Indicate for each stakeholder their main argument(s) for their position. 5,5. Stakeholders — Worldbusters. The management of the large company “Worldbusters” has decided has decided to move its operations to another state. Apparently, it has become too expensive for Worldbusters to get its products to market. Of course, the state and its major city want the company to stay. Worldbusters has a large employment base and its presence provides an important economic base for the state. Various transportation options are being discussed in an attempt to keep Worldbusters from moving out of state. Answer in short paragraphs the following critical questions:

A, What is the relationship of transportation and economics (growth, stability, development)? B. Who are the major stakeholders in a transportation investment decision, such as the move

of a major industry? C. What are the interfaces between the public and private sectors in transportation? 5.2 Engineering Economics 5.6. CNG Fueling station. If the Mythaca Bus Company acquires buses powered by Compressed Natural Gas (CNG) engines, it will also have to install CNG fueling station. Such a station costs about $2 million. The natural gas supplier may be willing to install the CNG fueling station in return for annual payments from MBC. If MBC wants to complete the annual payments in 12 years, how much should the annual payments be? Use a discount rate d = 0.04. a

oF

5.7, Net Present Value of three highway projects. Compute the Net Present Value of the following three highway projects, analyzed over a thirty-year period, with the local social discount rate of 8.76% discount rate. Note that when the service life is up for those not lasting 30 years you will need to spend the money to do it again. The cost is considered to be the same as the initial cost. You must,

A B Cc

Cece

however take the cost forward in time. M = million. Salvage Service Initial Project Value Life Investment

Annual

10yrs

$19M

$0.5M $2.5M

15 yrs

Benefits $1.8M $2.3M

$33M

$3.6M

30 yrs

$3.7M

$I0M

Reduction of travel costs Incr. @ 3%/yr

Decr. @

A%lyt

5.8. Cash Flow Analysis — Leasing the Indiana Toll Road. In 2006, a consortium paid the State of Indiana $3.8 billion for the right to operate the Indiana Toll Road (ITR) for 75 years. When the County Engineer heard about the plan, he decided to do a “back of the envelope” calculation. On the Web, he found that, during the previous 5 years, the ITR’s net revenues were sometimes negative, but

of $25 million. A. Using the optimistic value of $25 million per year and an annual discount rate of 3.5 percent over 75 years, would the state have earned more than $3.8 billion in present value of net revenues? the best year had positive net revenue

B. Using a 3.5 percent discount rate, what uniform annual net revenue over 75 years is equivalent to $3.8 billion in Year 0? C. Based on these calculations, was leasing the ITR for $3.8 billion a good deal for the state? Fricker & Whitford

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5.9.A proposed National Infrastructure Bank. $50 billion in bonds would be sold to corporations. These funds would be loaned by an American Infrastructure Fund (AIF) to states and local governments for public-private partnerships to carry out projects to maintain, improve, or repair infrastructure, A. If$50B must be paid back by the AIF to the original investors at 1% per year after 50 years, how much money should the AIF have on hand after 50 years? B. States and local governments are required to pay back the bondholders at an AIF-specified rate

(say, 3.5 percent). What equal uniform annual repayment over 50 years will provide the AIF with enough funds to repay the original investors? 5.10. Cable median barriers. The barriers are intended to prevent (or at least reduce the number and severity of) crashes caused when a vehicle crosses the median of a divided highway and enters the lanes of oncoming traffic. A DOT staff member surveys four states and finds: ¢ 1436 miles of cable median barriers (CMBs) have been installed in those states. ©

CMBs cost an average of about $145,000 per mile to install and about $6500 per mile per

year to maintain. The expected life of a CMB is 20 years. e The average number of fatalities on highway sections where CMBs have been installed has dropped from 64.4 per year to 3.4 per year. What is the EUAC of total CMB installation and maintenance in the four states? Use discount e

A.

rate

d= 3.1 percent.

B. At what value of a human life will the cost of the CMBs be justified, strictly on an economic basis?

Value of Time — Choice of Parking Lot. The County Engineer plans to attend a workshop at the DOT Headquarters in the state capital city. The workshop organizer sends a map of perking lots near the DOT HQ. Normally, the County Engineer parks near the courthouse, which is 7 blocks from the DOT HQ and costs $5 for the whole day. After looking at the map sent from the DOT, he finds

5.11.

several lots that cost less than $10 per day and are closer than his courthouse lot. One particular lot — near a canal is only 3 blocks from the DOT, but costs $7 per day. There are 12 blocks per mile in --

the capital city and the County Engineer walks at about 4 f/sec.

If the courthouse and canal lots are to what is his value of in $/hr? Show the steps in your analysis equally acceptable him, apparent time, clearly,

5.3 Economic Evaluation of Transportation Alternatives

Benefit/Cost — Roads to Econoly. Two possible new road routes are proposed to improve the traffic flow into Econoly from near-by “bedroom community”. One road is 15 miles long and will cost $12 million to construct. The maintenance of the road is expected to cost about $0.5 million per year. The second road is 24 miles long and will cost $20 million to construct with a maintenance cost of about $700,000 per year. Both roads will last 20 years and have a salvage of 25%. The benefit to the residents using the first road in fuel expense and time saving is fixed at $2 million per year. The second road will have increasing benefits. They begin at $3 million and grow at 2% per year. (Hint: use a new rate that includes the discount rate and the growth rate). The County commissioners who must approve the road use a discount rate of 8.8% and prefer to look at Benefit/Cost ratios. What are the B/C ratios for each?

5.12.

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Planning and Evaluation for Decision-Making

Annual Costs —Airport Capacity Project. A proposed option for the Mythaca airport capacity improvement will cost $15 Million and have a lifetime of 12 years with no salvage value. The increase in O&M costs will be negligible. Air traffic is growing at the rate of 3% per

5.13.

year, The benefits ($3.5 Million) at the time the runway improvement comes on line are significant, but they will decline proportional to the traffic increase. The discount rate is 6.5% A. What is the Equivalent Uniform Annual Cost of Construction?

B. What is the dollar value of the benefit in year 12? C. What is the discounted value of the benefit in year 127 D. Determine the Benefit/Cost Ratio over the twelve-year life of the project. Hint: the decline in benefits will look just like a larger discount rate. Choosing between two proposed traffic safety projects. The intersection of Renner Blvd and Dell Ave has a very high crash rate. Two solutions are proposed. e Project A: Build a $5.57 million overpass to separate the two roadways. The estimated value of the crashes avoided will be $513,000 per year over the next 20 years.

5.14,

Project B: Improve the geometry and signal timing at the intersection, at a cost of $418,000. The estimated value of the crashes avoided will be $61,800 per year over the next 20 years. A. (10 points) What are PWB and PWC for each project? Show your cash flow diagrams and calculations. The current government interest rate is 5.4 percent/year. +

B. (5 points) Using NPW, which project is better? C. (5 points) Using BCR, which project is better? 5.15. Annual Costs — Road Improvement. A road is to be built to accommodate traffic between two industrial sites and a major metropolitan area that is located between them (not on a straight line). There are two specific routes A and B that have been proposed. Route A on the north would be built over very hilly and curvy terrain, while B, the southern route is considerably longer but flat, level and on good soil. Traffic is expected to be about 7 million vehicles per year, with 9.3 percent trucks. The

major benefits include travel time, safety and fuel as indicated below. e Automobile time is valued at $12.00 per automobile hour saved e Fuel: Average auto fuel economy on the hilly terrain is 16 mpg while on the flat terrain is 24 mpg. ©

Fuel costs are $1.25 per gallon

“5 Convenience/Service'/Safety is valued as (vie)! times $1 per auto trip Truck time and fuel can be valued at $50 per minute. Determine the equivalent annual cost including the Operations and Maintenance (O&M) of Routes A and B using an 8.5% discount rate. ®

Project

Length

A

48 mi

B

68mi

Investme

Annual

nt

O&M

$80M $140M

$4M $8M

Service Life‘

Salvage

25 years

$4.8M

S50yeers

nil

Truck

Auto

Value_—-Velocity 45mph 65mph

‘Velocity 30mph SSmph

=” 0.5 0.8

5.4 Ranking Transportation Alternatives

When do weights get too heavy? Repeat Example 5.13 with increasingly disparate maximum and minimum weights, until you think you have reached a “preemptive” set of weights. Did the 3:1 rule of thumb work? If not, what ratio limit should be applied to these exampies?

5.16.

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Ranking County Road Projects. Various County Council members and citizens groups have

been demanding that work be done on certain road segments in Mythaca County. Of course, there is not enough money to work on all of them. The County Engineer's staff has prepared a table of factor

values for each of the segments nominated for repair, resurfacing, etc. Apply the Range Index method to only one of the twelve segments listed below. (Choose a segment that never has either the neediest or least needy value for any of the factors.)

A. Which segment did you choose? B. What Range Index values did you compute for that segment? Show your method and calculations clearly,

C. Does anything about the values in the table bother you? If so, what is a potential problem? Road

Peak V/C

Project Cost

Segment

(Weight = 36)

(Weight = §2)

A

0.55

B

D

0.18 0.93 0.36

39.9 49.2 82.0

E F

0.36 0.87

G H I

0.81

Cc

J

K L

0.90 0.74 0.28 0.19 0.70

aap

Composite Range Index

(Weight = 12) 1.84

9.79 17.82

76.8 62.4 43.6 28.7

15.38

20.7

12.74

14.0

8.70

13.68 17.40

3.70

79.8

2.12

45.1

13.74

18.1

3.03

Evaluating alternative CNG paratransit vehicles. Mythaca Bus Company (MBC) provides service to eligible individuals under the Americans with Disabilities Act. MBC uses 14-passenger

5.18.

“body-on-chassis” (BOC) buses for this service, and they need to be replaced. MBC has asked vehicle suppliers to submit bids for BOC buses powered by compressed natural gas (CNG). As advertised in the request for bids, MBC staff examines the bids according to the criteria listed in the table below. Criteria 1 and 2 are rated subjectively, with a higher score being better. For Criteria 3 and 4, a lower value is better.

Criterion Design and Performance

Weight

Zebra

3. Cost per vehicle ($)

0.40 0.25 0.25

8.5

4. Time to Delivery (wks)

0.10

1.

2. Manufacturer's References

Total:

United 6.4

9.1

73

$75,511 36

$84,988 20

Shorburg 7.6 9.9

$92,145 38

1.00

A. Use the Percentile Method to rank the bids. Using a spreadsheet is acceptable, in fact, encouraged. e

Show how the Percentile value for United’s Cost/veh is computed.

¢

Which vehicle should be chosen, according to the Percentile Method?

B. Use the Range Index Method to rank the bids. Fricker & Whitford

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Chapter 5 Planning and Evaluation for Decision-Making

Show how the Range Index value for United’s Cost/veh is computed. Which vehicle should be chosen, according to the Range Index Method? C. Based on your experience with the two ranking methods, which method do you prefer? Why? e

e

5.19,

Evaluation of Alternative Airlines. Mythaca Airport is becoming an increasingly important

part of the regional air transportation system. Several major airlines are interested in offering service to Mythaca. But Mythacans are fussy. They want only the best airlines to be considered. A local consumer protection group has acquired performance data on ten major airlines. Note that a high value for "Percent of on-time flights" is good, but a high value for "Complaints per 100,000 passengers” and "Mishandled baggage per 100,000 passengers” is bad. A. Explain how you will modify these data for use in a ranking procedure, then use a spreadsheet to implement your modifications.

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In parts B-D below, use a spreadsheet to rank the ten airlines using the following weights: 0.40 for "Percent of on-time flights" 0.30 for "Complaints" 0.30 for "Mishandled luggage"

ee

¢

and the following ranking methods: B, The Range Index method The Percentile method D. At this point, which three airlines (in order of performance) would you recommend Mythaca Airport to invite? Explain your recommendation.

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SAFETY ON THE HIGHWAY SCENARIO ‘The newspaper headline was

“A 2-hour extraction with a surprise ending—a survivor”,

a middie-aged man whose car left the road and rolled down a ravine

wrapped around a tree, (Figure 6.1) A couple said “hey were driving north when they saw an

The story tells of

until itecame to rest with i tss roof

oncoming driver make what appeared to be a turn into a driveway at a high rate of speed.” An

investigating officer stated that “it appeared [the driver’s] southbound car partially ran off the right side of the road. [He] overcorrected to the left, then veered right. You can see where if, started striking some trees, We believe alcohol is one of the factors in the crash because of odor from [the driver].” The crash occurred on ea stretch of highway with a history of crashes, FIGURE 6.1 Driver survives dramatic one-vehicle crash, which was one reason for the construction of a Photo: Join Terhune, Lafhyette Journal & Courier, 14 retently-opened limited access highway parallel December 2013, to this one. The man was airlifted to a hospital in a larger city. (The quotes are based on an article in the Lafayette Journal & Courier, 14 December

2013, pages Al and A4.) Speed, alcohol, and roadway geometry — all three factors may have contributed to this crash. What can a transportation engineer do to improve safety on the highway?

CHAPTER OBJECTIVES By. the end of this chapter, the student will be able to .. 1. Conduct a Roadway Safety Management Process. 2. Use Human Factors in the design and analysis of highways for safety. 3. Evainate and design roadway sections for safe stopping sight distance. 4, Apply prescribed standards in the use of roadway signs and markings.

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Chapter 6 Safety on the Highway

Introduction

3

i

nN

8

wo

> 8

Rates and values 23 indiented

The number of fatalities on U.S. highways has deolined to about 30,000 per year. (Figure 6.2) The number of miles traveled has increased, but the crash rate has improved. This does not change the fact that the highway death toll is the equivalent of one major plane crash killing almost 100 persons each day. This chepter deals with the aspects of highway design, automobile performance, and human/driver behavior, which together form the basis for assessing safety on our highways.

8

i i

1965

1975

1985

1994

2005

2015

2025

Year Fatalities (104)

—®-VMT (10412)

FIGURE 6.2 Highway fatality data since NHTSA was formed in

--»—-RHMVM 1967. Source:

FHWA

2017

THINK ABOUT IT From 2000 to 2009, 718 deaths were atiributed to commercial airline travel in the US, Since 2009, only 5 airline passengers have-died, Source: Airflects.net 2018. Compare these values with those for highway travel in Figure 6.2.

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Chapter 6 Safety on the Highway

HIGHWAY SAFETY DATA AND ANALYSIS

6.1

Despite his limited budget, the Mythaca County Highway Engineer is expected to keep the county's roads in safe operating condition. Hardly a week goes by without an impassioned cail or a letter to the area newspaper about some dangerous intersection or stretch of road, Why can’t the County Highway Engineer do sdmething about the obviously hazardous situation? A wise engineer bas a system in place

to (a) identify locations within the county that are hazardous, (b) determine which remedies are appropriate, and (c) establish the sequence in which the improvement projects will be accomplished, The system should be as objective as possible, using the limited funds as effectively as possible.

6.1.1 History aud Perspective Figure 6.2 shows how much highway safety has improved since the formation of the National Highway Traffic Safety Administration (NHTSA) in 1967, While total vehicle miles traveled (VMT) has grown from about | trillion to about 3 trillion, the number of total fatalities has been reduced from more then 50,000 to about 30,000. As a result, the fatality rate per hundred million vehicle-miles (RHM'VM) has dropped from more than 5,0 to about 1.0.

~

a

FYi

“Inthe summer of 1997, NHTSA began using the term “crashes” instead of the traditional term “accidents”. This change was in recognition of the fact that most crashes have a cause, and are not simply the result of uncontrollable circurnstances.

}

6.1.2 Factors that Contribute to Highway Safety The major elements that have improved highway safety include (1) vehicle safety regulatory standards for such items as roof design, side door supports, motor mounting, headlights, and windshields; (2) the design of highways, especially the interstate; (3) the social pressure to reduce drunk driving; (4) enhanced driver training; and (5) the installation of seat belts and airbags. Law enforcement and public education efforts continue on matters of seat belt use, driving under the influence, and distracted driving.

Highway crashes sometimes have more than one causal factor, as suggested in this chapter's Scenario, but driver behavior is involved (at least in part) in more than percent of US roadway crashes. Each of the areas in the Venn diagram in Figure 6.3 is the subject of a section in this chapter or in Chapters 7 and 8:

.*

Driver behavior in Section 6.2 Vehicle capabilities in Section 6.3 Traffic control in Section 6.4 and Chapter 8

'*

Roadway environment in Chapters 7 and B

*

*

The values in Figure 6.3 are based on a study done by K. Rumar [1985]. update these numbers for the US could not be found,

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A more recent study to

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Chapter 6 Safety on the Highway

Driver

Readwa

57%

2%

Vehicle

FIGURE 6.3 Venn diagram showing factors by percentage involved in US road crashes, Lum and Reagan 1995

6.1.3

Highway Safety lmprevement Programs and the Highway Safety Manual

Highway safety remains a primary concern to highway engineers and public officials, despite the progress illustrated in Figure 6.2. The Highway Safety Improvement Program (HSIP, established in 1979, remains to this day a good framework for planning, implementing, and evaluating sefety programs and projects. [HSIP 2010] A related reference, the Highway Safety Manual [HSM 2010], offers tools to conduct a quantitative safety analysis. In the HSM, individual chapters are devoted to the six steps in the

&

wb

Roadway Safety Management Process: 1. Network Scresning A. Collect crash data B. Calculate crash rates Diagnosis Select Countermeasures Economic Appraisal Prioritize Projects Safety Effectiveness Evaluation

In this section, methods to carry out these steps will be introduced and demonstrated.

Step 1. Network Screening Crashes and collisions occur at intersections and on roadway segments within Mythaca County, but which locations are the most dangerous? A safety analyst needs a consistent way to identify problem locations that should be considered for corrective action. The Network Screening step begins with data.

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Highway

1A. Collect crash data Properly collected crash data can help identify the scope and nature of traffic safety problems in a community. Traffic crash data depend on collisions beig reported to law enforcement agencies, so that the events can be documented. Once a crash report is filled out and filed, it.becomes the basis for an analysis of that crash and the compilation of summary data. These locaily-created reports eventually become part of a national database. See, for example, the Fatality Analysis Reporting System [FARS

undated]. From these data, the analyst can compute crash rates, look for patterns in the history of crashes at a particular location, propose solutions, and evaluate their expected effectiveness.

THINK ABOUT IT Have you ever been involved in a traffic collision? If so, did a police officer fill out a , crash report? Lf not, why not? 1B. Calculate crash rates Although there are more than 6 million crashes each year on US roadways [NHTSA 2016], a traffic collision is considered a "rare event".

~.

V7

q

-

THINK ABOUT IT If you were asked to go to a busy intersection of your choice and wait for the next collision te occur, how long would you have to wait?

To help determine how dangerous a roadway section or intersection is, a local agency could refer to the crash reports on file, then determine the total number of crashes at that location. the safety performance of a location is to compute its crash rate,

A better way to assess

Crashes at Intersections For an intersection, the standard measure is crash rate per million entering vehicles (RMEV). The key "ingredients" are (a) the number of crashes in a given year and (b)} the annual average daily traffic

{AADT) on all

approaches to the intersection.

RMEV =

crashes / year approach AADT

*

days / year

#10°

(6.1)

,

Example 6.1 Crash rate at Fisk and Kissimmee Several intersections in Mythaca had an apparent increase in collisions last year. One intersection Fisk at Kissimmee had 13 crashes and may need some special attention. The four legs of that intersection had two-way AADT values of 9671, 2893, 9506, and 2611 vehicles per day last year. Calculate the intersection’s crash rate, so that it may be compared with the rate for other intersections like it. --

--

Solution to Example 6.1 Equation 6.1 uses approach AADT, not 2-way AADT. That part of a road's AADT that is moving away from the intersection must be excluded. A reasonable way to estimate approach AADT is to take half of

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ww ww

FUNDAMENTALS OF TRANSPORTATION ENGINEERING Chapter 6

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Fisk and Kissimmee last

year was 13

RMEV = 0.5 * (9671+ 2893 +9506



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Safety on the Highway

the total 2-way AADT for each leg. Therefore, the intersection crash rate at

~.

i

+

2611)

*365

#10°

=

13

0.5* 24,681 *365

*10° =2.886

THINK ABOUT IT Why must we exclude the departing AADT from the calculation of RMEV?

In Example 6.1, the AADT values for each approach were given. At another intersection, a north-south state highway with AADT = 10,000 vpd crosses an east-west US highway with AADT = 20,000 vpd. (See Figure 6.4.) In this case, what would be the approach AADT? Recall that AADTis a 2-way count.

On the state highway, 5000 southbound vehicles and 5000 northbound vehicles pass through the intersection, so there are 10,000 vehicles approaching the intersection on the state highway. (We are neglecting turning movements here.) Likewise, the 20,000 vpd passing through the intersection are treated as both approaching and departing vehicles. The total daily approach volume is simply 10,000 +

20,000 = 30,000 vpd.

(b) AADT given for two roads that cross

(a) AADT given for all four approaches

FIGURE 6.4 Is

Approach traffic volumes for calculation of RMEV

RMEV = 2.886 in Example 6.1 a high crash rate? The average RMEV in various states is

[Monsere et al. 2011]:

;

*

0.96 for 1,148 urban intersections on the Wisconsin state highway system [Knapp et al. 2005, Table 21]

*

0,80 for signalized intersections and 0.60 for unsignalized intersections in Massachusetts

e

0.26-0.37 (rural) and 0.43-0.57 (urban) in Kentucky [Agent and Pigman 1993]

*

0.34 for 413 intersections in Oregon.

Because of the differences between states and between intersection types, a better way to evaluate an RMEV is to set up a comparison group or reference population of intersections with similar characteristics. Fisk at Kissimmee is a two-way stop-controlled (TWSC) intersection. There are many

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TWSC intersections in Mythaca, but (to keep the forthcoming examples manageable) the data for a small random sample of such intersections are listed in Table 6.1.

‘TABLE 6.1 Traffic and Crash Data for TWSC Intersections (Based on HSM 2010, Table 4-4) Number of Crashes Intersection »

Major AADT Minor AADT

2

12,000

1,200

3

18,000

800

Year

Year 2

|

Year

3

li

9

8

6

9

14

7

6

4

9

-

©

7

21,000

1,000

10

15,000

1,500

15

26,000

500

6

3

8

17

14,400

3,200

4

4

5

19

15,400

2,900

5

2

4

.

The critical rate for any intersection can be calculated using Equation 6.2 [HSM 2010, Equation 4-11):

Roi where

= R,

fe

I

MEV,

(6.2)

2* MEV,

R,j= critical crash rate for intersection i Ra = weighted average crash rate for the reference population, not just an individual intersection.

z=z-value for the corresponding confidence level.

1.645 for the 95% confidence level

MEV; = million entering vehicles for intersection i during the years being studied For Intersection 7 in Table 6.1, the three-year crash rate is:

RMEV _

11+94+14

(21,000 + 1,000)*3*365

10

34

~

24,090,000

#105 =1,41

R, is the weighted average crash rate for the reference population in Table 6,1,

and is computed as

follows: *

> (TEV; RMEV,) Ree

tl

>

alli

where

(6.3)

TEY,

RMEV; = observed crash rate at site i

TEV; = total entering vehicles per day for intersection i. The elements used in Equation 6.3 for each intersection in Table 6.1 are shown in columns 2-4 of Table 6.2. The weighted average crash rate for the reference population is Ra = 136,986/132,500 = 1.03. 3

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TABLE 6.2

Critical Rate Calculations for TWSC Intersections

(6)

(5)

(4)

(1)

(2)

Intersection

TEV

RMEV

TEV*RMEV

2

13,200

2.42

31,963

14.454

1.51

3

18,800

1.12

21,005

20.586

1.43

7

22,000

1.41

31,050

24,090

1.40

10

16,500

0.94

15,525

18.068

1.46

15

26,500

0.59

15,525

29.018

1.36

17

17,600

0.67

1

1,872

19.272

1.44

19

17,900

0.56

10,046

19.601

1.44

(3)

|

MEV

Critical Rei

136,986

132,500

The critical crash rate R., for any intersection in the reference population can now be computed. For Intersection 7, using Equation 6.2:

Ro7=R,+] z*

1 _] |— MEV, | [| 2*MEV; Ra}

21.0341 1.645+

3* 365 * 22,000 10°

Roz =1.03 +] 1.645*, [1:03 24.1 ?

Heel 2* 24,1

1.03

__.

1.03

+ 0.35 + 0.02 =

10°

1.40 crashes/MEV

Only Intersections 2 and 7 have RMEV in Column3 greater than Critical R.j in Column 6. These intersections will be considered for a safety improvement project. Adding Fisk at Kissimmee from Example 6.1 to the reference population of TWSC intersections will form the basis for an end-of-chapter exercise.

~

Vd

THINK ABOUT IT

|

there were six years of data (instead of three) for the analysis in Tables 6.1 and 6.2, but crash patterns did not change, only MEV in Equation 6.2 would change. How

“would this affect the value of R.ji?

Crashes on Road Segments Crashes occurring “near” an intersection are usually assigned to the intersection. Mythaca and many other (but not all} jurisdictions define “near” as within 250 ft of the center of an intersection. Crashes on roadway segments between intersections are quantified using a crash rate per hundred million vehicle

miles (RHMVM):

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RHMVM =

crashes

ADT*

__+498 */ year days / year miles in section

"

Example 6.2 Crash rate on a road segment

A 6.1-mile section of Tyler Road in Mythaca County had six crashes

last year. The two-way AADT was

755 vehicles per day. What was the crash rate on Tyler Road last year?

Solution to Example 6.2 Unlike the intersection crash rate, the roadway section crash rate uses the two-way AADT.

M=——_octahes 198 356.9 755 vpd *365 days 6.1mi *

~~

Vi

THINK ABOUT IT Why are several years of data preferable to using just last year's data when computing

RMEV or RHMVM?

In general, RHMVM>200 is cause for concern, but this threshold may vary by road type and location. Does Intersection 2 in Example 6.1 or Tyler Road in Example 6.2 have a crash rate high

enough to qualify as a dangerous road? RMEV and RHMVM are useful measures, but they may not be sufficient when identifying hazardous locations. The Highway Safety Manual [2010] has introduced a

Predictive Method for comparing a site’s crash frequencies against a representative sample of similar roadways or intersections. “Similar roadways or intersections” are defined in terms of their characteristics (e.g., geometrics, AADT, and/or traffic control). Crash frequencies for the similar sites are collected, using several years

of data.

Repression to the mean Because crashes are rare events, their frequency from year to year can be quite volatile. Even if three years of data are used, the corresponding crash frequencies can be misleading. As Figure 6.5 illustrates, a three-year short-term average may significantly overestimate or underestimate the site’s long-term average crash frequency. If a high average frequency for the past three years is used to justify a safety

improvement project, any resulting reduction in the crash frequency might have happened without the project and the money spent on it. See Figure 6.6. This phenomenon — called regression to the mean

(RTM) — is

common in crash data.

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‘Observed Gragh Frequency erin Average Crash Frequency

.

Expected Average Crash Frequency

Short-Term Average Crash Freque

Year.

FIGURE 6.5

Variations in Crash Frequency [HSIP 2010, Figure 2.1]

selected for

ent due to Term Trend



.

_s

/

eg

#

Per Effe

> of

ctual

Reduction

di 1a to Treatment

Expected

AVEr

Crash Frequency (without Treatment)

Years FIGURE 6.6 Regression-to-the-Mean and RTM Bias. From Highway Safety Manual, 2010, Figure 3-5, by the American Association of State Highway and Transportation Officials, Washington DC, Used by permission.

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Safety Performance Functions

Safety Performance Functions (SPFs) can reduce the effects of RTM by estimating the predicted safety on similar facilities. SP¥'s are constructed by plotting crash and exposure data on similar facilities then fitting a curve through the data using an appropriate functional form. Hauer et al. [2001] used the example of a 1.8-mi road segment with annual crash counts of 12, 7, and 8, and AADT of 4000 in each of the three years. The SPF for similar road segments estimates Np, the predicted number of crashes per mile-year, on those similar road sogments, The SPF used by Hauer et al. was: Np = 0.0224 *

AADT

%$(6.5)

Using the AADT for the 1.8-mi road segment as input to the SPF in Equation 6.5: Np = 0.0224 *

4000°° = 0.0224 *

107.538 = 2.41 crashea/(mi-yr)

|

For a road segment of length L, the predicted number of crashes Nety over Y years is:

New =Ne*L*

¥

(6.6)

Tn the Hauer example, L= 1.8 mi and Y = 3 years:

Nevy = 2.41 crashes/(mi-yr) * 1.8 mi * 3 yrs = 13.01 crashes

Because of the inherent variability of crash data, the variance of the annual number of crashes in the reference population is often greater than the mean value. This is called overdispersion. An overdispersion parameter d

= 2,05 per mi was estimated as part of the SPF fitting process for the Hauer

roadway. This parameter will be used in the Empirical Bayes method below.

Empirical Bayes

(EB)

meth

The EB method combines a site’s observed crash frequency with the crash frequency predicted by the SPF for that site, A weight W is needed to combine the observed 3-year crash history with the SPF prediction: t

We

tt

*

(6.7)

(™a *)

where Np =the predicted number of crashes per mi-year at the site, as estimated by the SPF for that site YY = the number of years d=

in the analysis

the overdispersion parameter

For the 1.8-mi road segment,

W

_

1



= 8,221,

2.95 | (28

To estimate the site’s weighted expected crash frequency Ne, use: Ne = (W*Nozy) + ((1-W)*Notel where

Not, = total crash frequency observed over the number of years in the analysis.

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For the case at hand, the expected crash frequency at the site is: Ne = (0.221%13.01) + ((1-0.221)*(12+-7+8)] = 2.88 + 21.03 = 23,91 crashes in 3 years In the foregoing analyses, three terms were used carefully and consistently: *

Observed crash frequency — based on data collected at the site of interest over the last Y years

-

©

Predicted crash frequency estimated by using data for the site of interest (AADT in the example above) in the SPF for similar sites

«

Expected crash frequency — the weighted sum of the predicted and observed crash frequencies

The SPF-based expected value of the three-year crash frequency (23.91) is less than the 12+7+8 = 27 crashes observed over the past three years on the 1.8-mile segment. This adjustment in the crash frequency on the 1.8-mile segment reduces the tendency of three-year data to be too far above or too far below the long-range average crash frequency.

After applying the EB method, the crash frequencies on the 1.8-mi segment and on any other

facility in the group of similar sites can be compared on a more consistent basis. Example 6.3 shows how intersections can be analyzed and ranked for possible safety problems.

if

Example 6,3 Ranking road segments for HSIP projects Four road segments in Mythaca are being considered for HSIP projects. Table 6.3 lists their traffic characteristics and recent crash histories, A statistical analysis of similar roads in Mythaca has produced a Safety Performance Function of Np = 0.0224 * AADT°*, with an overdispersion parameter of d = 2.05, [Hauer et al. 2001) The city wants to rank the road segments, in case funding is not available for all projects this year, Note that Segment B is the Hauer roadway, used earlier in this section to introduce the tmethods and equations.

TABLE 6.3 Road Segment

A

Length 2,2 1.8

Cc

10

DB

Lo

©

Yearl

Year2

Year3

N(obs)

N(obs)

Niobs}

3-yr N(cbs)

3060

8

13

8

29

4600 4950 8725

12

7

8

27

8

12

14

34

12

12

7

31

AADT

&mi)

B

A. Calculate RHMVM

Road Segment Data for Example 6.3

for each of the four road sepments.

B. Calculate Np and Nery for each of the four road segments.

C. Calculate the 3-year Nz for each road segment, Show how to oalculate the weights using the overdispersion parameter.

D. The Highway Safety Manual lists thirteen ways in which to identify “problem sites”. [HSIP 2010, Section 2,4], The excess predicted average crash frequency found as:

EPF =

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6.12

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2

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Calculate EPF for each road segment, using the three-year value for Nom and Np.

E. Rank the road segraents by RHMVM and by the BPF value. Solution to Example 6.3

The results are summarized in Table 6.4. The values have been computed by spreadsheet, Sample calculations are given below the table,

TABLE 6.4 Road

RHMVM Segment

Solutions for Example 6.3

lyr

3-yr

Np

Nery

W

3-yr

3-ye

RHMVM_

EPF

Nea

EPF

Rank

Rank

A

401.3

2.05

13.52

0.250

25,13

3,87

2

2

B

342.5

2.41

13.01

0.221

23.91

3.09

3

3

Cc

627.3

2.72

8.16

0.201

28.80

5,20

1

i

D

170.8

3.74

11,23

0,154

27.95

3.05

4

4

A. Calculate RHMVM for Segment A by (6.4): RHMVM, A =

(8+13+8)crashes

#*10%=

"3000 vpd #365 days *2.2 miles *3

401.3.

yrs

Note that, because we are using three years of crash data, we must use three years of traffic volume.

B. In this example, the SPF is Np = 0.0224 * AADT°5%, 2,72 crashes/mi-yr by Equation 6.5. For intersection C, 1-year Np = 0.0224 * 4950°** =

For the 3-year Np.y, use Equation 6.6:

Ney = 2.72 crashes/(mai-yr) * 1.0 mi * 3 yra = 8.16 crashes. C. For Segment D, Equation 6.7 with Y = 3 years computes the weight as W =

| +

= 0,154.

1

3.74 1] 2.05 2)

27.95,

EPF = No — Nz by Equation 6.9. The No values are listed in Table 6.3. For Segment B, EPF = No Ng = 27 ~ 23.91 = 3.09. —

E, Segment C has the largest RHMVM value; Segment D has the smallest. Segment C has the largest EPF value and Segment D has the smallest. The ranks are unchanged, but using Safety Performance Functions and the Empirical Bayes method guards against Regression to the Mean. Sites with the largest positive EPF values have the greatest potential for safety improvement, ca

en

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Step 2. Diagnonis Once problem sites have been identified as most likely to benefit from safety improvements, each site is examined for patterns and characteristics that may explain safety deficiencies. The best single resource for our purposes is the Collision Disgram. (See Figure 6.7.) The diagrams that were drawn as part of each crash report for a given intersection or road segment are transferred to a single graphic representation

of that location,

FIGURE 6.7 Collision Diagram.

Source: FHWA 2010

in Figure 6.7, 19 crashes are depicted with arrows. Bach event can be tagged with a date, time, and conditions (“nite”, snow, wet). The legend gives the symbols used to represent the type of collision: and “single rear-end, left turn, right angle, and sideswipe. Other collision types could be “head-on” If shown in the in collisions so, specific diagram. vehicle”. It is often possible to detect a pattern the are classified are: trends countermeasures oan be proposed for evaluation, Common categories by which *

Type of collision

©

Severity: fatal, personal injury, or property damage only

*

Contributing circumstances: driving under the influence (DUD, reckless driving, equipment failure, etc.

*

Environmental conditions: weather, roadway surface, lighting conditions

«

‘Time of day: daylight, night, dawn, dusk

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H any of this information is not present on the collision diagram, the original crash report should be checked. After one or more recurring characteristics have been identified, a list of possible causes can be developed. If, for example, right-angle collisions are prevalerit at a signalized intersection, contributing factors to look for include [HSM 2010, p. 6-3]:

«

Inadequate sight distance

*

Inadequate signal timing

»

Poor visibility of signals

©

Excessive speed

Step 3. Countermeasure Identification

For each of the possible causes identified in Step 2, one or more countermeasures can be proposed. Table 6.5 shows some of the countenneasures that could be considered for a signalized intersection that has had a high rate of right-angle crashes.

TABLE 6.5

Sample collision pattern table

Probable cause

Crash patieri

collisions Right-angle at a signalized

General countermeasure

(CMF, if published)

obstructions Remove sight Restrict parking near corners

Inadequate sight distance

Install warning signs

intersection

.

Inadequate signal

;

Modify clearance interval (0.96)

timing Poor visibility of

Replace Incandescent Traffic Signal Bulbs with LED bulbs (6.959)

signals

Install red light running cameras (0.74) Reduce speed limit on approaches

Excessive speed

Install rumbte strips Improve pavement friction (increase skid renistanes) (0.898)

Sources: CMF (undated); HSIP 1981, p. 117; HSM 2010, p. 14-41

Step 4. Economie Appraisal After countermeasures have been proposed, they must be evaluated. The basic evaluation procedure is to estiniate the effectiveness of a particular countermeasure, then compare that estimate against the countermeasure's cost, Estimating a countermeaaure's effectiveness is not easy. A common method is to determine by how much the crash rate will be reduced, then convert that reduction into a benefit in economics terms. There are two serious problems with this method.

i. Itis far from certain how effective a certain countermeasure will be, [f, in Table 6.5, “install red light running cameras" is chosen as the countermeasure, by how much will "right-angle collisions at a Signalized intersection" be reduced? After numerous independent attempts to develop Crash Reduction Factors (CRF) for this purpose, FHWA has established a Crash Modification Factors (CMF) Clearinghouse to standardize CMF data collection and facilitate sharing of CMF values.

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= [FHWA undated} The CMF is a multiplicative factor, related to CRF by CMF 1- CRF. Ifa = and CMF = particular countermeasure is expected to reduce crashes by 23 percent, CRF 0.23 = 0.23 = 0.77. For red light running cameras, the HSM suggests using CMF 0.74, ifno local value [|

has been determined.

2.

Itis difficult to translate any given estimated reduction in crashes into benefits, How much is a human life worth,

if its loss because of a traffic collision can be avoided?

How much is a personal

injury worth? How much should be spent to prevent each Property Damage Only crash from happening? — of ‘Table 6.6 shows crash cost values associated with three levels injury severity fatal, personal costs are based on estimates injury (PD, and property damage only (PDO). [FHWA 2010] The economic of the goods and services that must be purchased or on produotivity that is lost as a result of motor vehicle crashes. They do not represent the more intangible consequences of these events to individuals

and families, such as pain, suffering and loss of life.

TABLE 6.6

Sample Crash Costs for Collision Countermeasure Analysis

Economic Cost [HSM 2010]

Crash Severity

£7,400

Property damage only

$79,000

Personal Injury

$4,008,960

Fatality

If the effectiveness of a particular countermeasure is known, either of the following two equations can be used to determine its benefit: * Crashes prevented = BC

Crasheses

where

predicted predicted

=

EC

*

cre +

forecest ADT base ADT

CMF¥ forecast ADT

6.10) (6.11)

bass ADT

EC = expected number of crashes over a specified time (usually a year) if the countermeasure is not implemented and the traffic volume remains the same

CRF = crash reduction factor (percent) CMF = crash modification factor = — (CRF/100) |

base AADT = traffic volume per day before countermeasure is implemented

forecast AADT = traffic volume per day for specified time after countermeasure is implemented

Note that there may have to be a separate CRF or CMF for each degree of crash severity. A particular countermeasure might be expected to reduce fatal crashes by 12 percent, PI crashes by 33 percent, and PDO crashes by 24 percent. Or, for each crash prevented, the severity of the prevented crash could be drawn from a probability distribution, e.g., 41 percent fatal, 40 percent PI, and 19 percent PDO, A further complication is that a countermeasure may not prevent a crash, but may instead reduce its

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Chapter 6 Safety on the Highway severity, The basis for the CRF value and the use of Equations 6.10 and 6.1 1would have to be adjusted accordingly. In Example 6,4, we use Equation 6.10in a relatively simple form.

Example 6.4 The Mythaca County Engineer's staff believes that installing stop signs at a previously uncontrolled intersection will reduce crashes by 26 percent. In the base year (last year), there were 11 right-angle collisions at the intersection, whose approach volume was 3273 vehicles per day. Ten years from now, the approach AADT is forecasted to be 4000 vehicles per day. How many crashes will be prevented ten years from now, if the stop signs are installed? Solution to Example 6,4

Using Equation 6.10, the estimate of right angle crgshes prevented= 11*0,

26+ fn

a Example 6.4 tells only part of the story.

3.50 per year,

fin

A more complete analysis would include:

a

A. The crashes prevented in the years between the base year and the tenth year. B. Years beyond the tenth year, if the life of the countermensure extended that far. C. An estimate of the cost of the project, apread out over the life of the project.

Let us extend the periad of analysis to

15 years. In those 15 years,

same vate aa in the 10-year analysis. Because

(1+r)” =

traffic is expected to increase at the

— = 1,222, the annual traffic growth rate r=

2.0 percent. In the absence of any countermeasure, CRF = 0,0 in Equation 6.4 and the number of rightangle crashes wili also increase 2.0 percent per year. So, for any year k, Crashes prevented in year k= CP(k) =(EC)* (1+

rj * ORF,

(6.12)

11° During Year 1, CP(1)= 11 * (1.02)'* 0.26= 2.917 crashes prevented. During Year 2, CP(2) = (1.02) *0.26= 2.975 orashes prevented, Over a 15-year period, the total number of crashes prevented would be calculated as follows:

pcre) -|$incva Keo

sa],

+rjP*

(6.13)

one

For EC = 11,

0,02, n= 15, and CRF = 0.26, a total of 50.448 crashes would be prevented. See the calculations in the “CP(k)” column of spreadsheet Table 6.7.

The spreadsheet in Table 6.7 has also been used to estimate the benefit of the crashes prevented.

If one half of one percent of the crashes at the intersection ate fatal crashes and the cost of

a

fatal crash in

Table 6.6 is used, the corresponding value of the countermeasure in the first year is Fatal benefit = 2.917 crashes prevented

*

0.005 fatal * $4,008,900/fatal crash = $58,474.

A similar calculation is done for the proportion of crashes that are expected to be Personal Injury (PD and Property Damage Only (PDO), year by year for all 15 years, The present worth PWB(i) of the estimated

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total benefits TB(i) in each year | is calculated using PWB() = TBG)1+d), where d = 0.03 is the discount rate. Theae yearly present values of benefits are shown in the far right column of Table 6.7. Their sum over the next 15 years is $1,642,960,

Now that the benefits side of the analysis has been completed, the cost estimates for the countermeasure must be made.

If it costs $85 to install each of four stop signs and an average of $15 per

year to maintain or replace each sign, use the [P|A] equation in Figure 5.4 to compute the present worth (at d= 3.0 percent) of the cost to implement the stop sign countermeasure for 15 years: PWC

=P,° +[P|A]=P,° +A

(+4)

=

-1

d(i+d)"

(1+0,03)°-1

(4* $85.00) +(4*$15,00) “| 0,03(1 40.03)" | ~

PWC = 340.00 + 60.00 [11.938] = $1056.28.

TABLE 6.7 11°

0.02

Traffic growth rate

0.195 0.860

PDO

Yeark

15

«EC

Fatals PI

0.005

Crashes prevented over life of countermeasure project 0.26

$4,008,900 $79,000

$7,400

CP(k)

Fatal benefit

Plhenefit

$38,474

$44,939 $45,838 $46,755

1

2.917

2

2.976

3

3.035

$59,643 $60,836

4 § 6

3.096 3.158

$62,053 $63,294

3.221

$47,690 $48,644 $49,617 $50,609 $31,621

years of project Hit

d=

0.03

PDO unit benefit Total benefits PDObenefit

PWB

CRF Fatal unit benefit PI unit benefits

$17,270

$120,683

$117,168

$17,615

$123,097 $125,559 $128,070 $130,631

$116,031

$113,788 $112,684

$133,244 $135,909

$111,590 $110,506

$109,433 $108,371 $107,319

$17,968 $18,327 $18,693

$19,067

$114,904

7

3,285

$64,560 $65,851

8

3.381

$67,168

9

3.418

$68,511

$52,654

$19,449 $19,838 $20,234

10

3.486

$69,882

$20,639

1

3.556 3.627

$71,279 $72,705

$53,707 $54,781

$138,627 $141,399 $144,227

$21,052

$147,112

$106,277

$55,877

$21,473

$105,245

i4

3.700 3.774

$75,642

$21,902 $22,340

15

3.849

$77,155

$56,994 $58,134 $59,297

$150,054 $153,055

50.448 = $1,011,212

$777,157

12 13

Total

$74,159

$104,223 $103,211

$22,787

$156,116 $159,239

$298,654

$2,087,023

$1,642,960

$102,209

In this case, the benefits of the proposed countermeasure far exceed the costs. Often, the analysis is not so clear-cut. Some analyses are very sensitive to the choice of the value of human life, the CRF, etc. An analyst must be clear in stating his/her assumptions, and may find sensitivity analyses helpful. Even

when such crucial values can be agreed upon, there are usually more projects proposed than can be funded in a given budget cycle. For that reason, a system for ranking competing projects must be adopted. Chapter 5 covered ways to rank alternatives.

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«a!

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THINK

IT

ABOUT Do the relative values of the total benefits in Table 6.7 for each crash type seem

|

:

reasonable to you?

£

Step 5. Prioritize Projects

The projects found to be most cost-effective are placed on the safety improvement project list. The scheduling of projects is a management and budgeting activity, but the proper implementation of the projects depends on good design and construction practices.

Step 6. Safety Effectiveness Evaluation

By monitoring the performance of the implemented projects, the agency can collect infertnation that will help make future decisions regarding highway safety improvement projects. To the extent that data can be collected to calculate or update crash rates, safety performance functions, and crash modification factors, Step 6 can be used to provide feedback to the first steps in the Roadway Safety Management Process,

6.2 HUMAN FACTORS AND TRANSPORTATION ENGINEERING

A pavement resurfacing project on 1-46 causes the two northbound (NB) lanes to be closed. NB traffic must cross the median and use one of the two SB lanes until the 3-month project is completed. (See Figure 6.9.) The contractor follows the procedures for workzone signs and markings that are given in the Manual on Uniform Traffic Contral Devices, but a fatal crash and several other collisions occur on the

NB approach to the median crossover in the first few weeks of the project. The County Highway Engineer takes his video camera to an overpass with a clear view of the NB approach during the Sunday afternoon peak period. In the first ten minutes, he records several dangerous maneuvers on video, What can be done to make the workzone safe?

FIGURE 6,9

Northbound Approach to Median Crossover. : i

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7)

“.. oc,

sel

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6.19

More than two miles after being told by a series of signs to merge left, drivere of five vehicles in the right-hand lane (four of which are next to the semitrailer truck) slow down, looking for gaps in traffic in the ieft-hand lane. Traffic seeking to use the off rarnp jnat ahead must either wait ‘behind them in the right-hand lane or use the shoulder, as two drivers are doing here. Photo: Jon D, Pricker

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Human Factors Concepts for Design

6.2.1

Human Factors, also called ergonomics or engineering psychology (Wickens 1999), is the study of how human beings fimetion in their natural or constructed surroundings. (Kantowltz and Sorkin 1983) There ate many examples in everyday life. The design of some devices may have significant consequences

with respect to safety: « «

A punch press

‘The unfamiliar position of the various controls in a rented or borrowed car, especially in the dark

« e e

On which side of this car is the gasoline filler cap? Where on a particular TV remote control is the "previous channel” button? Which way does this door swing? In or out? Are the hinges on the left or right?

While many designe (or the lack of a standard design) may cause unwanted inconvenience or inefficiency, in the case of the punch press, an inefficient design may be the best design. By requiring that the operator use both hands to activate the machine's functions, neither hand is in danger. tm,

gJ

THINK ABOU

iT

‘Think of at least one example of a design (good or bad) that h is safety consequences, then provide at | ast one example of design that causes (or av ids) inefficiency or inconvenience. our examples do not have to be related to tr nsportation activity. —

A classic human factors example in transportation is the aircraft pilot who is surrounded by instruments in the cockpit (or flight deck), The location of the instruments, how readings are displayed, and what physical actions the pilot must take to achieve the desired results are all elements of the design of the cockpit. With the advent of highly-automated flight operations, a different problem may occur: a pilot may need to assume control of the aircraft on a moment’s notice. Will the pilot be able to execute quickly enough the tasks needed to avert disaster?

A more familiar situation is the driving task. Each driver is operating a motor vehicle on 4

of the roadway, The design of the vehicle and the design of the roadway will affect the performance the wide range of driver. At the same time, the design of the vehiele and roadway must take into account Some drivers possible abilities, attitudes, backgrounds, and preferences of drivers using the roadway. as others’, Some drivers are keen is not as drivers! than others. Some have slower reaction times eyesight — new to the country. Some more aggressive than others. Some drivers are new to the area or even drivers prefer certain styles of driving that may not be compatible with other motorists’ expectations. In this section, the challenge of designing for most (if not all) types of drivers and situations will be presented,

Of the approximately 30,000 highway deaths in the US each year, more than 40 percent involve an intoxicated driver, [NHTSA 2013] The remaining fatal crashes are due to highway design, weather, or “driver error". The road environment contributes to 17-34 percent of crashes, and is the sole factor in 2-3 percent of the cases. (O'Cinneide 1995) Of crash causes, driver error is by far the most frequent. According to the Human Centered Systems Laboratories (TFHRC 2001), inappropriate driver

orashes. Even perceptions and behaviors are implicated in 80 to 90 percent of all highway

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has been “adequately” designed to conventional standards, it may not be possible for an enhanced roadway design to counteract some of the effects of weather or “driver error". If an enhanced design is possible, it would be helpful to know how to do it as cost effectively as possible.

h,

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THINK ABOUTIT Is Driving While Intoxicated a highway design issue? How about overly aggressive driving or road rage? If any or all of these are design issues, haw would the study of human factors help the highway designer?

The Driving Task, Operating a motor vehicle on a street or highway can be complex and detnanding at times, but it can be boring at other times. This range of circumstances — coupled with the range of driver

capabilities ~ presents a challenge to the highway designer. It is helpful to begin by considering the three essential elements of the driving task: (Ogden 1990, AASHTO 2001) 1) Navigation (Route Selection). Because most trips are made repeatedly, or in familiar street networks, this is usually the least complex of the driving task elements. However, when a driver

is looking for information to reach a destination in an unfamiliar network, that activity may detract from other driving task elements. Bad examples: Street signs that are missing or hard to

a

Ee

read, Good examples: Signs to frequent destinations (downtown, university, stadium) within a city; notice of the next main cross street (Fig. 6.10) before that intersection,

viee

252

FIGURE 6.16 (above)

Overhead signs help motorists find desired path through intersection. Photo: Jon D. Fricker

FIGURE 6.11 (right)

White line marking roadway

edge, Photo: Jon D. Fricker

2) Guidance (Vehicle Tracking). Staying on the roadway and staying in the proper Jane have obvious implications for safety. Examples: Lane and edge markings (Fig. 6.11) on the pavement, and delineatora along the roadside. (These topics are covered in the section on Traffic Control Devices later in this chapter.)

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3) Control (Object Avoidance). This activity involves proper application of steering and speed control skills, At the basic level, steering around clearly visible fixed objects and maintaining a safe distance from vehicles ahead and to the side constitutes the control element. However, unexpected maneuvers by other vehicles, or objects that appear suddenly, can require a high-

level response (in terms of reaction time, decision-making, and action) that is quite complex.

The three driving task elements are interrelated. For example, failure by one driver to accomplish the Guidance element may cause another driver to exercise Object Avoidance to prevent a collision. Although sounds and feel can provide useful information to a driver, most information comes in a visual form. (Lay 1986) A driver operates in a zone ofspatial commitment that varies by driver and operating environment. (ITE 1982, Hulbert 1972) In Figure 6.12, a vehicle is moving from left to right.

The driver samples cues about what is ahead from a field of vision that is constantly changing. Examples of cues include other vehicles, pedestrians, traffic signs and markings, sharp curves, crests of hills, or any object or circumstance that could create an unsafe condition, At speeds around 30 km/hr, the driver's effective lateral field of vision is about 100 degrees — 50 degrees to the left and 50 degrees to the right. Normally, the driver pays more attention to the objects and cues nearer to the center of the visual field.

Cues may also be detected in the peripheral vision of the driver, outside the normal effective visual field. At 100 kuw/hr, the driver's field of vision narrows to about 40 degrees. (Cole 1972) The closer objects or

visual cues require immediate decisions; the more distance cues provoke a provisional commitment. If the scene is cluttered with too many visual cues, the driver may miss important cues or get confused. The roadway designer's job is to reduce the number of negative cues, while providing just enough positive cues to assist the driver. Of course, many negative oues are beyond the control of the roadway designer, and driver responses to positive cuss may vary. For the 1-46 workzone described af the start of this section, how many warning signs are needed along the approach to the workzone, and where should they be placed?

FIGURE 6.12

Driver's Zone of Spatial Commitment. Source:

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\



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oppINK ABOUT

IT

Give examples of how sounds andfeel can provide information to the driver that ia useful in the driving task.

Perception-Reaction Times. A driver sees most cues (signs, potential threats) soon enough to process them safely by routine driving actions -- reduce speed, change vehicle path, or simply monitor the situation. On rare occasions, the cue appears suddenly and unexpectedly. It requires immediate action by the driver. The time needed for a driver to recognize and respond to the cue is called the PIEV (Perception/Identification/Emotion/Volition) time. [MUTCD 2000, p. 2C-3] Ifthe cus is a sign, * Perception is the time it takes to see the sign. This ia the time needed to locate the cue and classify the cue as a sign to be read, A commonrily used sign wiil be classified quickly, if the driver is paying attention, Unusual cucs may take up to two seconds to be perceived, * Identification is the time to read and understand the sign. Section 2.6A of the Washington State

DOT Traffic Manual (1996) states that "the average driver compreliends three words per second". ©

e

Emotion is the time to consider the sign's meaning and make a decision. Sometimes, the decision is that no action is needed. In other cases, the type of action must be decided. Volition js the time to react or execute a maneuver. A typical driving maneuver is to apply the brakes or tum the steering wheel. Once the maneuver has begun, the volition time (and the PIEV

time) has ended.

According to the MUTCD [2000, p. 2C-3], the “PIEV time can vary from several seconds for general warning signs to 6 seconds or more for warning signs requiring high road user judgment.” Many sources prefer to use the term perception-reaction time, instead of PIEV time.

SOMETHING TO TRY With a good Internet search engine, you can use the string "reaction time test” to find a very large number of tests on the World Wide Web. Try several different reaction time teats. Describe the tests you tried, summarize your results, and comment on the validity

of the tests.

If you tried a reaction time test as suggested in the box above, you were actually measuring your PIEV time, although under special circumstances. The cue was probably very well defined in terms of type of cus and location, The meaning of the cue and the proper response were also clear, at least after your first trial or so, Your PIEV or reaction times on the tests must be considered as your best-case performances, They will not transfer well to actual driving situations. Tanka (1989) looked at several studies of the brake reaction times for unalerted drivers. He found that the typical mean reaction time was about 1.2 seconds, with a standard deviation of about 0.7 seconds. The brake reaction times of

drivers tend to be log-normally distributed. (See Figure 6.13.)

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35

= TA cence a

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papa

tors

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01°63

O05

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09

11

9533

15

#17

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2.11

23

@ Reaction Time ~ Seconds

FIGURE 6.13

Distribution of unaleried driver brake reaction times. Source: Gazis et al. (1960)

AASHTO [2011, Table 3-1] suggests using a driver perception-reaction time of 2.5 seconds for design purposes, even though this value exceeds the 95" percentile reaction time found in most of the studies reviewed by Taoka. When designing roadways and placing traffic signs, clear sightlines and adequate decision sight distance must be provided, especially for the less capable driver. The usual "braking-reaction-response time" for most persons is between 0.6 second and one second. However, we must design public highways to accoramodate a wide range of drivers, whose response characteristics are like those depicted in Figure 6.13. When people are surprised, their reaction time tends to be longer than reaction times that are measured under laboratory conditions. It has been determined that a response time of 2.5 seconds covers over 90 percent of the drivers and should be used in making design decisions. By using standardized-shapes, colors and symbols, and locating the signs in consistent locations, the engineer can simplify the driving task. If traffie signs are easy to see and easy to read, the driver will have more time for the emotion and volition phases of PIEV.

~

L

o

_

THINK ABOUT IT The AASHTO "Green Bo ok" (2011, Table 3-1] suggests usi 1g a driver perceptionreaction time of 2.5 secon ds for design purposes. Based on Taoka’s findings, this is a d. Can a design ever be too conservative? very conservative design :

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Example 6.5 Eastbound County Road 200 South ends at a T intersection with CR 300E.

EB traffic on CR2008

approaches this intersection on a crest vertical curve, requiring the placement of an advance warning sign, especially for nighttime traffic. Ifa typical EB driver is traveling at 50 mph when he sees the

waming sign, how much distance will his vehicle travel before he begins to brake?

Solution to Exampie 6.5 The "T Intersection Ahead" Advance Warning Sign is diamond-shaped, with a black "T" on a yellow background, This sign has a familiar shape and a symbolic (versus verbal) message. According to

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Chapter 6 Safety on the Highway

Figure 6.13, the typical driver encountering the sign on an unsxpected basis has a reaction time of about 1.12 seconds, At 50 mph (or 73.5 fl/sec), the PIEV distance is 1.12 * 73.5 = 82.3 feet. The braking distance calculation will be covered later in this chapter.

pe

fe

Example 6.6

A crash occurred in which the driver stated that she was diving at the 55-mph speed limit, when she came over the crest of a hill and spotted a deer crossing the road. However, the skid marks were found on the roadway for only the last 90 feet before the deer was struck. If the skid marks indicate the beginning of braking and the crest of the hill was about 250 feet from the point of impact, what was the

driver’s response time?

Solution to Example 6.6

—=

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a 6.2.2

250ft-90ft

braking

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Human Factors Applications in Transportation

Subsection 6.2.1 introduced some basic ideas underlying the application of human factors to transportation problems. Elsewhere in this text, Gap Acceptance and the Dilemma Zone are topics that have a strong human factors component. In this subsection, several examples of how human factors can be used to analyze or improve certain situations are presented,

Changing the status quo. Normally, expectancy is a design feature that helps motorists. A straight road will stay straight until a sign that warns of a curve ahead appears. Traffic signals are usually placed above the intersection, on cables or on masts.

However, one kind of expectancy can be a problem ~ the case of being ioo familiar with a location. Consider an intersection that, for many years, has been controlled by stop signa on two of its four approaches. Eventually, the traffic volumes or crash history at that intersection justifies the installation of stop signs on the previously “uncontrolled” approaches. At least some of the motorists

who have driven on the uncontrolied approaches on a regular basis are not likely to notice the new stop signs, even if they are installed according standards, What is the to

solution? Some localities install oversized stop signs on a temporary basis, then replace them with stop signs of standard size aftera

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FIGURE 6.14 ®

to supplement

Temporary stop sign "€W stop sign. Photo: Jon D. Fricker

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week or two. Another strategy is to place temporary stop signs on barrels at the previously “uncontrolled” approaches (see Figure 6.14), to supplement the new stop signs, This method overcomes the habits of drivers who are too familiar with the intersection.

Railroad grade crossings. In the three years 2010-2012, there were 742 deaths at grade crossings in the US. [FRA 2014a] More than half of such deaths are attributable to motor vehicle operator inattention or impatience [Farnham 2000]. Motorists fail to see the train, misjudge its speed, or simply lose a race to the tracks. Many of these fatal collisions occur at crossings with active warning devices. There are about 212,000 grade-level railroad crossings in the US, but only about 62,000 were equipped with active

warning systems, such as gates, lights or bells. [FRA 2014b] How many lives would installing more active warning devices save? In some cases, limited sight distance can be addreased by installing active warning devices. But sound-only warnings may not be enough. A train’s “whistle” and a crossbuck’s clanging bell may not be heard by a driver distracted by conversation, music, or other anabient sounds. Leibowitz [1985] wrote about driver impatience and how poorly many drivers judge the speed of an approaching train. The size of the locomotive and the angle at which the motorist views it deceives the motorist into thinking that the

train is much farther from the crossing than it really is and that it is moving much slower than it actually 18.

As is often the case in human factors, the time at which gates or other warning devices are actuated with respect to the train's arrival is difficult to specify for all drivers. If the devices are not actuated early enough, some drivers may not have enough time to clear the tracks comfortably. If the devices are actuated too early, they will be too conservative for many drivers, especially the impatient ones.

Thirty-six percent of incidents at gated railroad grade crossings are caused by a driver going around or through the gates. [FRA 1998] A segment on the NBC newsmagazine "Dateline” called *Bicod on the Tracks", first shown in October 1997, showed a series of horrifying scenes in which motorists drove around functioning gates, only to miss being hit by locomotives by mere seconds. A young man who was interviewed for the program admitted to trying to beat a train to a grade crossing. He saw the train coming, but he didn't quite clear the tracks and his passenger — his sister — was-killed.

How should a transportation engineer respond to suoh driver (mis)behavior? The "easy" solution is to install barriers that cannot be circumnavigated by impatient or inattentive motorists. One such device is called a “four-quadrant gate". (See Figure 6.15.) The four-quadrant gate blocks vehicular access to the tracks on bath sides of the roadway’s centerline on both sides of the tracks. Another idea is placing barriers along the median on the approach to the grade crossing, to keep motorists from driving around a lowered gate. (See Figure 6.16.)

Ni

THINK ABOUT IT Compare Figures 6.15 and 6.16. Why is the crossing in Figure 6.16 calied a twoquadrant railroad grade crossing?

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FIGURE 6.15

BIGURE 6.16 Two-quadrant railroad grade

Four-quadrant railroad grade

crossing pate. Graphic courtesy of Azatrax, Www wzalray com,

LLC,

crossing gate with median barriers. Photo by Jon D.

Fricker

if the four-quadrant gate is such an easy solution, why aren't more of them being installed? The first problem is cost. Moreover, some people oppose the installation of the four-quadrant gate because it could trap motorists on the crossing. The Federal Railroad Administration studied a variety of supplemental safety measures, [FRA 1998] The results are summarized in Table 6.8, TABLE 6.8

Supplemental Safety Measures for Railroad Grade Crossings

Supplemental Safety Meese

Temporary closure of grade

[FRA

1998]

Coste to Agency

Effectiveness 100

crossing,

Four-quadrant gates

77-82

Gates and circultry: $244,000-5318,000

Annual maintenance: $3746 Mountable curb medians for 60

75-80

$11,006

feet Photo enforcement

78

Capital: $55,000-$75,000 Annual operations: $20,000-830,000

Full grade separation

160

Bridge/road: $1,000,000 (added by authors)

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7

THINKABOUTIT

"in Table 6.8, the “Cost to Agency” for “Temporary closure of grade crossing” is not given, because it is negligible. However, what other costs (and to whom) should be taken into account when considering this action?

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ri on we

Exarple 6.7 Using the information in Table 6.8, estimate the cost to install four-quadrant gates at all 62,000 grade means the percent crossings that now have active warning devices, If effectiveness" in Table 6.8 reduction in fatalities, how many of the 114 fatalities per year at crossings with active warning devices would be prevented? Assuming a 25-year life cycle for the four-quadrant gates and a discount rate of 4.0 fourpercent per year, what would be the equivalent uniform annual cost of installing and maintaining value of a human quadrant gates at the 62,000 grade crossings? Is it possible to determine the apparent

life, based on these calculations? Solution to Example 6.7

Using the midpoint of $244,000 and $318,000 in Table 6.8, the average cost to install a four-quadrant now have active gate aystem at # grade crossing is about $281,000. If all 62,000 grade crossings that * warning devices were to be upgraded in this way, the total installation cost would be 62,000 $281,000 = $17.42 billion. Applying an 80 percent effectiveness (between 77 and 82 percent in Table 6.8) to the 114 fatalities means that 91 lives could be saved: 0.80 “ 114=91.2. The equivalent uniform annual cost

of installing four-quadrant gates at the 62,000 grade crossings is found using the equation aqp|

1620" (+i)? -1

|

g17.420p]

2.040.09% (1.04)> -1

|

O20

sir4ane| 1.665836

A= $17,422B [0.064012] = $1,115,212,000 per year Add to this value the $3750 annual maintenance cost for the upgraded grade crossings: 62,000

* $3750

= $232,500,000

The equivalent uniform annual cost of installing aad maintaining four-quadrant gates at the 62,000 grade = crossings is $1115.212M + $232.500M $1347,712M, The question of the value of a human life is a sensitive one, but it must be confronted in some way.

Given our calculations in this example, the cost to save each life is

$1347-712M million, Isa _ lives 914.81

91

human life worth at least this much? It would have to be, for a rational analysis to support the installation of four-quadrant gates at the 62,000 grade crossings. Of course, it would not be feasible for all grade crossings to receive upgrades in one year. A fifteen-year program [Farnham 2000] will be analyzed later in an example. In this way, the economic burden of such a program may be spread out

aver time, but some of the safety benefits will be delayed. cae

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License plate design and law enforcement. The license plate on a motor vehicle serves two principal functions: (1) to indicate that the vehicle is registered and (2) to uniquely identify the vehicle for law enforcement, data collection, or toll collection purposes. A variety of human factors concepts can be be used to address applied to the design of an effective license plate. [Fricker, 1986] The concepts can two key questions. 1,

Can the license plate be seen? The size and form of the characters on the plate determine the legibility of the plate's "message". All U.S. license plates for cars are 6 in by 12 in. Most states use characters that are 69 mm high. How far away can such letters and numbers be read? That depends

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Chapter 6 Safety on the Highway on the eyesight of the observer. An observer's visual acuity can be mensured in terms subtended visual angle shown in Figure 6.17,

Viawing Distance,

— =Tan &

FIGURE 617

=. 6

of the

DB

tor small angles

Subtended visual angle, 6 [Fricker 1986}

The degree to which visual acuity can vary from one person to another is illustrated in Smith's [1979] results from 2007 subjects. In Figure 6.18, the mean visual angle is 6.0019 radians (0.11 degree), Visual acuity also depends on the character being observed. If a character is easily confused with another character of similar appearance — E vs, F or O vs.Q — an observer may need to be closer to the target to be sure of its true identity. For example, Townsend [1971] found that subjects identified the letter "Q" as an "O" in 23 percent of the cases he tested. (See Table 6.9.)

TABLE 6.9,

Excerpt from Confusion Matrix [Townsend 1971]

agERATI cay

j

ib ny

Se

SENN w

f

RBS GATOS

Stimulus

Response

Percentage

Q

o

28

R

18

F

T

18

T

I

16

H

N

15

J

I

15

.

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FIGURE 6.18

Distribution of visual angle at the limit of legibility (Based on Smith 1979)

Other factors that affect visusl acuity are color contrast between character and background, lighting conditions, and the age of the observer. Older observers tend to have less visual acuity and need mote illumination on the target than they did when younger. This is a major design consideration, especially for traffic contro! devices, as the average age of the driving public continues to increase.

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Chapter 6 Safety on the Highway 2,

Will the symbols be remembered? Even in an era when using video recordings and optical character for recognition are being used to automate the “reading” of license plates, it is still important

it. For this reason, eyewitnesses to remember the plate's message long enough to record it or report in factors the content of the license plate can be designed with human principles mind. The license vehicle in a state with as many vehicles plate number needs to be long enough to uniquely identify a

as Californie, but be as short as possible to assist an observer's short-term memory (STM). The consensus [van der Heijden 1981] is that individuals can process about seven “chunks” of information for retention in STM. The value of seven, however, can be affected by such things as the to "rehearse" the message content as the target is being viewed. This is much easier to

ability

(a)

do if an oncoming vehicle has a license plate on the front, even “NYD”) (b) the ability to combine individual characters into pronounceable chunks, "NID" (or is probably easier to remember than "PGW" or "H9X".

ft

in Example 6.8 Visual acuity.

The county engineer was a front-seat passenger in a car traveling on an interstate highway. When he saw that his car was closing the gap on the car ahead, he decided to try to read the license plate of the car ahead. As soon as he was sure of the number on the plate ahead, he started a stopwatch while noting (a) the location of the plate ahead with respect to a roadside object and (b) the speedometer reading (60 mph) for his car, Because they were traveling through Indiana, he was able to repeat this experiment several times for Indiana license plates. The average “time to target" for Indiana plates was 1.20 seconds. Later, the engineer determined that the numbers on Indiana license plates are 69 mm high. What was the @ for Indiana license plates under those conditions? Use metric units in the visual angle

engineer's calculations.

Solution to Example 6.8 1609.3m

First, convert 60 mph to metric units, meters/sec. 60ai hr

mi

»_t_ 3600 sec

26.83 m/sec.

Using the equation in Figure 6.17,

(6.14)

dan =tane ‘ = distance distance tto target, and of fttarget, D where h H= = height D =

.

@

Here, © is small. il. Here, 9

0,069m * 76 B3ai/eco ¥1D0ece

0,00214. Note that, in Figure 6.18, the mean 6in Smith's experiment was 0.0019, se the result here is reasonable. et

ne

lf

tafe mt

fn

in

ns

nln

ef

me

sar fn ee

Driving with Distractions. How many things can humans do at once? That is a crucial question where the driving task is concerned. The National Highway Traffic Safety Administration

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[NHTSA 2017] estimates that almost ten percent of fatal crashes (3450 people) in 2016 were caused by distracted driving. Erie Insurance

compiled the most common distractions found on fatal crash reports. [Insurance Journal 2014] The order found is given in the list below:

i. Generally distracted or lost in thought (daydreaming) — 62 % 2. Cell phone use (talking, listening, dialing, texting) 12% —

3.

Outside person, object, or event

(rubbernecking) ~ 7%

4,





FIGURE 6,19 Use of cell phones are involved in almost ten percent of fatal crashes. Photo: AAA Foundation for Traffic Safety, 2001

Other cecupants (talking with or

looking at other people in car) — 5% 3. Using or reaching for device brought into vehicle, such as navigational device, 2% headphones

(7,

Hating or drinking —2% Adjusting audio or climate controls -2%

8,

Others ~8%

6.



Twelve percent of the distraction-affected fatal crashes involved at least one driver using a cell phone at the time of the crash. Redelmeier [1998] found that the distraction caused by the use of a mobile phone - even a hands-free device can delay an average driver's reaction time by 3 to 5 seconds, increasing a driver's risk of crashing fourfold. --

Example 6.9 Cell phone distraction.

If it is true that using a mobile phone delay an average driver's reaction time by about 4 seconds, how many extra fect would a driver travel at 30 mph? Assuming an average car length of 15 ft, how many car lengths are involved?

Solution to Example 6.9 30 mph * 1.47 fps/mph

ls a

*

= 4 sec = 176.4 ft. This distance is equivalent to 176.4/15 11.76 car lengths,

mii

ae

lf

in

fn

Gther studies point to drowsiness as a more frequent factor in highway crashes than previously thought. According to a 2005 poll [NSF 2014], “60% of adult drivers say they have driven a vehiole while feeling drowsy in the past year, and more than one-third have actually fallen asleep at the wheel!

Four percent

approximately eleven million drivers — admit they have had an accident or near accident because they dozed off or were too tired to drive. The National Highway Traffic Safety Administration ~-

conservatively estimates that 100,000 police-reported crashes are the direct result of driver fatigue each year. This results in an estimated 1,550 deaths, 71,000 injuries, and $12.5 billion in monetary losses. These figures may be the tip of the iceberg, because it is difficult to attribute crashes to sleepiness.”

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FUNDAMENTALS OF TRANSPORTATION ENGINEERING Chapter 6 Safety on the Highway

Among the countermeasures proposed to counter drowsiness [NCSDR 2001], only rumble strips have a demonstrated effect on crashes. They reduce drive-off-the-road crashes by 30 to 30 percent.

Traffle Control at Workzones. In 1999, 868 workers and motorists were killed in workzone-related crashes. [Walls 2001] The problems with the I-46 workzone described at the start of this section are not unusual, When the County Engineer had a friend drive him through the workzone, he recorded 12 signs over the 4-mile approach to the workzone, warning drivers of the potential hazard ehead, Still, as Figure

6.9 shows, some drivers do not merge until the last few yards.

traffic engineer who wants to warn motorists of a workzone ahead faces several challenges, Temporary signs such as the twelve signs used along I-46 can be placed on the approach to the workzone. If the message is, for example, “Merge Right”, most motorists will comply. The time between when the message becomes visible to a driver and when the desired action is taken will probably be widely distributed. Some drivers may not ever comply. Was the lack of compliance by these drivers a result of not having seen the sign or because of something related to driver attitude? Depending on the answer to this question, lack of compliance becomes a matter of better sign design and placement, or a matter for A

,

law enforcement,

oe Example 6.10

A Zipper Merge.

tn tt

ne

i

Because of a workzone, traffic must merge from two lanes down to one. When the traffic flow rate on the 2-lane approach is less than the capacity (or service rate) of the 1-lane workzone, drivers are given advance warming on a changeable message sign (CMS) that they must “MERGE RIGHT”. Under this “garly merge” system, some drivers merge 23 soon as they can; while other drivers stay in the left lane until just before the merge point. When the approech flow is greater than the workzone capacity, the advance sign’s messages change to “MERGE AHEAD” and “USE BOTH LANES”, A CMS at the merge point has the alternating messages “MERGE HERE” and “TAKE TURNS”. This is called a

“zipper merge”.

A. Using a jam density of 176 vpm, how long would a queue of 1000 vehicles be if all drivers merged early into a single approach lane?

B, Using a jam density of 176 vpm, how long would a backup of 1000 vehicles be if the zipper merge method caused two equal queues?

C. Why is the second method called a “zipper merge”? D. Why is the zipper merge method not used when the approach flow rate is lower than the workzone service rate?

Selution to Example 6.10 ,

——L000veh

_

/la 176veh / mi

ae

= 5,68 mi with the early merge — all approach vehicles in one approach lane

on 7éveh/mi/ia*2ia

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= 2,84 mi with the zipper merge — all approach vehicles on two approach lanes

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C. If drivers take turns entering the workzone, it is much like the teeth on opposite sides of a zipper being connected inte one fastening device.

D. When arrival rate < service rate, approach speeds can be high enough that it would be unsafe to have drivers attempt to make last-second merges.

ff

\

?

Ney,



THINK ABCOT IT Asadriver ayiproaching a we»rkzone with service rate < approach arrival rate (queue building), woruld you prefer

ving the early merge or the zipper merge in effect?

Why?

6.3

VEHICLE ATTRIBUTES THAT AFFECT SAFETY

In roadway situations that involve other cars, large trucks, motorcycles, bloycles and pedestrians, the driver’s ability to cause an automobile to stop, accelerate, or maneuver quickly may determine if'a crash

will occur. Key factors that affect stopping distance are the automobile’s braking capability, the road surface, and the tire tread, 6.3.1

Forees Acting on Automobile

Consider a vehicle traveling up an incline. The forces resisting forward (uphill) motion in Figure 6.20 are

« *

Rayon

=

fox

is the coefficient of rolling resistance, approximated by fon = 0.01*[1+(V/147)] when V is

W

*

frou

cos 8

= the sum of the rolling resistance from the tires of a vehicle weighing

W

Ibs.

vehicle velocity in fps. *

§=the angle between the grade and the horizontal.

©

Ram is the agradynamis force, which will be treated as negligible in this chapter.

©

Reade

= Wain 6 =the component of gravity acting down the incline,

Brot

eee,

“ET

FIGURE 6.20

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Forces acting on an automobile traveling uphill

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There is also the resistance to acceleration caused by the vehicle's mass m, which is

g&

where W= weight of the vehiole, lbs

gis the gravitational constant, 32.2 ft/sec" a= vehicle acceleration, f/sec". ‘The tractive force F, from the vehicle’s engine acting through the wheels must overcome theve resistive forces. According to Newton’s second law of motion, an object accelerates when the net force acting on it is not zero. If the car is moving uphill at a constant speed, the tractive force equals the sum of the

resisting forces.

t

B=

Reon

+

Ryrncta

+

(6.15)

Reco

By substitution, Equation 6.15 becomes Equation 6.16:

+R

(6.16) Wain The same relationships apply to braking, with the rolling resistance being replaced by the force deceleration rate is operating to stop the car through the friction applied to the highway. The braking usually assumed to be a constant, if the car does not go into a skid. If the coefficient of friction is f, the

R=

La+(Wf,cond)+

initial velocity is vo, and the final velocity is vy the distance Dpe traveled during the time the brake is applied is given in Equation 6.17.

D,,

If braking takes place on

a

ott

(6.17)

hill with grade G, the braking distance will be DL

«

vive

FF

nv

(6.19)

erence

2e(f+G) and fis the dimensionless coefficient of friction for the 100 in divided where G is the grade percent by road,

me Example 6.11

in

"€On(f

me

ttan®)

i

lp

fie

a

a

John is driving his 14-foot long automobile at 50 mph, when the traffic signal in front of him changes to the brakes after a yellow, He is 130 feet from the stop bar at the entry to the intersection when he applies one-second reaction time, A. Hf John’s car can decelerate at a rate of 15 feet per second per second, at what velocity will he be moving when he reaches the stop bar? the yellow light is 4 seconds long, where will John be when the light turns red? B. = C, Based on the answers to Part A and Part B, will John be able to clear the intersection (width 50 found in feet) before the light tums red? If not, let us assume he will continue through at the speed Part A when the light changes to red. How long will the light have been red when he clears the intersection?

If

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Chapter 6 Safety on the Highway

Solutions to Example 6.11

A. Use Equation 6.17 to find John’s speed upon reaching the stop bar. Solve for vr 2

4

139 =

SOLA)

yt

= 38.76

Vp

ove,

fps

= 26.4mph

B. The first one second ofthe four seconds of yellow is used to react to the signal. The light turns red three seconds after John applies his brakes. During these 3 seconds, his vehicle travels

X= Vot

sat? =(73.5it/

seo*

sueo)+ (24-158 /se")*(30:)}

= 220.5 ft

- 67.5 fi = 153,0 &

This is 153 — 130 = 23 ft beyond the stop bar. C. The distance at which John’s 4-foot vehicle clears the 50-foot intersection {s 50 ft+ 14 ft - 23.0 f=

4] ft,

The 2



tim time

.

needed

ded at a 38.76 ips is

4)feet

38 Téfs

= 1,06 sec.

THINK ABOUT IT

Under the conditions described in the preceding example, should John attempt to stop upon seeing the start of the yellow light, or should he proceed through the intersection?

6.3.2 Vehicle braking

The design of the highway for safety is based on driver reaction time and the friction coefficient, which is related to the condition of the pavement on which the braking ocours. Although many individuals typically respond to stimuli in one second or less, the reaction time of 2.5 seconds is used in most design calculations.

Table 6.11 summarizes the resulta of using Equation 6,19 on level terrain (G = 6) with friction coefficient values that vary with speed.

TABLE 6.11 Design Speed

(mph) 20 25

30 35

40 45 50 55 60 65

70

Reaction Time (sec)

Stopping distances for different design speeds

Reaction

Coefficient of

Distance

Friction

Braking Distance on level

Computed Stopping Sight Distance (ft)

terrain (fi)

25 25 25 25 25 25 25 2.5

25 2.5 2.3

Fricker & Whitford

13 92 110 128 147 145 183

202 220 238 237

0.40 0.38 0.35 0.34 0,32

33 55

107 147 196

249 314

0.31

120 167 218

0.30 6.30 6.29 0.29 0.28

278 337 415 487 585

462 §38 635

6.35

«86

383

725 B41

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FUNDAMENTALS OF TRANSPORTATION ENGINEERING

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Edition,

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Chapter 6 Safety on the Highway

_oe

The “computed stopping sight distance” caption in Table 6.11 means “the distance needed for a driver to detect an unexpected or otherwise difficult-to-perceive ... condition ..., select an appropriate speed and path, and initiate and complete the maneuver safely and efficiently.” [AASHTO 2001, p. 115]

This distance Is calculated from the following: The distance covered during the driver reaction time trn at the initial speed. That time may be as it short as 0.5 seconds, if a person is very attentive and is capable of quick reactions, or may extend to several seconds for elderly drivers or drivers who are under the influence of alcohol or drugs, or are impaired or distracted,

=

b.

The actual physical distance traveled while the car is being braked (decelerated) to a stop.

These two components combine to form Equation 6.20 for stopping sight distance (SSD): 2

SSD =(t,,. *¥.)+ een nen een 2* 2 (Fysting £ Grade) Vv

6.20 (6:20)

*

The second term in Equation 6.20 is Equation 6,19 with ve= 0, because v= 0 at a stop. The friction coefficient between the road and the tires can cover a wide range of values, depending on the pavement surface materials, the tread on the tires, and whether the road is dry or wet. Icy roads exhibit a coefficient of friction closer to 0.1, but drivers are expected to uso extreme caution and drive slowly under these conditions. The coefficient of friction vsed in Table 6.11 has been assumed to be constant for a given design speed.

Stopping Distance Formula

fxr Coefficient of Feiction as Measured Drect ly or as Compu ted From Standard

0.8

(BATA

AASHTO 2001 uses

f= 0.35 In Table 7.4. 0.3

Example 6.12

f= 0.40-(6.0024*(v-20))

0.2 206

Oe

&0

$0

60

70

Speed o? Vehicle

~

Saf

FIGURE 6.21 Skid resistance for various tire and pavement conditions Source: AASHTO 1990, Figure Hl-1

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FUNDAMENTALS OF TRANSPORTATION ENGINEERING Chapter 6 Safety on the Highway

The presumed road conditions chosen for design purposes are a wet concrete road. It is assumed that the brakes are applied evenly, If the brakes were "jammed-on", the car may be put into a skid. The friction coefficient is actually much lower when skidding; hence the stopping distance is greater. Table 6.11 indicates stopping distance when on level terrain. If there is a hill, the stopping distance may be greater or smaller, depending on whether the car is traveling uphill (in which case gravity will help the driver to stop) or downhill (where the effect is just the opposite). The computed distances in Table 6.11 can be used in highway alignment, traffic signal setting, passing (including road marking), and avoiding objects in the road when on a curve, The “design” values for stopping sight distance are given in Table

7.4, which uses f= 0.35 for all design speeds. cm

mae net

in

et

en

come

if

me

at

a

fn ent fi

an

ten

mi

an

rey mii

re

seen

ifn

en

oe

Example 6.12

As Figure 6.21 shows, the friction coefficient varies with speed. A linear approximation to the f= 0.40 — 0.0024*(y-20). relationship between Design Speed and Coefficient of Friction in Table 6.11 is

f

If increases as a vehicle’s speed decteases during braking, f based on initial will a constant produce a more conservative solution than using the linear using speed that the distance and time to stop for an initial speed of 60 mph are more stopping approximation. Show conservative when using the constant value of f= 0.29 suggested for 60 mph in Table 6.11 rather than the See the heavy solid line on Figure 6.21.

linear approximation,

Solution to Example 6.12 Before combining the linear equation f= 0.40 - 0.0024*{v-20) from Figure 6.21 with gravity in the — — = equation a g"f, recognize that a and g have the same units fi/sec/sec and that f must be unitless. so that f= 0.40 — [0.6024 Because v has units mph, the coefficient 0.0024 implicitly has units hr/mi, hr/mi * (v-20) mi/hr], Let us modify the linear equation so that v in fi/sec can be used: f= 0.40

|e

*Ty—(2041

a]

= 0.40 — (0.0016334(v-29.4)) = 0,448 — 0.001633v. The equation a=

= 14.4-0.053v. The deceleration due to the friction coefficient = + can be approximated as a -14.4 0.053v, where v is in feet per second and a is in feet/second/second. g*f

= becomes a 32,29(0.448-,001633v)

Because a represents deceleration here, the signs change.

The braking time is governed by the equation dv = a dt = (-14.4 + 6.053v) dt or dt=

dv

-14,4+0.053v-

Solving this equation accounts for the changing value of f as the speed of the braking vehicle decreases from an initial speed vo = 60 mph * 1.47 fps/mph = 88 fps: 0

ji—_—* —14.44 .053v -la 0

Yo

~inl44 _ in(l4.4—0.053* v9) _ 50.3 - 42.9 = = 7.4 see The time to brake from 88 fps is tes = 7.4 seconds, when f is allowed to vary as the vehicle slows down. 60 mph is used, When the constant value £0.29 in Table 6.11 for

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Chepter 6 Safety on the Highway

0

t=

83_ 9 aneo

=

32.2%F 32.2*0.29

Likewise, the stopping distance using Equation 6.17 ia given by Xen

_~

88"

2*32,2°0,29

= 415 fi.

Using the constant friction factor yields a slightly more conservative result than the use of the more realistic friction factor that varies with speed. (Seo Table 6.12.) Using Table 6.11 is conservative because it assumes a vehicle moving at 60 mph will need 415 feet to stop. Accounting for the increase in fas speed decreases during braking leads to a lower stopping distence of 380 feet. .

TABLE 6.12 Answers to Example 6.12 Constant £0.29

f= 0.40 — [0,001633(v-29.4)]

Time to stop (sec)

9.4 ses.

7.4 sec,

Distance to stop

415 feat

380 feet

in

se

ne err

if

fone et wifi

6.3.3 Stopping Sight Distance

The stopping sight distance (SSD) in Table 6.11 can be calculated for any given speed. For example, for

V = 55 mph, the SSD includes the time to react plus the time to brake. If $5 mph is the design speed, f= 0.30 in Table 6.11. Equation 6.20 gives us

SSD

=

(55*1.477 = 202.1 + 338,3=540.5 ft

(1.47 *55*2.5)+ 2*32,2*0,30

This is ologe to the entry of 538 feet in Table 6.11, which was computed by a spreadsheet. When the design speed is 65 mph, the coefficient of friction in Table 6.11 at the 65 mph design speed is lower (£0.29) and the stopping distance is longer. The SSD is

SSD =(1.47765* 2.5)+ (65*1.47):

2*32.2*0.29

=s

238,9 + 4883,9 = 727.8 feet

In Table 6.11, the computed value is given as 725 feet, Design standard values of SSD given in the far right hand column of Table 7.4 are to be used for geometric design problems. Ifthe minimum design standard canmot be met under the specified conditions of speed, grade, and/or radius of curvature, then at least one of the conditions must be altered in the design.

en

in

tp

in

fin

i

Example 6.13

A

car is travelling down a 3 percent grade at 50 mph. How much longer than when it is traveling at 50 mph on a level surface?

will the stopping distance be

Solution to Example 6.13

Ifthe AASHTO Green Book's 2,5-second suggested perception-reaction time (see Section 6.2) is used in Equation 6.20, the stopping distance on level terrain is

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FUNDAMENTALS OF TRANSPORTATION ENGINEERING Chapter 6 Safety on the Highway D =

(50*1.477 = (2.5*1.47*50)+ 2*32.2°03 183.8

+

279.6 463.4 =

On a downhill, however, gravity acts to reduce deceleration and increase the speed. Equation 6.20 is used,

D=(2.5*1.47*50)+_—__ 2*32.2*(0,30-0.03)

= 183.8 + 310.7

=

494.5 feet.

-

The difference when gravity is acting with you means that it takes 494.5 feet 463.4 feet = 31.1 feet longer to stop. Table 6.13 shows how downhill grades up to 3 percent affect stopping distance.

TABLE 6.13

f

Vmph

2%

3%

4%

5%

320 392

326

«332

«4339

«(346

400

408

#417

483

495

506

552

565

578

593

427 519 608

10.96%

473

652668685

704

724

13.62%

932

315

AS

031 030

385

030 029

55

Si

Increase from 0% to 5%

Nograde1%

49 50

Braking distance for downhill gradea

464 340

637

987% 12.07% 12.52%

(50*1,.47)7 = 183,8+254,2 D= (2.5 47" 50)+ 2*32.2*+0.03)

With an uphill grade of 3 percent at 50 mph,

= 438 fi, which is 464 - 438 = 26 fi shorter than stopping on a level road. pe

eee

ee

fin art

ant wei

ffce

amt

if

mr

(0.30

effi

Example 6.14 The driving manual for the Department of Motor Vehicles in the State of Alaska states the braking distance for several speeds as indicated in Table 6.14 For the numbers given, what values have been assumed for driver respanse time and the coefficient of friction?

TABLE 6.14 Speed

Speed

Reaction

mph 20

fv/seo

Distance

29

22

30

44

Braking distances (f)

Braking Distance 24

Total Distance

33

57

90

44

102

146

50

74

55

160

60

88

66

70

103

227 310

215 194

7

Source: Alaska DMV Manual, Page 44

Time

~~

|

Coefficient

47

59

49

Response -*|Frictlon

-

387

0.75

£75 0.74

EOS

OO,

Solution to Example 6.14 The answers are given in the shaded portion of Table 6.14. For example, the calculations for v = 50 mph are

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Jon D. Fricker and Robert K. Whitford

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Chapter 6 Safety on the Highway

:

55ft

dist

i

speed 74 ft/sec

..

¥

=

,

=

2*g*dist

8,74 see

(74% / see)

3

2*32.2f/sec™ 1608

ear

= 0,53 from a rearranged

: Equation

6.20,

"

Example 6.15 A. teen-age driver hits a barricade at

a

workzone on a rural county road. The county sheriff's orash

investigator determines the following:

The road is straight and level, with a posted speed limit of 55 mph until the approach to the workzone. « A friction coefficient of 0.30 can be applied to this case. ® The first sign that warns of the barricade can be seen 1000 feet before the barricade, and the second sign can be seen 600 feet before the barricade. Skid marks from the car begin 300 feet before the barricade,

;

*

*

;

The car hit the barricade while moving at about 25 mph. According to the Weather Service, the road was wet but visibility was good.

*

You are asked to testify before a jury about your findings. What will you tell them about braking and .

response time?

Solution to Example 6.15

.. ~~

The car traveled 700 feet from the first warning sign to the initiation of the skid marks.

If the teenager

was traveling at the speed limit, her response time would have been 700 feet/(SS mph*1.47 fps/mph) = 8.66 seconds, This time is far greater than even the conservative 2.5 sec used in Table 6.11. The driver must not have seen the first sign.

The car traveled 300 feet from the second warning sign to the initiation of the skid marks. If the teenager was traveling at the speed Jimit, her response time would have been 300 feet/(55 mph*1.47 fps/mph) = 3.71 seconds. This time is still much greater than the conservative 2.5 sec used in Table 6.11. She must have missed the second sign, too.

If the velocity at impact was 25 mph and f= 0.30, the initial velocity before 300 feet of skidding was, using a rearranged form of Equation 6.19,

~

¥,

=

Vv? +

2g f dass

(25 *1.47) +(2*32,2*0.30* 300)

24.5

fs

57.5 oops.

This speed is a little above the speed limit.

mah

~

/

Y

Fricker

&

~|

THINK ABOUT IT iF you were an expert witness hired to testify on behalf of the teenager, what parts of the analysis in Example 6.15 would you question, in an attempt to weaken the case presented by the sheriff's crash investigator?

Whitford

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6.4

TRAKFIC CONTROL DEVICES

Among his many duties, the Mythaca County Highway Engineer must ensure that roadway signs and markings (Figure 6.22) in the County are properly installed and maintained, Ifa crash occurs where someone thinks that a sign should have been installed, the County may be sued. If the Engineer installs signs without proper justification, his expenditures will increase and the consistency of the sign’s message may be lost. If any sign is stolen,

vandalized, or allowed to become unreadable, and a crash occurs, the County may be sued. In theory, the rules for installing traffic contro! devices (T'CDs) are

FIGURE

6.22 Traffic Signs

Souree: Public Roads, Vol. 56, No. 1, June 1992

quite simple. In practice, placing and maintaining TCDs requires diligence and good management practices. and the County may get sued. Otherwise, public safety may be compromised

64,1 Traffic Control Devices Needed for Safety Although roadway signs and markings are familiar to everyone who uses the roads, there are wellestablished procedures to determine where certain TCDs are needed and how they should be installed. This section will introduce those procedures and the references on which they are based. In doing so, will be presented. Most of the material in this section is based on numerous examples — good and bad — the Manual on Uniform Traffic Control Devices [MUTCD 2009], Ths MUTCD is “the national standard for all traffic control devices installed on any street, highway, or bikeway open to public travel.”

[MUTCD 2009, Section 1A.07]

Rules Governing Traffic Control Devices

6.4.2

A Traffic Control Device (TCD) is a sign or pavement marking that is used to regulate, warn, or guide drivers as they operate their vehicles. An effective TCD meeta five basic requirements.

[MUTCD 2009, Section 14.02] The TCD must: 1. Beneeded. The transportation engineer must identify the need and select the most appropriate TCD, This section will cover warrant analysis, which helps an analyst decide when a regulatory TCD is justified. Too often, TCDs are inatalled where they are not warranted, because of demands by citizens groups or politicians.

~~, ««

THINK ABOUT IT Have you ever seen a stop sign that is clearly unnecessary? What made you think it waa unnecessary?

2,

Command attention. To be effective, the sign or marking must be seen, and seen without distracting the driver from his/her driving task. A sign blocked by other vehicles or foliage (Figure 6.23) will not get the desired response.

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FIGURE 6.23 branches.

FIGURE 6.24 A poorly-fabricated set of traffic

Speed limit sign obscured by

© 1974 Institute of Transportation

signs. Photo by Jon D. Fricker

Engineers, Used by permission 3.

Convey a clear, simple message. Using a standard combination of shape, color, and other graphic design elements, the TCD should be immediately recognizable to the driver and its intended message should be unambiguous.

4,

Command respect. Signs and markings that are poorly designed and fabricated (Figure 6,24) will not have the credibility of properly-installed TCDs. Likewise, unwarranted TCDs can instill a greater degree of disregard for similar TCDs among some drivers. A common example is stop signs used in

residential neighborhoods in an attempt to control speeds. 5.

Be placed to get the proper responsefrom the driver. Sign location is important. So is the placement of pavement markings. The advance warning sign must be placed far enough ahead of the potential hazard to allow the driver time to respond. The solid line that denotes a no-passing zone must not start too early or too late with respect to the aotual section of highway that has inadequate passing sight distance.

643

Signs as'TCDs

Traffic signs are placed into three major classifications, defined by their function — Regulatory, Warning, and Guide Signs. A sample of signs from each category, organized by the chapters in which they appear in the MUTCD, are shown in Figure 6.25. Although there are several exceptions, in general, traffic signs can also be categorized by shape and color [MUTCD 2009, Sections 2A.16 and 2A.11]: » Regulatory: rectangle; black on white or red @

«

Warning: diamond; biack on yellow School Zone: Schoolhouse shape; black on fluorescent yellow-green

®

Work Zone: Diamond; black on orange

*

Recreational and Cultural Interest: rectangle or trapezoid; white on brown

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28. Regulatory Signs. These TCDs carry the farce of law. Violation of the message on the sign can be

punished, normally by fines.

2C. Warning Signs. Although these signs do not carry the direct force of law, a driver’s failure to heed them can be used as an indication of failure to maintain control.

gai

Guide Signs for Conventional Roads and for Freeways and | (2D)

|

| Expressways

"|

(2B), These signs help drivers navigate through complex or unfarniliar road networks, Specific Service Signs (2F), TouriatOriented Directional Signs (2G), and Recreational and Cultural Interest

Area Signs (2H) 6H. Temporary Traffic Control Zone Signs. Almost always, work zones have reduced speed limits, which penalties for violations,

7B. School Zone Signs.

{SCHOGL

case

SPEED LiMit

PM.

A special

of warning

| signs. Note the difference between |

20

the old advance

o

wim

crosswalk gign

(right) and the new “orosswalk ahead”

FLASHING

sign (far left),

8B. Highway-Rail Grade Crossings. These signs are intended to permit the safe operation of both highway

vehicles and @ains in the area ofjoint DSE.

FIGORE 6.25 Traffic sign classifications, with examples by MUTCD chapter [MUTCD 2009]

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ey,



6.4.4

»

THINK ABOUTIT

Besides the signs shown in Figure 6.25, can you think of any other common signs that do not follow the standard shape or color for their cutegory?

Roadway Markings as TCDs

In addition to the signs classified above, the other kind of TCDa are Roadway Markings, They consist of Pavement Markings, Delineators, and Object Markings.

Pavement Markings, like roadway signs, are used to warn, regulate, and inform motorists. Knowing what various pavement markings mean is important to the motorist, because they have the same force of law as signs. Dashed (or broken) lines usually indicate that the driver has permission to pass, if it is safe to do so. Solid lines indicate that maneuvering across them is strongly discouraged (when solid white) or prohibited (when solid yellow). Figure 6.26 shows several common pavement markings for two-lane and multilane roadways.

Yellow Markings ¢

Yellow markings such as centerlines separate traffic flow going in opposife directions.

*

Dashed (or broken) yellow lines on the motorist’s side indicate where passing is permitted on twolane two-way roads.

®

Solid yellow lines indicate where passing is not permitted, although turning into a driveway across them is allowed where not prohibited.

e

Asingle yellow line indicates the left edge of a divided roadway.

(d) Solid and Broken

(c) Broken White

FIGURE 6.26

Examples of Centerline Markings on Highways Source: Florida Depatiment of Highway Safety and Motor Vehicles, 2000

White Lines ¢

White markings, such as fune lines, separate traffic going in the same direction on multi-lane or one-

way roads,

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*

Dashed (or broken) lines separate lanes of travel where changing lanes is not restricted and where the lane use is not restricted.

«

Solid white lines are restrictive. 1.

They tell the driver to remain within a lane and do not move from it until it is safe to do so.

2. They indicate the edges of tanes specified for certain uses where changing lanes Is to be discouraged, 3.

They also mark the outside edge of the pavement or to Indicate the edge of'a shoulder. (See Figure 6,11.)

Transverse pavement markings include crosswaiks, stop lines, tum movement restrictions, and parking spaces. Whenever possible, turn movement restrictions marked on the pavement should be supplemented with signs over the respective lanes. (See Figure 6.10.)

Delineators. Delineators are used to guide drivers through turns, especially at night or at times of poor visibility. The reflecting head of a delineator (Figure 6.27(a)} should be four feet above the roadway, between 2 and 6 feet from the outer edge of the shoulder. Although technically a warning sign, the chevron alignment sign can be used effectively at changes in horizontal alignment. [MUTCD 2009, Section 2C.10] In Figure 6.27(b), chevrons guide drivers through a right-hand curve on a one-way urban arterial.

(b) Delineators. (a) New delineators along dangerous curve. (b) Good use of chevrons as delineators. Photos by Jon D, Fricker

FIGURE 6.27

Object markers are used to mark obstructions within or adjacent to the roadway. The three types of object markers are designated as OM-1, OM-2, and OM-3, as illustrated in Figure 6.28. The Type 3 object marker features diagonal yellow or white stripes on a black background, The stripes should slope downward and toward the vehicle being warned. Thus, as shown in Figure 6.28(c), an OM-3 on the left side of the roadway should have its stripes sloping from "northwest" to "southeast", The stripes on an OM-3R (R = right) would slope from “northeast” to "southwest", as shown in Figure 6.28(c).

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(c)

FIGURE 6,28 Object Markers. (a) OM-1, (b) OM-2, and (c) OM3L and OM-3R. 6.4.5

Photos by Jon D. Fricker

Installation of Signs

The placement of Traffic Control Devices is not an advanced engineering topic, but there can be serious Traffic Control Devices [MUTCD consequences for incorrect installation. The Manual on Uniform still be required. Figure 6.29 shows but some of is a valuable source judgment may guidance, 2009] soine exanyples,

@

fence and Examples of obstructed sign. (a) Stop sign on short post is obstructed by Photos by Jon D, shrubs. (b) Taller post and reroval of obstructions make stop sign visible at same site,

FIGURE 6,29 Fricker

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Figure 6.29(a) shows a shopping center exit that was "controlled" by a stop sign that not only was on a very short post, but it was also placed behind the corner of a fence. In rural areas, the bottom of the sign should be at least 5 feet above the level of the pavement. In areas where cars are parked, the

.

standard height becomes 7 feet. Although the sign in Figure 6.29(a) was located on private property, for safety and lability reasons, the MUTCD requirements should be followed. After several years, the sign

was replaced and the fence was removed, as shown in Figure 6.29(b). Signs that are “cute" as in Figure 6.30(a) should be used sparingly, if at all, because of their tendency to distract rather than inform. On the other hand, just because a sign is not in the MUTCD, does not mean that a minor variation on a standard sign cannot be used effectively, as shown in Figure

i

6.30(b). [MUTCD 2009, Section 14,03]

|

|

i

FIGURE 6.30

Other examples of good and bad TCD use. (a) Caution: Peacock Crossing. (b) Nonstandard sign with clear message. (c) Signs with International origins. Sources: (a) atid (b) Jon D. Fricker; ( c) Source: MUTCD 2009, Figure 2B-11

~\ ==.

@



THINK ABOUT IT Based on the "message" conveyed by the sign in Figure 6.30(b), what would you expect to see ag you continue to drive along the road ahead?

Because of the many languages that may be involved in traveling even modest distances in Europo, road signs there have relied more heavily on graphic representations than written text, Some of the European designs are being adopted by the MUTCD. Examples of sign designs that originated in Europe but are now employed throughout the United States are the DO NOT ENTER signs in Figure

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FUNDAMENTALS OF TRANSPORTATION ENGINEERING Chapter 6

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Safety on the Highway

the second sign 6.30(c). Instead of words, a “slash” is used to indicate prohibited behavior, as shown by in Figure 6.30(c).

6.4.6 Stop Signs for Speed Control

When citizens get concerned about what they consider excessive speeds in their neighborhoods, they often call upon their City Engineer or elected officials to install stop signs at intersection approaches where they do not already exist, However, numerous studies have found that, not only is such a strategy ineffective in reducing speeds, it also lessens the respect that motorists have for other stop signs in the vicinity. When Mythaca’s City Engineer was faced with neighbors requesting stop signs for speed control, he mentioned it to the County Engineer, Example 6.16 describes the subsequent study. (Note: Some students may not been exposed in previous courses to the hypothesis testing procedure that is essential to this example's solution. In that case, the student will have to trust the method shown and concentrate on the interpretation of the results.)

a

a

we

ifn

fie

nan

le

if

et

sem

iit re

an

et

ef

me

Example 6.16 Do stop signs affect speeds?

When the County Engineer’s son Darren was in sixth grade, he had to choose a science project. Even before his father mentioned it, Darren had heard his friends” parents complain about the speed of cats in their neighborhood, known as Archer, (See Figure 6.31.)

FIGURE 6.31 The Archer neighborhood. Only stop signs thet faced EB or WB traffic on Dodge and Evergreen are shown. Block arrows show location and direction(s) of radar gun.

The parents wanted the City Traffic Engineer to install stop signa as a speed control measure. In of stop signs and, furthermore, response, the City Traffic Engineer said that it would be an improper use or to wanted verify challenge the City Traffic he seid that it would not slow vehicles down. Darren asked his father help him Engineer's last statement. He borrowed the county’s old radar detector and decided that getting speeds design the data collection activity, After discussing it with his father, Darren a him would on directions good basis for checking out for EB traffic on Evergreen and both Dodge give mid-block locations in to those the City Traffic Engineer's theories. Then, Darren and his father went Fricker & Whitford

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the Archer neighborhood, haoked the radar gun onto a side window of the family station wagon, and recorded vehicle speeds.

THINK ABOUT IT

bY

Why did Darren choose the locations and directions he did? Would you have done anything differently?

A. Because there isn’t much traffic on the Archer neighborhood streets, it may take a long time to get an adequate semple. Darren wanted to determine the minimum sample size to (2) avoid spending any more time than necessary collecting data while (b) avoiding the need fo return to any sites in the study area. How many vehicle speeds should Darren record at each site? Hint: Recall how the sample size for the speed study in Example 2.7 was determined. From previous speed studies on urban two-lane streets in Mythaca, S = 4.8 mph. The speeds Darren recorded are summarized in Table 6.15. Did Darren collect a large enough sample?

Darren’s dad explained hypothesis testing to him. Darren decided that the generic hypothesis should be: Vehicle speeds at midblock are the same, whether the block ends with a stop sign or not, After

all, this seemed to be the City Traffic Engineer’s position. Did the data that Darren collected support this hypothesis?

TABLE 6.15

Darren’s Speed Data for Archer Neighborhood Evergreen, between Allen end Garfield

Dodge between Garfield and Allen

WB (8-U)

Eastbound (U-S)

EB (8-8)

S$

= stop-controlled

intersection

Allen Intersection Midblock | Midblock

Midblock 21,610

24,324 4.378

23.410 3.837

1,96

1.96

22.539 2,841 1.96

1

1

i

i

B&

56.6

37

39

31.0 34

39.0 4\

3.165 1.96

U = uncontrolled intersection

€ Mean Speed € Standard deviation

© Z for 95% confidence interval

© Error permitted,

B=]

mph

€-Desired sample size n

€ # vehioles observed

= hypothesis: Dodge WB midblock speed Dodge EB midbiock speed 2™ hypothesis: Evergreen EB midblock speed = Dedge EB midblock speed 3" hypothesis: Dodge WB midblock = Evergreen EB midblock 1*

Solution to Example 6.16

A.

The standard z = 1.96 value for 95 percent confidence is chosen from Table 2.7a. The choice of E is less obvious. Knowing that the radar gun has a digital readout that only registers integer speeds, and guarding against the case in

If the mean midblock speed is desixed, Equation 2.4 applies.

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which mean speeds at different sites are not significantly different, a small value of E was chosen: B *1.0mph, Equation 2.4 becomes

N=

Ca

1.96)

=(9.408)"

2=

89 vehicle speeds

B, Table 6.15 shows that Darren was able to record only 39 midblock speeds on EB Dodge between Garfield and Allen before he and his dd had to go home. This was far fewer than the 89 speeds Darren should have collected. However, when Darren calculated the standard deviation for his = sample, he found that S 3.837, If he had used S‘= 3.837 in Part A, he would have calculated N= N= 37. The good 57. What ifhe relaxed the E = 1.0 requirement to, say, E = 1.25 mph? Then

= = things about E 1.25 are that it is only 0.25 mph higher than the E 1.0 value originally chosen and it makes another trip to the neighborhood unnecessary, A problem, however, is that the mean speeds shown in Table 6.15 are about 0.9 mph apart. It is probably unwise to let your “precision parameter” be larger than the differences in the variables you are trying to compare. For a paid consultant's job, more data might have to be collected. For a sixth grade science project, let us concentrate on the

methodology and learn from the experience.

C.

The first hypothesis Darren wants to test is: WB and EB mean speeds on Dodge are equal. This is of interest because, for the observed block, EB Dodge ends at a stop sign at Garfield, while WB = = Dodge at Allen has no stop sign. In Table 6.15, “S” stop sign and “U” unsigned. Thus, EB is the

“UJ-§” direction and WB is the “S-U" direction. To test the hypothesis Ho: [igs = awn, you may have to refer to the textbook or your notes on “two-sided tests” from your probability and statistics course. (The reference used here is Hypothesis Testingfor Comparing Two Means in Lapin [1990], Section 12-3,) If you haven’t yet completed such a course, you will have to trust the method about to be demonstrated. The steps in the method are:

the test statistic 1) Because the number of observations in each direction is greater than 30, compute ws

Zz

where



Xga —

XK

we

po

ed

22,559 23.410tee

nr

=1,086

(6.21)

(¢.837) (28417! 34 39

of the speeds in the observed sample,

X=

fhe mean value

s’=

the variance of the sample speeds,

n=

the number of speeds observed in the sample.

2) For a two-sided test at a 95 percent confidence level, the critical value of

zis

£1.96, If the test

statistic falls ontside the range {-1.96,+-1.96}, the hypothesis must be rejected, Here, Zex=1.086, which lies within the specified range, so the hypothesis Ho: pra = pws cannot be rejected.

Asa result of this analysis, Darren can say that there is no statistically significant difference between the 23.410 mph average speed on EB Dodge (heading toward a stop sign) and the 22.559 mph average speed on WB Dodge (with no end-of-block stop sign). In fact, what little difference that exists between the EB

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and WB speeds is the opposite of what was expected by the Archer neighborhood parents: EB traffic heading toward a stop sign is the (slightly) faster traffic! Perhaps not having to stop at the previous

intersection is an important factor. That is a second hypothesis that we can test in the guise of a

homewerk problem.

ce

mn

ee

CHAPTER 6 SUMMARY Improving safety on a roadway depends on the performance of three components — the vehicle, the driver, and the roadway itself. Each component can contribute to the safety (or lack of it) on 4 roadway. By understanding each of the three components, the transportation engineer can design roadways for safer performance. A framework called the Highway Safety Improvement Program establishes the basis

for diagnosing roadway hazards, proposing solutions, and evaluating their efficacy. An appreciation for how individuals operate their vehicles in the roadway environment — a field of study known as Human Factors ~ can contribute to a better roadway design. Especially important is the recognition that drivers have a wide range of capabilities when it comes to vision, reaction time, and decision-making. Designing for the least capable driver may actually induce less safe behavior on the part of other drivers. Vehicles can have a wide range of capabilities, too. Size, weight, acceleration, and other characteristics can vary significantly from vehicle to vehicle. Something as simple and familiar as traffic signa can have an important impact on roadway safety. Following published standards and adapting them ta particular circuntstances can assist motorists in operating their vehicles safely on a roadway.

ABBREVIATIONS AND NOTATION FOR CHAPTER 6 acceleration capability of a vehicle (usually a constant in this book)

Gace

AADT Annus! Average Daily Traffic AASHTO American Association of State Highway and Transportation Officials Crash Rate, crashes por year crash modification factor Crashes Prevented (year)

Cc

CMF

CPi}

crash reduction factor or percent reduction in crashes

CRE d

DUI

overdispersion parameter driving under the influence of alcohol

De EB

braking distance Empirical Bayes method

EC

expected number of crashes over a specified time (usually a year) implemented and the traffic volume remains the same

EPF

excess predicted average crash frequency

F;F,

fips

engine force applied at the front and rear wheels, respectively. Fr-+ F,= F; tractive force applied by vehicle engine through wheels to overcome resistive forces dimensionless coefficient of friction of the road coefficient of rolling resistance at constant velocity feet per second

FRA

Federal Railroad Administration

F,

f

fron

.

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FUNDAMENTALS OF TRANSPORTATION ENGINEERING

« Whitford

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Chapter 6 Safety on the Highway B

G HSIP

gravitational constant, 32.2 feet per second per second grade in percent divided by 100,

Highway Safety Improvement Program light emitting diodes Million Entering Vehicles MUCTD Manual on Uniform Traffic Control Devices Ne Expected crash frequency

LED MEV

Note

Observed crash frequency

Ne

Predicted crash frequency

NHTSA National Highway Traffic Safety Administration OM Po

PI

PIEV PDO PWC Raccel

Object Markers Initial Cost or Investment personal injury crashes time for Perception / Identification / Emotion / Volition property damage only crashes present worth of a series of Costs weighted average crash rate for a site’s reference population resistance to vehicle acceleration

serodynamic resistance to vehicle motion component of gravity acting normal to the road observed crash rate at site i

Rey

critical crash rate for site i sum

RMEV

of rolling resistance from the tires

crash rate per million entering vehicles erash rate per hundred million vehicle miles

RTM SPF SSD STM

regression te the mean safety performance function

Vo

Stopping Sight Distance Short-term Memory reaction time when driving a car, usually in conjunction with braking Traffic Control Devices total entering vehicles two-way stop controlled intersection velovity at the beginning of vehicle changes in speed

ve

final velocity of the vehicle

TCD

TEV TWSC

instantaneous velocity velocity yehicle miles traveled weight used in Empirical Bayes method weight of the vehicle in pounds

of crash data observed at a site of visual acuity

number of years measure

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GLOSSARY FOR CHAPTER 6 Collision diagram: a graphic summary of the collisions at an intersection for one year or another appropriate time period. Comparison group — a collection of highway segments or intersections that have geometric and traffic characteristics similar to a site being analyzed. Countermeasure: a project that is intended to reduce the crash rate at a site, especially in response to causes identified as part of the HSIP.

Crash Modification Factor: An estimate of how effective a certain countermeasure will be, based on historical data on crash reductions after the countermeasure has been applied. Crash rate: crashes per million entering vehicles at intersections; crashes per hundred million vehicle tiles on road sections,

Crash Reduction Factor: An estimate of how effective a certain countermeasure will be, based on historical data on crash reductions after the countermeasure has been applied.

Critical rate analysis:

A way to determine whether a particular site is dangerous.

Intersection. Use a

representative sample of intersections or roadways to establish a crash rate threshold, then determine

whether the site’s crash rate exceeds the threshold.

Delineators: roadside markers used to guide drivers through turns, especially at night or at times of poor visibility. Emotion is the time to consider the sign's meaning and make a decision.

Expectancy: A design feature that helps motorists by giving them consistent clues and guidance Expected crash frequency the weighted sum of the predicted and observed crash frequencies

Excess predicted average crash frequency — the difference between Observed crash frequency and Expected crash frequenoy

Highway Safety Improvement Program: a framework for planning, implementing, and evaluating safety programs and projects. Human factors: the study of how human beings function in their natural or constructed surroundings. Identification is the time to read and understand the sign.

Y

Observed crash frequency — based on data collected at the site of interest over the last years Overdispersion parameter — quantifies the variation in crash frequency data when the variance exceeds the mean Perception is the time it takes to see the sign, Predicted crash frequency — catimated by using data for the site of interest in the SPF for similar sites

Reference population — a collection of highway segments or intersections that have geometric and traffic characteristics similar to a site being analyzed,

Regression to the mean — a situation in which crash rates are temporatily much higher or lower than the long-term average tate, but are likely to move toward the long-term mean without any intervention. Similar site — a site that is similar to a site being analyzed, in terms of geometry (lane and shoulder width, intersection design) and traffic conditions (AADT, percent heavy vehicles)

Stopping sight distance: the distance needed by a driver to bring his/her vehicle to a anfe stop, given roadway grades, surface conditions, and operating speeds.

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Traffic Control Device:

A sign or pavement marking that is used to regulate, warn, or guide drivers

as they operate their vehicles. ®

*

the minor

Two-way stop conirolled intersection an intersection at which two approaches (usually volume approaches) are controlled by stop signs and the other two approaches are uncontrolled by —

stop or yield signs. Votition ia the time to react or execute a maneuver.

Zone of spatial commitment: the field of vision from which a driver samples cues about what is ahead.

INDEX FOR CHAPTER 6 acceleration, 34 advance warning sign, 24 braking distance, 40 braking-reaction-response time, 24

collision diagram, 15

field of vision, 22

Regulatory, 43

four-quadrant gate, 27 friction cocfficient, 35, 36 Gap Acceptance, 25

response time, 40 RHMVM, 9

grade crossings, 26

Highway Safety Improvement Program, 4

comparison group, 7 Confusion Matrix, 29

Highway Safety Manual, 4

countermeasure, 15, 16, 17,

Human Factors, 20

32

Crash Modification Factors, 16

hypothesis testing, 48 Identification, 23 license plate, 29

crash rate, 5

MUTCD, 41

Crash Reduction Factors, 16 crash report, 5, 15 delineator, 45

Network Screening, 4 object markers, 46

design speed, 38 Dilemma Zone, 25 distracted driving, 31 driver reaction time, 35 driving task, 21, 22 drowsiness, 32

overdispersion, 11 pavement marking, 42, 44 Perception, 23

carly merge, 32 Emotion, 23 excess predicted average crash frequency, 13 Expected crash frequency, 11, 12

Fatality Analysis Reporting System, 5

Fricker & Whitford

Observed orash frequency, 12

perception-reaction time, 24 PIEV, 23

Predicted crash frequency, 12 Predicted number of crashes,

li Predictive Method, 9 radar gun, 49 railroad crossings, 26 reaction time, 23, 35, 36 reference population, 7 regression to the mean, 9

6.54

RMEYV, 5 Roadway Safety Management Process, 4 Safety Performance

Function, 11 sample size, 50

sensitivity analyses, 19 signs and markings, 41 sitallar sitea, 9 aidd resistance, 37 stop signs, 48 stopping distance, 33 stopping sight distance, 36, 37, 38 tractive force, 34 Traffic Contral Device, 42,

47 traffic signs, 41, 43 two-quadrant gate, 27 unalerted drivers, 23

visual acuity, 29, 30 visual angle, 29, 30

Volition, 23 Warning, 43 zipper merge, 32 zone of spatial cornmitment, 22

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REFERENCES FOR 6.1 HIGHWAY SAFETY DATA AND ANALYSIS Airfleets.net (2018), Fatalities by year, https://wwew.airfleets net/orash/crash country USA.htm, Last viewed I July 2018.

CMF (undated). Crash Modification Factors Clearinghouse, Federal Highway Administration, U.S. Department of http://www.cmfclearinghouse.orp/index.cfm. Last viewed I July Transportation,

2018.

FARS (undated). Fatality Analysis Reporting System, U.S. Department of Transportation, National Highway Traffic Safety Administration, htty:/Aywww.nhtsa. gov/FARS. Last viewed 1 July 2018. FHWA (2017). Highway Statistics (Washington, DC: Annual Issues), tables FI-220 and VM-202,

U.S. Department of Transportation, Federal Administration, Highway hitp:/Ayvww thwa dot gov/policyintormation/statis mas of Mar. 30,2017. Laat viewed

1

2018.

Inly

Hauer, Ezra, Douglas W. Harwood, Forrest M. Council, and Michael S, Griffith (2001). “Estimating Method: A Safety by the

Empirical rences. payes

Tutorial”, %20B ic%20Tutorial%202001%20b

420Fiauer, pdf. Retrieved 1 inly 2018, HSIP (1981). Highway Safety Improvement Program, Federal Highway Administration, Document FHWA-TS-81-218, US DOT, June 1981 HSIP (2010), Herbel, Susan, Lorrie Laing, Colleen McGovern, Highway Safety Improvement Program (HSIP) Manual, Report No., FHWA-S4-09-029, Cambridge Systematics, Inc., January 2010

HSM (2010). Highway Safety Manual (HSM), American Association of State Highway and Transportation Officials, Washington, DC Monsere, Christopher M., Todd Johnson, Karen Dixon, Jianfei Zheng, and Ida Van Schalkwyk (2011). ASSESSMENT OF STATEWIDE INTERSECTION SAFETY PERFORMANCE, Final Report SPR 667 for Oregon Department of Transportation, June 2011, Retrieved 8 July 2015 from http://www. oreron,zoviODOT/TD/TP_RES/doce/reporta/201 L/sor667_intersectionsafety.ndf

NHTSA (2016). “2015 Motor Vehicle Crashes: Overview”, Traffic Safety Facts, Research Note, DOT HS 812-318, National Highway Traffic Safety Adrainistration, US DOT, August 2016. NHTSA (2018). Quick Facts 2016, DOT HS 812 45) October 2017 (Updated February 2018), file:///U:/Personal/Downloads/2016%20Quick%20Facta%420(1)ndf Last viewed

1

July 2018.

REFERENCES FOR 6.2 HUMAN FACTORS *

AAA Foundation for Traffic Safety, http:/Awww.aaafn viewed

org/text/research/distraction

phasel.ofm, as

July 2001. AASHTO 2001 and 2011. 4 Policy on Geometric Design ofHighways and Streets, American 1

Association of State Highway and Transportation Officials, 2001 and 2011. Cole, B.L., "Visual Aspects of Road Engineering", Proceedings, 6° Australian Road Research Board Conference, 1972, p. 102-148, As cited in Ogden (1990). Farnham, W.L., "An In-depth Analysis of the Most Effective Railroad Crossing Protection", October 18, 2000, http://www,lakesnet.net/mnnrsef/mnnrsef/farnham, btn. FRA 1998. Crossing Statistics, Federal Railroad Administration, 1998. As cited in Famham 2000.

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FRA 1999, Office of Railroad Development, Federal Railroad Administration, U.S. Department of Transportation, Draft Environmental Impact Statement, Proposed Rule for the Use afLocomotive

Horns at Highway-rail Grade Crossings, Washington, D.C. 20590, December 1999: BS-1, 4-27. As cited in Farnham 2000. FRA 2001. Office of Safety Analysis web site, Federal Railroad Administration, http://safetydata. fra.dot.gov/officeofsafety/Default.asp, as updated June 29, 2001.

FRA 2014a. Office of Safety Analysis, Federal Railroad Administration, updated Friday, January

17, 2014, Retrieved 17 January 2014 from hitp://safetydata fra dot.gow/officeofsafety/default.aspx

FRA 2014b. Highway-Rail Grade Crossing and Trespass Prevention, Office of Safety Analysis, Federal Railroad Administration, Retrieved 13 October 2014 from http:/Avww.fira.dot.zov/Page/P0040 Fricker, Jon D., "Human Information Processing and License Plate Design", Transportation Research Record 1093, 1986, p. 22-28.

Gazis, D., R. Herman, and A. Maradudin, "The Problem of the Amber Signal in Traffic Flow", Operations Research, vol. 8, March-April 1960, p. 112-132, Hulbert, Slade F., “Human Factors and Traffic Engineering”, Traffic Engineering, September 1968, p. 16-24, ITE 1982. Transportation and Traffic Engineering Handbook, Institute of Transportation Engineers, Prentice Hall, 1982. Insurance Journal 2014. Insurer Analyzes Top 10 Driving Distractions Involved in Fatal Car Crashes, http://www insurancejournal com/news/national/20 13/04/04/287259 him, retrieved 13

October 2014.

Kantowitz, Barry H. and Robert D. Sorkin, Human Factors: Understanding People-System Relationships, John Wiley & Sons, 1983. Lay, M,, Handbook of Road Technology, Gordan and Breach, London, 1986. As cited in Ogden (1990). Leibowitz, H.W., "Grade Crossing Accidents and Human Factors Engineering", American Scientist, Vol. 73, No. 6, 1985, pp. 558-562. Lum, Harry and Jerry A. Reagan, “Interactive Highway Safety Design Model: Accident Predictive Module”, Public Roads, Vol. 59, No. 2, Winter 1995. MUTCD 2001. Manual on Uniform Traffic Control Devices, Millennium Edition, Federal Highway Administration, US Department of Transportation, December 2000, including Errata No. 1 dated June 14, 2001,

NCSDR/NHTSA undated. Expert Panel on Driver Fatigue and Sleepiness, National Center on Sleep Disorders Research and National Highway Traffic Safety Administration, Droway Driving and Automobile Crashes, hitp://www.nhisa.dot.zov/seople/perform/human/Drowsy html, as viewed 1 July 2001, NHTSA 2013. Distracted Driving 2011, Traffic Safety Facts, Research Note, DOT-HS-81 1-737, nhtsa.dot.gov/Pubs/811737 nd, National Highway Traffic Safety Administration, http:// -nrd

retrieved 13 October 2014.

NHSTA 2017. 2016 Fatal Motor Vehicle Crashes: Overview, Traffic Safety Facts, Research Note, DOT-HS-812-456, National Highway Traffic Safety Administration, October 2017, last retrieved hitps:d/crashstats nhtsa.dot.gov/Api/Public/ViewPublication/#12456,

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Safety on the Highway

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NHTSA undated. “Mission of the Drowsy Driving Program", National Highway Traffic Safety Administration, hitp://www.tihtsa dot.cov/peaple/injury/droway driving] /index html, as viewed July 2001,

#

*

e

1

NCSA 1999. Traffic Safety Facis 1999 Alcohol, DOT HS 8059 086, National Center for Statistics & Analysis, National Highway Traffic Safety Administration, U.S. Department of Transportation, --

460 Seventh Street, S.W., Washington, D.C, 26590, NSF 2014. Facts and Stats, National Sleep Foundation, http://drowsydrivingorg/about/fucts-andstats/, retrieved 13 October 2014. O'Cinneide, D., "The Relationship Between Geometric Design Standards and Safety", Conference Proceedings, International Symposium on Highway Geometric Design Practices, Boston, Maasachusetts, August 30 - September 1, 1995 Ogden, K.W., "Human Factors in Traffic Engineering", ITZ Journal, August 1990, p. 41-46,

s « «

Redelmeier, Donald A., MD, “Talking Distractions", Recovery, Volume 9, Number 2, Summer 1998. Rumar, K. “The Role of Perceptual and Cognitive Filters in Observed Behavior," Hivnan Behavior in Traffic Safety, eds. L. Evans and R. Schwing, Plenum Press, 1985, as cited in Lum and Reagan 1995, Smith, S.L., "Letter Size and Legibility", Human Factors, vol. 21, no. 6, 1979, p. 661-570. Taoka, George T., "Brake and Reaction Times of Unalerted Drivers", /7E Journal, March 1989, p. 19-21,

*

«

Townsend, 1.T., "Theoretical Analysis of an Alphabetic Confusion Matrix", Perception and Psychophysics, vol. 9, no. 1A, 1971, p. 40-50. TFHRC 2001. Human Centered Systems Studies, Turner-Fairbank Highway Research Center, Federal Highway Administration, U.S, Dept. of Transportation,

httu://www.tibre.sov/safety/safety »

him#Human,

as viewed 22 June 2001,

van der Heijden, A.H.C., Short-term Visual Information Forgetting, Routledge

& Kegan Paul, Ltd,

Boston MA, 1981 e

» e

Walls, Ann, “National Work-Zone Awareness Week Commemorated Across the Nation”, Public Roads, May/Tune 2001, p. 40. Washington State DOT, Traffic Manual, Manual Number: M $1-02, | February 1996. Cited at http://www. wsdot.wa.gov/regions/northwest/signdgn/htm/dgneuide/Intrduction.him Wickens, C.D., Engineering Psychology and Human Performance, Third Edition, Harper Coiling, Publishers, 1999,

REFERENCE FOR 6.3 VEHICLE ATTRIBUTES THAT AFFECT SAFETY «

AASHTO 1990, 2001 and 2011. A Pelicy on Geomeiric Design of Highways and Sireets, American Association of State Highway and Transportation Officials, 1990, 2001 and 2011.

REFERENCES FOR 6.4 TRAFFIC CONTROL DEVICES «

ITE 1974. Introduction to Signs and Markings, Slides and Narrative Notes, Institute of

«

Transportation Engineers, 4 September 1974 MUTCD 2009, Manual on Uniform Traffic Control Devices, Federal Highway Administration, 2009. Latest version available online at http://mutcd.fhwa.dot.gov.

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Florida Department of Highway Safety and Motor Vehicles, Zhe 2000 Florida Driver's Handbook,

@

Chapter 4, htto://www hemv.state,fi.us/handbooks/English/ch_204. html

EXERCISES FOR CHAPTER 6: SAFETY ON THE HIGHWAY 6.1 Highway Safety

- Data and Analysis

Crash Rate on on Gifford Street. As it passes through a fast-growing part of Mythaca, a 0.79mile section of Gifford Street has begun to experience a much higher crash rate than in previous years. Over the past three years, there have been 14, 13, and 15 crashes on this section of Gifford. The 2-way AADT on this section of Gifford is 16,474 vehicles per day. What is the annual crash rate for this 6.1.

section of Gifford Street?

Crash Rate at Intersection of Gifford and Gregory. As Gifford approaches downtown at Mythaca, it crosses Gregory Avenue at a signalized intersection. The four approach volumes per day this intersection are 28,648, 23,856, 12,150, and 10,174. The crash totals for the last three years are 91, 6.2,

56, and 87, What is the annual crash rate for this intersection? Roundabout in West Virginia. The four approach AADT are 5242, 854, 3877, and 944, The 6.4. number of crashes at the roundabout for the previous three years were 9, 10, and 9, respectively. What is the crash rate at this roundabout?

6.4.

Critical crash rate at Fisk and Kissimmee. Although the intersection had

13 crashes

last year,

there were only 8 and 5 the previous two years. The major direction AADT has been 9588 and the minor direction AADT has been 2752 during the last three years. Create a spreadsheet to replicate Table 6.2,

Fisk and Kissimmee as Intersection 21. A. What was the average crash rate at Fisk and Kissimmee over the past three years? Show your

then add

calculations.

B . After adding Intersection 21, what is the value of R,? Show your caioulations., C. After adding Intersection 21, which values in Table 6.2 have changed? D. Show your calculations for Roo. Is Fisk end Kissimmee a candidate for a safety improvement project?

E. After adding Intersection 21, did any other intersections have their status changed with respect to their R.i? Explain,

6.5.

Applying Empirical Bayes Method to Tyler Road crash data, The RHMVM in Example 6.2

waa rather high, but it was based only on last year’s crash data (6 crashes), In the two previous years, there were 7 and 8 crashes on that segment of Tyler Road. Assume the AADT is the same for all years.

A. Caloulate the 3-year RHMVM rate for Tyler Road. B. Use the Safety Performance Function in Equation 6.5 to compute Np for Tyler Road. C, Show your calculations for Nrry, W, Nz, and EPP. D. How would Tyler Road rank against the four road segments in Table 6.4, based on RHMVM? Based on EPF? A collision diagram for the Scenario. The crash described in the Chapter Scenario was a one6.6. vehicle, run-off-road crash that struck several trees. Show how you would represent this crash on a collision disgram. Include all pertinent information that is given, especially directions. If you need to

“invent” any symbols, explain them.

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Crash witnessed by the County Engineer, At about 5 PM on a sunny Saturday in July, the driver of a small vehicle traveling west on Sagamore Parkway is waiting to left onto Blackhawk Lane. 6.7,

For some reason, she begins her turn as an EB pickup truck is approaching the intersection in the left lane at high speed. The pickup truck's brakes were applied, but the small car was hit in the right front fender by the front of the pickup truck. The intersection has four approaches and Sagamore Parkway has a rulsed median. There were no injuries. A. Draw the collision diagram (main box only) for this crash.

3. To begin an analysis of this crash, propose what you think are the two mioat likely "probable causes” of this crash. Explain if necessary. Crashea prevented on Easex Road. A 1-mile section has a current AADT of 6614 and 6.8, RHMVM crash rate of 68.2. Ifa countermeasure with a Crash Reduction Factor of 15.6 percent is applied and AADT is expected to be.9330 ten years from now, how many crashes will have been prevented? Assume the AADT will grow at a constant (compounded) rate over the ten years. Establish safety project priorities on SR361. 6.9. A, Crash Reduction Factors. On two different segments of SR361, a particular countermeasure was installed, The crash rates for the three yeara before and three years after the installation are given below. Compute the Crash Reduction Factors for each of the two sections.

Year: Segment 39,3

2

3

4

5

6

50.0 | 504{

55.2]

45.2)

41.5]

39,5

]

59.91 27.6) 35.9) 46.1 Segment 8.0 | 685 | 67.5) B. Crashes prevented. A 1-mile segment of road has a current AADT of 5650 and RAMVM crash rate of 71.6. If a countermeasure with a Crash Reduction Factor of 20.9 percent is applisd a

and AADT is expected to be 7430 ten years from now, how many crashes will have been prevented? Assume the AADT will grow at a constant rate (compounded) over the ten years.

C. Project selection. It has been determined that an intersection needs to have a traffic signal installed. Signal A will cost $75,778 to install and $1115 per year to maintain. Signal B will cost $86,506 to install and $950 per year to maintain, If the signal is supposed to last ten years before possible replacement, and the discount rate is 4.6 percent, which signal (A or B) has lower Present Worth of Costs? 6.10. Questioning authority. Three things about Equation 6.2 bother the County Engineer. Help him with his third concern by checking the units in the equation. Are the units in the left-hand side of the equation consistent with the units in the right-hand side?

¢.2 Kuman Factors and Transportation Engineering 6.11, Updating the Venn Diagram. Has the driving environment changed since the 1985 study by K. Rumar? If so, give your opinion on which percentages in Figure 6.3 have changed since then, and in what directions. 6.12, Human Factors in Daily Life. Make a list of items or environments that you have experienced that serve as examples of good or bad design from the perspective of human factors. They do not have to be related tc transportation, although transportation examples are preferred,

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Reaction Time Tests. With a good Internet search engine, use the words "reaction time test" to find two different reaction time tests on the World Wide Web. Try them. Describe the tests you tried, 6.13.

aummarize your results, and comment on the validity of the tests. 6.14. Visual Acuity Merge Ahead, The State DOT wants to erect a sign wating drivers of a merge in the road ahead, If the average driver must be able to see the sign from a distance of 400 feet, how tall must the letters be? Use the visual acuity data from Figure 6.18.

Visual Acuity Test — Letters on a Wall, Print out some letters and numbers onto a sheet of paper, using Arial font, bold, point size 36, Attach the sheet to a wall. Ask someone else to start at the opposite side of the room and move forward until a character can be read. Note the character, its height, 6.15.

and the distance to the target, Have the subject continue moving forward until the subject has identified all characters on the target. Which characters were misidentified? Which characters were easiest to see?

Compute the subtended visual angle for each case. What guidance does this visual acuity experiment offer for the design of traffic signs? 6.16. Stopping for a train. You are traveling at 70 mph on a slushy road (friction coefficient = 0,20) when you hear a train whistle. You then see the warning sign that is placed 1000 feet before the gatewill you be to the gate protected railroad grade crossing, You know you must to stop. How close

try

when you come to a stop? Your reaction time ia 1.5 seconds. 6.17. Racing the train. A friend is driving along a local road at 55 mph. This friend hates to wait for anything, even the train that he sees heading for the grade crossing ahead. There is no gate at this grade

crossing — only a cross buck aign and a bell. Your friend makes the decision to try to beat the train to the crossing. Although he can only guess at these values, the train is 1000 feet from the crossing and moving at 40 mph when your friend first sees it. At that time, your friend is §00 feet from the crossing. A. Assume your friend has a reaction time of 0.6 seconds. How far from the crossing will he be when he begins to accelerate?

B. Your friend’s car can accelerate at the rate of 28 R/sec/sec, but it has a maximum speed of 85 mph. How fast will it be going when it reaches the crossing? C. How much time did your friend take to reach the grade crossing? Did he beat the train?

6.3 Vehicle Attributes That Affect Safety

Stopping on a downhill grade. At one point on SR835, there is a 4.9 percent downhill grade. How much distance and time willit take to bring a car traveling at 48 mph to a stop on that downhill segment if the driver*’s reaction time is 2.0 seconds and f= 0.297 6.19. Stopping for a bicycle crossing. A motorist approaching a bicycle path crossing must be able to stop if he sees a bicyclist crossing the road. If vegetation obstructs the driver's vision on a curved approach to the crossing, so that he can only see 345 feet ahead while driving at 45 mph, what must his reaction time be? Use f= 0.35. 6.20. Hitting construction zone barrels. A student is driving on a level road on a cold rainy night and passes a sign warming of a lane closure 520 feet ahead. The student strikes barrels in the closed lane, 6.18,

but he claims that he was not violating the 55 mph speed limit. You are investigating the accident and you will testify in court.

A. What evidence will you seek? B. What will you tell the court? (Be specific about reaction times and possible initial speeds.)

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6.21.

Skidding to a stop. Redo Example 6.15, this time with fus-0.1. What values of initial velocity

time t, de you get? Does this change the conclusions about whether the driver reacted to either sign and was exceeding the apeed limit? 6.22.

Vp and apparent response

6.4

Traffic Control Devices

Traffic Contral Devices. Recently, the County Highway Engineer observed a two-person crew about to install a traffic contro! device in a workzone on the campus of Mythaca State University. At the base of the signpost were two signs, both with the message "Two Way Traffic Ahead", One sign had a 6.23.

rectangular shape with black lettera on white background; the other was diamond-shaped with black on yellow. Ifthe crew was making the correct change, which sign would be the correct one to put up?

A. Diamond-shaped with black letters on yellow background B. Rectangular shape with black letters on white background

Briefly explain your answer. 6.24. Traffic Control Devices. A driver on the northbound (NB) approach to a stop-sign-controlled intersection sees the sign and supplemental plaque shown below. Drivera on which approaches to that intersection will have to stop? Circle the approach directions that comprise your answer. A. EB D. WB B, NB C. SB

CROSS TRAFFIC DOES NOT STOP

|

Traffic Control Devices, The three SB lanes on Northwestem Avenue (as it enters the °T" intersection with Cherry Lane) are marked as shown in the figure below. (SB traffic moves from right to left in the figure. Lines "C-C" represent the ourb; it flares out to form a right turn only lane. Line "D-D* 6.25,

is the stop line af the intersection.) ¢

A. What color should the solid centerlines "A" be? B. What color should the dashed lines "B" be?

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6.28

The City Engineer wants to try to “help” SB drivers decide whether to stop immediately upon seeing a yellow indication on the traffic signal, He wants to convert the last X feet of the dashed line “B” separating SB through traffic into a solid line. If the signal turns yellow before the driver reaches the solid portion of the line, the driver should stop. Otherwise, proceed at a legal speed. Ifthe speed limit is 30 mph, but drivers typically approach the intersection at 35 mph and the approach is 2 percent downhill, how long should the solid line be? Assume driver reaction time is 1.5 sec and the coefficient of friction can be taken from Table 6.11. Stop sigus for speed control, Use Equation 6.21 to statiatically test the second hypothesis in Table 6.15 at the 95 percent confidence level. Based on this result only, does the presence of a stop sign affect mid-block speed? Use Equation 6.21 to statistically test the third hypothesis in Table 6.15 at the 95 percent confidence level. Based on this result only, does the presence of a stop sign affect mid-block

speed? Based on the results of Example 6.16 and Parts A and 8 of this exercise, do stop signs reduce mid-block speeds?

bays

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HIGHWAY DESIGN FOR SAFETY (GEOMETRIC DESIGN)

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SCENARIO As SR361 approaches Shoridan from the east, it crosses the Mythaca River by means of an old truss bridge. The bridge takes SR361 not only over the river, but also over the road that runs alongside the river — fittingly called River Road. Because of new trip patterns and increasing traffic volumes, Shoridanarea Officials have called for a direct connection between SR361 above and River Road below.

At present,

the connection must be made by driving to the outskirts of Shoridan, then doubling

back more than a mile to River Road. The other alternative is for traffic to leave SR361 several miles east of the river, then use county roads with limited capacity and poor sight distances to reach River Road. The proposed direct connection would involve a significant change in elevation, from the bridge level, down a hillside, to the river valley level. The proposed connector road presents safety problems, in that grades, curves, and be to speeds will have to controlled maintain safe driving conditions. To make the design challenge even more difficult,

7

FIGURE 7.1 Highway 361

bridge over River Road. Photo by Jon D. Fricker

the hillside to be used for the connector road has already been developed. Numerous homes have been built to take advantage of the views of the Mythaca River Valley and Murdoch Bay. Any connector road

to the valley will have to remove several of the homes. It would be desirable, of course, to remove as few hillside homes as possible. Moreover, there may be environmentally sensitive areas in a preferred right of way that will have to be avoided or mitigated. In many ways, highway design is a three-dimensional “puzzle” that must be solved by the engineer and supporting staff.

CHAPTER OBJECTIVES By the end of this chapter, the student will be able to ... 1. Determine the elevation of specified points along a vertical curve. 2. Calculate the key dimensions of a horizontal curve. Design vertical and horizontal curves using safe stopping sight distance. 4. Determine the appropriate bank angle (superelevation) for safe travel around a horizontal curve. 3.

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FYI Many of the equations, tables, and design curves in this chapter are credited to “AASHTO”. AASHTO stands for the American Association of State Highway and

Transportation Officials, the organization that publishes 4 Policy on the Geometric Design ofHighways and Streets. This publication, commonly called "The Green Book", contains the standards for geometric design that are followed by most jurisdictions in the United States.

7.1

THE CHALLENGE OF ROADWAY ALIGNMENT

7.1.1, Overview Geometric Design is the term used to describe the way in which highway designers try to fit the highway to the terrain while maintaining design standards for safety and performance. Initially, a preliminary idea of the road alignment will be laid out. This will be followed by careful geometric design that will:

A. Adhere to design standards pertaining to hills and curves. The ability of the driver to sce (and avoid) obstacles ahead will be brought into the design specifications.

B. Provide a context in which to analyze and evaluate the construction and marking of a proposed highway section.

C. Determine the extent to which design standards will permit realignments to route a proposed roadway around specific locations of special value or to handle environmental situations such as wetland protection.

D. Produce “blueprints” for construction. The challenge of geometric design can be summarized as “fitting ‘conventional curves’ onto irregular terrain with specified benchmarks while maintaining smooth transitions between roadway segments.” [AASHTO 1994] The results of geometric design are a set of coordinates through which the roadway will pass to connect specified starting and ending points. Figure 7.2 shows the “plan and profile” of an alignment that requires both horizontal and vertical changes in roadway direction and elevation. Note that the horizontal layout and the vertical layout appear on the same drawing. However, the engineer will have to relate the station numbers on one diagram to the other. They do not necessarily appear directly above one another in the figure. To further illustrate The Challenge of Geometric Design, consider Figure 7.3.

Figure 7.3 shows four alternative schemes for crossing the Charles River in Boston as part of the gigantic Central Artery and Third Harbor Tunnel project. These four alternatives were among a large number of alternatives that were evaluated. The criteria for evaluation included the homes and businesses that would have to be moved, the amount of open space that would be lost, the wetlands that would have to be protected or replaced, as well as adherence to modern highway safety standards. The challenge in Boston was a vastly more complex version of the SR361-River Road project presented in this chapter’s scenario, because there were many more connections that had to be made or preserved.

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Four alternatives for crossing the Charles River. Source: Holly Sutherland, Central Artery/Tunnel Project, Boston MA

The photographs in Figure 7.4 show just how complex a modern urban alignment can be. Engineers must design curves, bridges, and other structures for the transportation facilities that will disrupt as little of the urban area as possible.

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Bocas FIGURE 7.4 Aerial photos of Boston’s Central Artery Project Above: Bridge construction over the Charles River. At right: The elevated Central Artery (I-93) winds its way through downtown Boston. Photos used by permission of Dennis Rahilly, Central Artery/Tunnel Project, Boston MA.

7.1.2

Geometry of Vertical Curves

Vertical alignment of highways consists of grade tangents connected by parabolic vertical curves. The beginning of the vertical curve is designated as the vertical point of curvature (VPC) and the end is the vertical point oftangency (VPT). (See Figure 7.5.) The grade of the initial (back) tangent is G; as it reaches the VPC. The grade of the final (forward) tangent is G2 as it leaves the VPT. If the initial and final tangents were to be extended as straight lines over the parabolic vertical curve in Figure 7.5, the two straight lines would cross at the vertical point of intersection (VPI). The length L of a vertical curve is measured horizontaily between the VPC and the VPT, not the along roadway surface. Likewise, any distance x from the VPC is measured horizontally. “A parabolic curve ... centered on the VPI is usually used in roadway design.” [AASHTO 2001, p. 270] This means that the VPI is at the halfway point (L/2) of the vertical curve, even when the approaching grade is different from the departing grade. (See Figure 7.5.) Such curves are called equal tangent vertical curves or symmetric vertical curves. When the tangent grades G; and G2 are equal, the VPI will occur over the highest point of a crest vertical curve or below the lowest point of a sag vertical curve. (See Figure 7.6) The usual maximum grade for urban streets is about 8 percent. [AASHTO 2011, p. 3119] Higher grades may exist in areas where the topography requires it. Vertical curves in which the initial grade G, is greater than the final grade G: are crest vertical curves. Sag vertical curves (see Figure 7.6) have Gi< G2. Grades can be expressed in terms of percent, or they can be expressed as change in elevation (feet) in relation to change in horizontal distance (feet). For example, a 4-percent grade would have the equivalent value 0.04 feet/foot, which is actually dimensionless. In this chapter and in other sources, always check the units being used in a particular equation or example.

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Highway Design for Safety

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Chapter 8 Design of Intersections for Safety and Efficiency

8.3

ANALYSIS OF SIGNALIZED INTERSECTIONS

Introduction It is a little-known fact that motorists can drive through downtown Mythaca on eastbound Acorn Avenue and never have to stop for a red light. The reason that this fact is such a secret is that it only works if eastbound drivers maintain a constant speed ofa little less than 20 mph. This section of Chapter 3 introduces ways to summarize a signal timing plan and analyze how well a series of signals are coordinated. In addition, actuated traffic signals are explained and a method to estimate the delayy caused by is by traffic signals

8.3.1

gna

caused

an

FIGURE 8.12 The light is green at 3 Street, 4% Street, 5%

Street, and

9

Street. Photo: Jon D. Fricker

Traffic Signal Timing

The standard traffic signal cycle consists of green, yellow, and red indications, but how long should each indication last? As the green indication on one street is lengthened, less time out of the cycle is available for the green indication on the cross street. The respective green indication durations will depend in large part on the traffic flows on each intersection approach and the capacity of the intersection to allow certain traffic movements to take place. Ifa large number of drivers want to turn left, a separate left-turn-only indication may be necessary. At this point, some basic definitions that will be used in this section are in order.

Indication: What the user sees (green, yellow, red, arrow, etc.) on the traffic signal as (s)he approaches the intersection. The user may be a motorist or a pedestrian. In this section, to keep things simple, we will focus on what the motorist sees. [FHWA 2013]

*

Phase.

®

Cycle. The length of time between consecutive occurrences of the same point in the green-yellow-red

£

@

Ff

A movement or set of movements governed by a given signal indication.

C



of indications. A common point to use is the start of the green indication on the major street approach. If the time from one “start of green” to the next “start of green” is constant, the signal sequence

e

cC

timing is “pre-timed”. If the signal timing varies in response to traffic flows detected by sensors such as loops in the pavement, the signal is “actuated”.

At any time during a signal’s cycle, the indication in effect for each approach (and turing movement, if present) can be noted. This combination of indications is known as the interval. As the FHWA Traffic Signal Timing Manual puts it, “The duration of time during which the indications do not change their state (active or off).” [FHWA 2013] The simplest example is when all approaches showa red indication. This is called the all-red clearance interval. When any of the indications that Interval.

define the current interval changes, a new interval has begun. A simple form of a Traffic Signal Timing Form is shown in Table 8.4. (The timing plans used by traffic engineers employ a much more detailed and complex format.) Note that there are nine intervals at the intersection being studied. The first interval consists of a green indication seen by both left-turning

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entering the intersection during green, and is leaving the intersection as the signal turns red. The NB solid vehicle is entering the intersection as the signal turns red. The lesson: Establish rules that represent driver behavior, then draw vehicle trajectories according to those rules. In the example that follows, the SB dashed vehicle is illegal, but the other three vehicle movements will be permitted.

—-i-

—-—





Example 8.7 Drawing a Time Space Diagram After numerous complaints about the signal progression (or lack of it) on Acorn Avenue from 1" to 5® Streets have gone unheeded, some citizens decide to study the situation themselves. They collect data on current signal timings and put them into a data file with the format shown in Table 8.5. (The citizens used their wristwatches and recorded events to the nearest second. They could have asked the City Traffic Engineer for the signal timing plans, but (a) the plans might be too complex for untrained citizens to read and (b) they wanted to record what the actual timings are.) On this section of Acorn Avenue, the cross streets are 50 feet wide and 330 feet apart, but only 1*, 2", and 5" Streets are signalized. The westernmost signal is at 1* Street. The speed limit on Acom is 35 mph. The “04” appearing before “FIRST STREET” in Table 8.5 means that four cycles were observed at that signal. The first three fields contain the clock times (HR MIN SEC) at which the signal turned green. The last three fields in each data row contain the clock times for the start of red. Thus, the signal on Acorn at 1" Street turned green at 9:57:51 AM and tumed red at 9:58:20 AM. A. Determine the length of the G+Y and Red indications at each signal. Are the signals pre-timed? What is the cycle length for each signal? B. Is it possible for a vehicle to maintain a constant speed and proceed through the three signals on Acorn? If so, in which direction(s) and at what speed(s)?

TABLE 8.5

TABLE 8.6

Signal timing

data for Acorn Avenue

GY

Red

Cycle

29 sec.

31 sec.

60 sec.

0 sec.

2m

21 sec.

39 sec,

60 sec.

11.5 sec.

50

25 sec.

35sec.

| 60sec.

Cross street at 1*

Ut FIRST SC Rastal (S731 09 84 20 OG

383i

OB Ay

af

(Py SO Sty

Vy

100 40 TOM

2h

OM

SECOND STHOiT

10.05 33 1004 02 10.04 25 1G YR OF

ID GS02 43

105 23

Summary of data for Acorn Avenue

(master)

| Green Offset

|

27.5 sec.

TABLE 8.7

|

Event coordinates for Acorn Avenue Time Space Diagram RI G2 G3 R3 Approac | Dist. | G1 R2 h

EB at

0|0

1*

29

60

89

120.

| 149

120

149

KU

WBat 1*

BIFI1 STREET

EBat2™ | 330/115

[32.5

|71.5

|925

WBat | 380/115

|325

[71.5

[925

27.5

| 52.5

87.5

W125

| 147.5

| 172.5

27.5

| 52.5

87.5

112.5

| 147.5

| 172.5

4% iO Re TE 10 GU 19 10 1343

TOTE TE

bE

fa

131.5

| 152.5

[131.5 | 152.5

gad

EB at 5* |

WBat 5" Fricker and Whitford

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Solutions to Example 8.7

A. During the four cycles observed at 1" Street, the G+Y indications lasted approximately 29, 29, 29, and 30 seconds. The slight variation is probably because the citizens used wristwatches, not stopwatches. Use G+Y = 29 seconds. The first red indication started at 9:58:20AM and ended at

9:58:51AM — a duration of 31 seconds. The next two red indications were measured as 30 and 31 seconds. Use 31 seconds. The cycle length is 31+29=60 seconds. Enter these data into Table 8.6 for 1* Street and carry out similar calculations for 2™ and 5“ Streets. Because the indications are constant (within measurement error), the signals appear to be pre-timed. All the cycles are of the same length, so signal coordination is possible.

B.

A Time Space Diagram will allow us to look at the quality of the signal progression in either

direction. One necessary ingredient is the offset of the signalized intersections with respect to the master signal. Let us adopt 1* Street as the master signal. The master signal has been observed (in

Table 8.5) to turn green about 50 or 51 seconds into each minute. At 2™ Street, green starts about 2 seconds into each minute. Thus, for any given minute, you can expect the signal at 2™ Street to turn green about 11 or 12 seconds after the green starts at 1" Street. A green offset of 11.5 seconds is entered into Table 8.6 for 2™ Street. Likewise, the 5“ Street signal turns green either 27 or 28 seconds after the 1" Street green. Use 27.5 seconds as the green offset. We are now ready to draw the Time Space Diagram for this section of Acorn Avenue. A good way to organize the drawing of & TSD is to determine the coordinates of each event to be included in the TSD. For example, because Acorn at 1" is the master intersection at the west end of the corridor being studied, it becomes the point of reference or “origin” for the time-distance coordinates used to draw a TSD. In this example: e e

The stopline for EB traffic on Acorn at 1" Street is the point where distance = 0. The start of green forEB traffic on Acorn at 1" Street is the point where time = 0.

The time and distance coordinates for start-of-green and start-of-red events at each intersection for a time frame 3 minutes long have been computed and entered into Table 8.7. Plotting these points and using them as the corners of the bars to represent red indications produces the TSD shown in Figure 8.14, The effort to draw the TSD is worth it. It is clear that an EB vehicle could avoid red lights at

ali three signalized intersections, if it could maintain the right speed. One example is the vehicle represented by the dashed line starting at coordinates (time=60, distance=0) in Figure 8.14. The dashed line is defined by the time-distance coordinates (60,0) at 1* Street and (71.5,330) at 2™ Street.

The corresponding speed for the dashed line is

_G30-O)R_ _ 28.7 ft/sec =19.5 mph.

Part B

(71.5 —60)sec

asked for a range of speeds at which a vehicle could avoid all red lights. What this means is finding (1) the “flattest” vehicle trajectory that can fit through all the G+Y indications in the TSD and (2) the “steepest” vehicle trajectory that does not exceed the speed limit. In the Acorn Avenue TSD, the flattest non-red trajectory is from the start of green at 1* Street until the end of G+Y (or start of red) at

5 Street. The corresponding speed is

(1320-0) ft (112.5

-

60) sec

= 21.1 ft/sec =

14.3 mph. The steepest no-

red vehicle trajectory starts at the end of GtY at 1" Street. A vertical line (infinite speed) will not encounter a red signal. Therefore, the acceptable “green wave” speed range is from 14.3 mph to the

35-mph speed limit for EB traffic.

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In the WB direction, two “green waves” appear possible. First, all signals are green on Acorn between 27.5 and 29 seconds in the TSD. However, a WB vehicle would have to cover the 1320 feet between 5" Street and 1* Street in 1.5 seconds or less, meaning it would be traveling at least 600 mph. Instead, a WB vehicle crossing 5“ Street at 27.5 seconds could reach 2™ Street at 71.5 seconds and .

continue through a green indication at

1"

st

Street, maintaining ac onstant speed o:f

(3*330)feet

(71.5-21.5) sec

_ 22.5 =

ft/sec or 15.3 mph. A green wave line drawn from t = 52.5 seconds at 5“ Street to t = 71.5 seconds at 2™ Street will pass through the green indication at 1" Street with a constant speed of 52.1 ft/sec or 35.5 mph. WB traffic on Acorn Avenue can enjoy a “green wave” at a constant speed between 15.3 mph and the 35mph speed limit. —

The method for drawing a Time-Space Diagram used in this section involved several simplifications. One was the rule that all drivers would enter an intersection on green or yellow, but would not enter an intersection when the signal was showing red. A greater simplification is that vehicles assume a constant speed S instantaneously — no acceleration from zero to S is accounted for. Likewise, the deceleration from speed S to zero is assumed to take place immediately. Once the fundamentals of drawing a Time-Space Diagram are learned, an analyst can incorporate a non-linear trajectory that reflects vehicle acceleration and deceleration.

THINK ABOUT IT Using a facsimile of Figure 8.14, show what the vehicle trajectories would look like for starting and stopping vehicles with realistic acceleration and deceleration characteristics. In what way would these details improve the analysis in Example 8.7? Besides the extra effort to draw non-linear trajectories, in what way do these details make the analysis more

complicated?

8.3.3 Actuated Traffic Signals Pre-timed signals are easy to understand and analyze, but they can be an inefficient way to use the available intersection capacity. Each intersection approach has a saturation flow rate, which is the number of vehicles per hour that could enter the intersection if the signal were always green. Of course, the various approach directions must share the amount of time out of each cycle that is devoted to green indications. As more green time is allocated to, say, the EB and WB traffic, there is less for the ather

If the EB and WB traffic clears the intersection well before its pre-timed green indication is finished, and traffic on other approaches are waiting, the result is unnecessary delay. Likewise, pre-timed intervals for pedestrian use that are not fully used are also wasteful. The alternative is demand-actuated signals. Actuated signals adjust signal timings in response to information provided to the traffic signal controller by detectors. Normally, the detectors are inductive loops placed in the pavement on the approaches to an intersection. However, video technologies are becoming more common. (See Section approaches to use.

2.1.4.)

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THINK ABOUT IT Without measuring the length of indications and signal cycles at a signalized intersection, what is a good (but not perfectly reliable) way for an observer to determine whether the signals are actuated?

If only the minor street approaches are equipped with detectors, the major street will be given a indication until a vehicle is detected on the minor street. This is known as semi-actuated control. green (See Figure 8.16.) Fully-actuated signals rely on detectors on all approaches. The typical data gathered from detectors are: @

The presence of a vehicle in the detector's "field of view"

The time at which that presence was detected. The traffic signal controller translates these data into information needed in order to apply some rules for traffic signal control. Examples of the information needed are: @ Presence time. How long has a vehicle been continuously detected by a detector? The detector for this purpose is probably located at the stop line for the approach. @ Passage time: How long has it been since the most recent vehicle has been detected? The detectors for this purpose are probably located 100 feet or more "upstream" of the approach's stop line.

fc

¢

(b)

(a)

FIGURE 8.16 (a) Semi-actuated Intersection. (b) At same intersection, the loop beyond the stop bar detects each right turn on red, Photos: Jon D. Fricker

To illustrate how such information can be combined with some rules to produce more efficient signal timing for an intersection, consider the case of the intersection shown in Figure 8.17. Stadium Avenue is the major street. University Street (one-way NB) is considered the minor street, although it can carry heavy traffic at times. Stadium Mall is a dead end street with few vehicles, except at peak periods. In the

“Traffic Signal Logic“ box below, rules convert the information generated by detectors so that (a)

Stadium Avenue keeps the green whenever possible, (b) University Street gets green until there is too great a gap between consecutive vehicles or it reaches its limit, and (c) Stadium Mall gets a little green

only when necessary.

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G———— G> min —_—P

Corte Be.

him

CJ

Sage ee pliides COURnia)

hure ae Mai

G< mm

FIGURE 8.17

Intersection with Actuated Signal Control

Traffic Signal Logic at Stadium and University Streets 0. Initial status = G on Stadium. 1.

Wait until Stadium has had its min G, then go to Step 2.

2.

Ifno vehicle is present on University approach, go to Step 7.

3.

Give G to University for "min Gy" seconds.

(Optional) If passage time gap on University is too large, go to Step 7. 5. If current G on University has exceeded its "max Gu", go to Step 7.

4-

Goto Step 4.

6.

Ifno vehicle is present on Stadium Mall approach, go to Step 11. Give G to Stadium Mall for "min Gy" seconds (Optional) If passage time gap on Stadium Mall is too large, go to Step 11. If current G on Stadium

7. .

8.

9.

. .

Mall has exceeded its "max Gm", go to Step 11. Go to Step 9

Give G to Stadium. If LT loop is "active" and actuated, the first Ga seconds of Gs include a leading protected LT indication. Go to Step 1.

Notes:

G = duration of green time, S = Stadium St.,

LA =

U

= University St., M = Stadium Mall

left tum arrow for WB Stadium (which may not always be active)

"Give G" implies standard process of Y, all-red, etc., as appropriate. min Gia

min

= 5 with

passage time (PT)

= 7 Gy = 10 and min Gy

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= 20 1; min Gs with =

2;

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FUNDAMENTALS OF TRANSPORTATION ENGINEERING Chapter 8 Design of Intersections for Safety and Efficiency

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8.3.4 Estimating Delays at Intersections

Of the several commonly-used definitions of intersection delay, stopped delay has been used most often.

It is easy to measure and has been used by the Highway Capacity Manual as a basis for intersection Jevel on a ofservice. A manual procedure for measuring stopped delay at an intersection [HCM 2000] is based a count Vs is 8.18 indicates, set of observations made at regular intervals. As the field data sheet in Figure made of the number of vehicles stopped on a given approach each 15 seconds. The assumption is that each vehicle counted in this will, on the average, wait 15 seconds. If a particular vehicle is counted

way in consecutive time intervals, it contributes more to the total time spent waiting by vehicles on the the time the stopped vehicles V approach. The only other quantity is the total approach volume during the V, value may include some whereas are counted. This quantity counts each approaching vehicle once,

vehicles zero, one, or more times, depending on whether they were stopped on the approach when an interval count was taken. In Figure 8.18, the total number of stopped vehicles observed during the 10-minute study period. was 136. The total approach volume during those 10 minutes was 41. This is evidence that many vehicles were counted as stopped more than once. Because each stopped vehicle contributes 15 seconds = * to the total intersection stopped delay, the total delay is 136 vehicles 15 seconds/vehicle 2040 seconds. Therefore, the average stopped delay is

2040sec

4lvehs

_ 49.8 seconds per vehicle.

Variations and

refinements of this basic technique are given in Appendix 16A of the Highway Capacity Manual [HCM 2000]. A critique of the method is given in Mousa [2002].

~

=

THINK ABOUT IT Does the length of the time interval between V, counts always have to be 15 seconds? another interval length can be chosen, ... (a) How would the data collection and calculations need to be modified? (b) How would you decide which is the best interval length to use?

If

CHAPTER 8 SUMMARY The chapter began with the description of a rural intersection of two county roads. Recent collisions indicate that the intersection, with stop signs controlling two of the four approaches, needs to be reexamined. New residential developments and the corresponding growth in enrollment at the nearby high school have caused increased traffic at the intersection. Sight distances on the approaches may vary by time of year, if tall crops are grown near the intersection. The critical approach speed analysis described — in this chapter can be applied to such a case. The increased traffic flows — especially at peak periods and risky may have reduced the number of acceptable gaps on the main county road, causing impatience behavior on the part of minor road drivers. The gap acceptance analysis covered in this chapter may help in this part of the county, if diagnose such a problem. It may be time for the first signalized intersection the conditions at the intersection pass the traffic signal warrant analysis demonstrated in this chapter. If a as to whether to stop or signal is installed, the signal timings should be set so a driver can make a decision be avoided. Finally, zone should continue upon seeing the yellow signal indication. Creating a dilemma method to estimate average stop delay at the intersection can be carried out. The methods a simple

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Chapter 8 Design of Intersections for Safety and Efficiency contained in this chapter are examples are safe and efficient.

of techniques traffic engineers can use to create intersections that

INTERSECTION CONTROL DELAY WORKSHEET General Information

Site Information

Analyst(s): MG, AN Day and Date: Thurs. 14 Nov 2002 Time: 5:30PM to 5:40 PM

Approach street: Coliseum Avenue Cross street: Wildcat Avenue

Approach direction: WB

Weather: clear, 45°

Jurisdiction:

Lane(s): Left, Through, Right Area Type: | Other

CBD X_

City of Mythaca

Number of stopped vehicles,

——/

0

15

30

45

0

0

4

7

8

1

8

2

0

2

2

2

4

5

6

3

7

4

0

1

4

2

3

5

7

5

8

0

0

]

6

4

6

5

2

7

0

1

1

3

8

4

6

8

9

7

2

3

0 4

36

32

34

34

Totals:

V,

Computations

Total vehicles in queue, [Vs= 136 Total approach volume, V= 4] Interval,

I=

Average delay=

15 seconds

2s"

= 49.8 sec/veh

FIGURE 8.18

Form for recording the number of stopped vehicles and total approach volume Based on HCM 2000, Appendix 16A

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Fundamentals of Transportation Engineering - Volume 2 - Jon D. Fricker and Robert K. Whitford

FUNDAMENTALS OF TRANSPORTATION ENGINEERING Chapter 8 Design of Intersections for Safety and Efficiency

2nd Edition, 6* Printing

ABBREVIATIONS FOR CHAPTER 8 A, a, a’, a” B, b, b’, b” C, c, c’, c”

CAS D,d, d’, d”

dimensions on major street lane closest to minor street to determine dimensions on left side of minor street to determine CAS

CAS

dimensions on right side of minor street to determine CAS critical approach speed dimensions on major street lane nearest center line on lane farthest from minor street to determine CAS

rake

deceleration rate for braking

EB

Eastbound traffic

LA LH MN MF MUTCD NB

RA RH SB

TSD

t t

LH vehicle Accepts the gap Left-turning vehicle at the stop line or Head of the minor street queue Vehicle on Major street in lane Nearest the minor street intersection Vehicle on Major street in Far lane from the minor street intersection Manual on Uniform Traffic Control Devices Northbound traffic RH vehicle Accepts the gap Right-turning vehicle at the stop line or Head of the minor street queue Southbound traffic Time Space Diagram time to stop, in conjunction with braking reaction time when driving a car, usually in conjunction with braking duration of the caution or amber or yellow signal light time under the red signal light

ty teed

WB

Westbound traffic

Ww

velocity vehicle at the beginning of analysis final velocity of the vehicle Width of the Intersection from stop line to stop line

Xs

distance to stop

Vo

Vg

GLOSSARY Accepted gap or accepted lag: Gap or leg that the driver of a minor-street vehicle uses to move into the major street. Actuated traffic signal: A signal timing whose phase durations are influenced by the presence or absence of vehicles on some or all of the intersection approaches.

All-red clearance interval: A period when drivers on all intersection approaches see a red signal. Critical gap: The minimum size gap that a particular driver will accept. Cycle. The length of time between consecutive occurrences of the same point in the green-yellow-red. sequence of phases, Fixed time signal: See pre-timed traffic signal. Gap: Time elapsed between the rear bumper of one vehicle and the front bumper of the following vehicle passing a given point. Gap is thus always smaller than headway.

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e

Green wave: The situation when signal offsets are such that a vehicle traveling at a reasonable speed in a specified direction can encounter only green lights at a sequence of intersections.

©

Headway: Time elapsed between the front bumper of one vehicle and the front bumper of the following vehicle passing a given point. Indication: What the user sees (green, yellow, red, arrow, etc.) on the traffic signal as (s)he approaches the intersection. The user may be a motorist or a pedestrian.

*

+ =

Interval (traffic signal): A duration of time during which the signal indications do not change. [FHWA 2015] Lag: Time elapsed between the arrival of a minor-street vehicle ready to move into the major street and the arrival of the front bumper of the next vehicle in the major traffic stream. It may be that

drivers treat lags differently than they treat gaps. Otherwise, the only difference is the event that started the timing of the lag or gap. =

Master intersection: The intersection whose signal timings are used as the point of reference for such measurements as offsets

«

» «

®

e ‘*

e e

«

Offset: The time of an event in a signal cycle with respect to that same event occurring at the master intersection, e.g., the start of the green phase. Permitted phase: A green phase during which a given movement, e.g., a left turn, can be made by a driver only when gaps in conflicting traffic are acceptable to the driver Phase: The right-of-way, yellow change, and red clearance intervals in a cycle that are assigned to an independent traffic movement or combination of traffic movements. [MUTCD, FHWA 2009] For example, a phase may control both a through movement and a right turn movement on an approach. Platoons: Groups of vehicles approaching an intersection Pre-timed traffic signal: A signal whose indications are fixed in duration.

Protected phase:

A time during the signal cycle in which a movement can be made when all

conflicting movements are prohibited by red phases. Rejected gap or rejected lag: Gap or lag that the driver of a minor-street vehicle waiting to enter the major street does not accept. Saturation flow rate: The maximum number of vehicles that can pass through an intersection approach in an hour, assuming that the signal is always green. Untested gap: No minor street vehicle was present.

INDEX FOR CHAPTER 8 Accepted gap, 3 actuated, 20 Actuated signals, 28 all-red clearance interval, 14, 18, 20, 22

deceleration rate for braking,

clearing distance, 14 critical approach speed, 7 critical gap, 4, 5

Fully-actuated signals, 28 Gap, 2

Critical gap,

3

Cycle, 20

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demand-actuated signals, 28

dilemma zone, 15 events, 3

gap acceptance, 2, 6 green offset, 24 green wave, 27

8.32

Headway, 2 Indication, 20 intersection delay, 30 intersection sight distance, Interval, 20

Lag,

11

3

Passage time, 28 permitted movement, 22 Phase, 20 Presence time, 28

Chapter 8 End Materials

Fundamentals of Transportation Engineering - Volume 2 - Jon D. Fricker and Robert K. Whitford

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FUNDAMENTALS OF TRANSPORTATION ENGINEERING Chapter 8 Design of Intersections for Safety and Efficiency pre-timed, 20 protected movement, 21

Rejected gap, 3 saturation flow rate, 28 semni-actuated control, 28

signal offset, 24 stopline, 26 stopped delay, 30 stopping line, 13 Time Space Diagram, 22

traffic signal warrant, 10 Warrants, yield, 6

11

REFERENCES FOR CHAPTER 8 American Association of State Highway and Transportation Officials, A Policy on the Geometric Design ofHighways and Streets, Washington, D.C., 2001. 2. FHWA (1983). Traffic Control Devices Handbook, U.S. Department of Transportation, Federal 1.

Highway Administration, 1983. FHWA (2009). Manual on Uniform Traffic Control Devices (MUTCD) for Streets and Highways, Federal Highway Administration, U.S. Department of Transportation, 2009. Latest version available online at http://mutod.fhwa.dot.gov/.

FHWA (2013). Traffic Signal Timing Manual, Chapter 4. United States Department of Transportation, Federal Highway Administration,

hitp:/Avww.ops.fhwa.dot.gov/publications/fhwahop08024/chapter4. htm, last modified: August 2, 2013. Retrieved 26 October 2016. FHWA (2015). Traffic Signal Timing Manual, Chapter 5. United States Department of Transportation, Federal Highway Administration, ://www.ops.fhwa.dot.gzov/publications/fhwahop08024/ch: last modified: October 20, 2015, Retrieved 26 October 2016. Fricker, Jon D., Marlene Gutierrez, and David Moffett, “Gap Acceptance and Wait Time at Unsignalized Intersections”, Proceedings of an International Workshop, Intersections without Traffic 18-19 July 1991, Bochum, Germany, p. 297-307. Signals Harwood, D.W., J.M. Mason, and R.E. Brydia, “Design policies for sight distance at stop-controlled intersections based on gap acceptance”, Transportation Research Part C, December 1998, p. 199216. Institute of Transportation Engineers, Transportation and Traffic Engineering Handbook, 1976. Mousa, Ragab M., “Accuracy of Stopped Delay Method Measured by Stopped-Vehicle Counts Method”, Journal of Transportation Engineering, American Society of Civil Engineers, September/October 2002, p. 439-446. 10. Robertson, H. Douglas, editor, Manual of Transportation Engineering Studies, Prentice-Hall, 1994. 11. Schultz, Grant (2012). Personal communication, 30 September 2012.

I,

EXERCISES FOR CHAPTER 8: DESIGN OF INTERSECTIONS FOR SAFETY AND EFFICIENCY 8.1

ANALYSIS OF NON-SIGNALIZED INTERSECTIONS

8.1.Gap Events at 116" and Eller, Using a video recording of a "T" intersection, an analyst creates the database of gap acceptance events shown in columns | and 2 of the table below.

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|

(2) Time (sec.)

MN RH1 MN MN MN

44

accepted gaps, and note in column 3 whether the gap was accepted (A) or rejected (R). Follow the

8.7

method demonstrated in Example 8.1. Show how

you calculated the rejected and accepted gaps.

19.0 19.8

RH2

28.0 28.0 30.4 33.9

RH3 MN

Fill in column 3 with the length of rejected and

(3) Gap (sec.)

14,4 18.0

RAI RA2

|

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Gap Events at 96" and Eagle Road. Usinga video recording of a "T" intersection, an analyst creates 8.2.

of gap acceptance events shown in columns and 2 of the table at the right. Fill in column 3 with the length of rejected and accepted gaps, and note in column 3 whether the gap was accepted (A) or rejected the database 1

{R). Follow the method demonstrated in Example 8.1.

(1) Event | (2) Time (sec.) 00:26.6 RH1

RH2 MN MN RH3 MN

gaps.

(3) Gap (sec.)

00:26.6 00:29.9 00:33.6 00:34.5 00:35.9 00:37.8 00:39.1 00:42.8 00:49.9

RAI

RA2

Show how you calculated the rejected and accepted

|

RA3 MN

Estimating the Critical Gap at 96 and Zionsville Road. The top portion of a summary of gap events (using the format of Table 8.1) is shown below. Eighty-eight right-turning vehicles accepted gaps. Only the 54 vehicles with the shortest gaps are included in the part of the table shown below. A. Fill in the empty cells in Columns 4 5. Show your calculations for the row in which t = 5 sec. 8.3.

and

B. Estimate the critical gap to the nearest 0.01 sec. Show your calculations,

3)

(1) Length of gap (t sec.)

(2) Number of accepted gaps (less than t sec.)

0

Tejected gaps (greater than t

sec.)

0

145

1

1

125

2

2

63

3

6

34

4

8

20

5

14

7

6

18

5

7

28

2

8

33

2

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(4) Percent accepted paps

A(t) (less thant sec.)

6) Percent

rejected gaps R(t) | (greater than t sec.)

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Critical Approach Speed on Crowell Street. Somehow, a traffic control device has never been installed at the corner of Crowell and Ft. Jekk Streets in a residential neighborhood. The longtime 8.4.

residents have gotten used to it, but new families are wondering how safe an uncontrolled intersection can be. They contact the City. The City sends an intern to the intersection. The intern thinks the EB approach on Crowell is the one most likely to need a TCD, so he takes the following measurements: e © ®

e «

=

Ft. Jekk is 31 feet wide; Crowell is 23 feet wide.

Ft. Jekk 34 feet from building on NW corner to near curb on on Ft. Jekk from on SW corner to near curb 20 feet building 21 feet from building on NW corner to near curb on Crowell 18 feet from building on

SW corner to near curb on Crowell

Speed on Ft. Jekk=31 mph

Parking is allowed on both streets According to the CAS method, should a traffic control device be installed on EB Crowell at Ft. Jekk? If so, should it be a Stop sign or a Yield sign? Show clearly how you carried out the steps in the CAS e

method.

Critical Approach Speed Analysis near Shoridan. An uncontrolled intersection in an industrial park near Shoridan has been the site of several vehicle collisions that may have been 8.5.

attributable to limited sight distance. The 85th percentile speed on the major street is 48 mph. The major street is 76 feet wide; the minor street is 48 feet wide. Parking is permitted on both sides of both streets. The distances from curb to view obstruction, using the notation of Figure 8.5, are: a" = 40 feet, b" = 73

feet, c” = 94 feet, d" = 85 feet. A. Show clearly your calculations

of dimensions a=a’-+a”, b—b’+b”, c=c’+c”, and d=d’+d”.

B. Submit a copy of Figure 8.6 with the (a,b) and (c,d) points and the "anchor point" speed clearly marked.

C. What isthe CAS? Which type of traffic control device (f any) is needed at the intersection? 8.6.

Critical Approach Speed on Edgemont Drive. Example 8.2 just happens to describe the

situation at Eighth Ave. and Edgemont Drive in Mythaca. Eighth Avenue is the major street. A. How high must the approach speed on 8th Ave. be, so that a stop sign on Edgemont is required?

Explain or show clearly how you found that speed. B. In Example 8.2, it was determined that the Critical Approach Speed called for a Yield Sign on Edgemont as the appropriate Traffic Control Device. What if parking is no longer permitted on Edgemont? Will that change the situation as far as the best TCD is concerned? C. Ifthe 85" percentile speed on 8" Avenue in Example 8.2 had been 39 mph, rather than 31 mph, what TCD would be appropriate? D. Ifa” and c” were both 16 ft in Example 8.2, what TCD would be needed with the speed on 8" Avenue at 31 mph? Intersection Sight Distance at Major Street. The solution for the Critical Approach Speed in Example 8.2 was 13 mph. A. Which driver — Driver A or Driver D — was the driver that governed the CAS solution? Explain. 8.7,

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B. Using the assumptions listed in Figure 8.6, what would be the stopping distance for Driver C, approaching the intersection at 13 mph? C. What is the minimum intersection sight distance for the “governing” driver in Part A? Show

your calculations. D. Regardless of the answer to Part C, use ISD = 129 ft and the information in Example 8.2, compute the critical gap implied by Equation 8.2. 8.2

SIGNAL WARRANTS AND STOPPING DISTANCE AT SIGNALIZED INTERSECTIONS

8.8. Traffic Signal Warrants at Stadium and Russell. Repeat the analysis in Example 8.3, this time with using three approach lanes on SB Russell Street. Do the results change, as far as whether a signal is

warranted?

Other Traffic Signal Warrants. Go to Section 4C.03 of the Manual on Uniform Traffic Control

8.9.

Devices (MUTCD) online at http://muted.fhwa.dot.gov/htm/2009/part4/part4c.htm and apply the Warrant 2 Four-Hour Vehicular Volume to the data used in Example 8.3. Is a signal justified under this warrant? List your steps. Print out any table or figure you use to apply the warrant and mark it up to show how you used it.

Dilemma Zone on Lincoln Street. Drivers on Lincoln Street approaching Douglas Street do so at 25 mph. Douglas Street is 50 feet "deep", when measured from farside curb line to nearside stop bar. The yellow phase on Lincoln is 4 seconds long, Using a reaction time of 2 seconds, a deceleration rate of 10 ft/sec, and a vehicle length of 15 feet, answer the questions below. A. Is there a dilemma zone? Show your calculations for reaction distance x, braking distance x», 8.10.

distance covered during yellow indication xy, etc. B. Regardless of your answer to part A, let us say there is a dilemma zone of length 45 feet. How much all-red or extra yellow time will be needed to eliminate it?

A major Midwest city has been accused of changing signal timings so as to trap drivers into running red lights and having to pay fines. The city’s red light contractor has been using 3-second yellow, instead of the more commonly-used 4 seconds. Using FTE2 Example 8.4 as a starting point answer the questions below 8.11.

Dilemma Zone and Red-Light Cameras.

A. (5 points) How does the minimum stopping distance x(s) for the approaching vehicle change when Y=3 sec? Explain. B. (5 points) How does the distance traveled during yellow x(Y) for the approaching vehicle change when Y=3 sec? Explain. C. (5 points) How long is the Dilemma Zone when Y=3 sec? D. (10 points) In Example 8.4, the rule was “the vehicle must leave the intersection before the light turns red”. If, instead, the rule is “a vehicle may not enter the intersection when the light is red”, how long will the Dilemma Zone be when Y=3 sec? Will some drivers get trapped under this new rule? 8.3

ANALYSIS OF SIGNALIZED INTERSECTIONS Traffic Signal Timing. A. In the diagram shown below how many EB phases (indications) are there? B. How many intervals are there during the time that NB TH/RT traffic sees G?

8.12,

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Chapter 8 Design of Intersections for Safety and Efficiency

C. What is the length of the ail-red clearance interval? Wildcat Ave. Coliseum Avenue NBLT | NBTH/RT | SB Vehs EB Vehs | WB Vehs 1 R=13 R=56 R=56 G=9 G=52 2 | Y=3 3 R=85 4 G=39 5

Y¥=3

Y=3

6

R=42

R=42

7

G=37

8

9

G=37

Y=

Y=

=]

=]

8.13. Phases (indications) and Intervals in Traffic Signal Timing. Using the format shown in Table 8.4 and the data in Table 8.5-8.7, create a Traffic Signal Timing Form for the intersection of First and Acorn, Assume the yellow phase is 4 seconds long and that a 1-second all-red clearance interval is used.

8.14. Time Space Diagram — a wider green wave? Using Example 8.7 and the data in Table 8.5-8.7 as a starting point, what change in green offset at what intersection(s) would permit a wider “green wave”

in both WB and EB directions along Acom Street? Are there any reasons not to make those changes? 8.15. Time-Space Diagram for Main Street. Sixth Street is 660 feet east of Fifth Street along Main Street in Mythaca. Along Main Street, the (pretimed) traffic signals all have the same cycle length, and the speed limit is 30 mph. At 12:00:17 PM, the green phase (indication) for EB and WB traffic on Main

Street at Fifth is observed turning Green. From 12:01:05 PM until 12:01:47 PM, the signal is seen to be red for EB and WB traffic. At 12:06:35 PM, the signal for EB and WB traffic on Main at Sixth Street turns green. The signal at Sixth turns red at 12:07:23 PM. a. What is the green offset of the signal at Sixth Street with respect to the signal at Fifth? b.

What speed between the two signals would you recommend for EB and WB drivers to maintain on Main Street? Show your calculations.

Traffic Signal Study on Elm Street. The traffic signals on Elm Street are observed to be operating on a 75-second cycle length. Two streets that cross Elm are First and Second Streets, which are 8.16.

1/12 mile apart. The signal on Elm at First is observed "turning green" at 16:24:17 EST one afternoon. A few minutes later, we reach Second Street and see the beginning of the green phase on Elm at Second at 16:29:35. A. Ifthe Elm Street signal at First is the "master signal", what is the green offset of the signal on Elm at Second Street? B. The Green + Yellow phases on Elm at First Street total 47 seconds. These phases total 39 seconds at Second Street. What is the slowest speed any vehicle could travel through a green light at First Street and not be stopped by the next red light at Second Street?

Time-Space Diagram along Main Street. The green phases on EB Main Street in Mythaca at First, Second, and Third Streets, spaced 1/12 mile apart, are observed to start at the times given in the list 8.17.

below.

Cross Street

Green Start

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FUNDAMENTALS OF TRANSPORTATION ENGINEERING Chapter 8 Design of Intersections for Safety and Efficiency First St

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Second St.

17:22:03

17:23:18 17:24:33

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A. What is the cycle length at these signals? Br _Trthe master controller is at First Street, what are the offsets at

Second and Third Streets? C. Ifa driver EB on Main Street crosses First Street at the start of that signal's green phase (indication) and is not impeded by other traffic, what range of speeds will permit her to proceed through the green phase (indication) at Second Street without delay? Note: The Main Street approach gets 40 seconds of effective green

(G+Y).

17:34:21

17:35:36 8.18.

Actuated Traffic Signals. Is it possible for actuated signals to appear to an observer to be pre-

timed?

If so, explain how this could happen.

Pretimed and Actuated Signals. A. Give the best reason for having a pretimed (vs. actuated) signal at an intersection on a major

8.19.

arterial street.

B. What is the best reason to use an actuated signal at an intersection? Intersection Delay. Go to a nearby signalized intersection during a time in which long backups can be observed. Using a form that replicates Figure 8.18, estimate the average stopped delay at the intersection. For how many minutes did you collect data? Explain how you knew when to stop collecting data. Feel free to use a time interval between V, counts other than 15 seconds. If you can arrange it, have another student estimate average stopped delay at the same intersection at the same time, using a time interval different from yours. Comment on the degree to which your results differ. 8.20.

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