CFHR 3-18-72-184-4F

APPLICATION OF THE TEXAS MODEL FOR ANALYSIS OF INTERSECTION CAPACITY AND EVALUATION OF TRAFFIC CONTROL WARRANTS

Clyde E. Lee, Vivek S. Savur; and Glenn E. Grayson

RESEARCH REPORT 184-4F

PROJECT 3-18-72-184

CENTER FOR TRANSPORTATION RESEARCH BUREAU OF ENGINEERING RESEARCH

THE UNIVERSITY OF TEXAS AT AUSTIN

JULY 1978

PARTIAL LIST OF REPORTS PUBLISHED BY THE CENTER FOR TRANSPORTATION RESEARCH

This list includes some of the reports published by the Center for Transportation Research and the organizations which were merged to form it: the Center for Highway Research and the Council for Advanced Transportation Studies. Questions about the Center and the availability and costs of specific reports should be addressed to: Director; Center for Transportation Research; ECJ 2.5; The University of Texas at Austin; Austin, Texas 78712.

7-1

7-2F

16-1F 23-1

23-2

23-3F

29-2F

114-4

114-5

114-6

114-7

114-8 114-9F 118-9F

123-30F

172-1 172-2F 176-4 176-5F 177-1

177-3

177-4

177-6

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177-10

177-11

177-12

177-13

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177-16 177-17 177-18

183-7

"Strength and Stiffness of Reinforced Concrete Rectangular Columns Under Biaxially Eccentric Thrust," by J. A. Desai and R. W. Furlong, January 1976. "Strength and Stiffness of Reinforced Concrete Columns Under Biaxial Bending," by V. Mavichak and R. W. Furlong, November 1976. "Oil, Grease, and Other Pollutants in Highway Runoff," by Bruce Wiland and Joseph F. Malina, Jr., September 1976. "Prediction of Temperature and Stresses in Highway Bridges by a Numerical Procedure Using Daily Weather Reports," by Thaksin Thepchatri, C. Philip Johnson, and Hudson Matlock, February 1977. "Analytical and Experimental Investigation of the Thermal Response of Highway Bridges," by Kenneth M. Will, C. Philip Johnson, and Hudson Matlock, February 1977. "Temperature Induced Stresses in Highway Bridges by Finite Element Analysis and Field Tests," by Atalay Yargicoglu and C. Philip Johnson, July 1978. "Strength and Behavior of Anchor Bolts Embedded Near Edges of Concrete Piers," by G. B. Hassel wander, J. 0. Jirsa, J. E. Breen, and K. Lo, May 1977. "Durability, Strength, and Method of Application of Polymer-Impregnated Concrete for Slabs," by Piti Yimprasert, David W. Fowler, and Donald R. Paul, January 1976. "Partial Polymer Impregnation of Center Point Road Bridge," by Ronald Webster, David W. Fowler, and Donald R. Paul, January 1976. "Behavior of Post-Tensioned Polymer-Impregnated Concrete Beams," by Ekasit Limsuwan, David W. Fowler, Ned H. Burns, and Donald R. Paul, June 1978. "An Investigation of the Use of Polymer-Concrete Overlays for Bridge Decks," by Huey-Tsann Hsu, David W. Fowler, Mickey Miller, and Donald R. Paul, March 1979. "Polymer Concrete Repair of Bridge Decks," by David W. Fowler and Donald R. Paul, March 1979. "Concrete-Polymer Materials for Highway Applications," by David W. Fowler and Donald R. Paul, March 1979. "Observation of an Expansive Clay Under Controlled Conditions," by John B. Stevens, Paul N. Brotcke, Dewaine Bogard, and Hudson Matlock, November 1976. "Overview of Pavement Management Systems Developments in the State Department of Highways and Public Transportation," by W. Ronald Hudson, B. Frank McCullough, Jim Brown, Gerald Peck, and Robert L. Lytton, January 1976 (published jointly with the Texas State Department of Highways and Public Transportation and the Texas Transportation Institute, Texas A&M University). "Axial Tension Fatigue Strength of Anchor Bolts," by Franklin L. Fischer and Karl H. Frank, March 1977. "Fatigue of Anchor Bolts," by Karl H. Frank, July 1978. "Behavior of Axially Loaded Drilled Shafts in Clay-Shales," by Ravi P. Aurora and Lymon C. Reese, March 1976. "Design Procedures for Axially Loaded Drilled Shafts," by Gerardo W. Quiros and Lymon C. Reese, December 1977. "Drying Shrinkage and Temperature Drop Stresses in Jointed Reinforced Concrete Pavement," by Felipe Rivero-Vallejo and B. Frank McCullough, May 1976. "A Study of the Performance of the Mays Ride Meter," by Yi Chin Hu, Hugh J. Williamson, and B. Frank McCullough, January 1977. "Laboratory Study of the Effect of Nonuniform Foundation Support on Continuously Reinforced Concrete Pavements," by Enrique Jimenez, B. Frank McCullough, and W. Ronald Hudson, August 1977. "Sixteenth Year Progress Report on Experimental Continuously Reinforced Concrete Pavement in Walker County," by B. Frank McCullough and Thomas P. Chesney, April 1976. "Continuously Reinforced Concrete Pavement: Structural Performance and Design/Construction Variables," by Pieter J. Strauss, B. Frank McCullough, and W. Ronald Hudson, May 1977. "CRCP-2, An Improved Computer Program for the Analysis of Continuously Reinforced Concrete Pavements," by James Ma and B. Frank McCullough, August 1977. "Development of Photographic Techniques for Performing Condition Surveys," by Pieter Strauss, James Long, and B. Frank McCullough, May 1977. "A Sensitivity Analysis of Rigid Pavement Overlay Design Procedure," by B. C. Nayak, W. Ronald Hudson, and B. Frank McCullough, June 1977. "A Study of CRCP Performance: New Construction Vs. Overlay," by James I. Daniel, W. Ronald Hudson, and B. Frank McCullough, April 1978. "A Rigid Pavement Overlay Design Procedure for Texas SDHPT," by Otto Schnitter, W. R. Hudson, and B. F. McCullough, May 1978. "Precast Repair of Continuously Reinforced Concrete Pavement," by Gary Eugene Elkins, B. Frank McCullough, and W. Ronald Hudson, May 1979. "Nomographs for the Design ofCRCP Steel Reinforcement," by C. S. Noble, B. F. McCullough, and J. C. M. Ma, August 1979. "Limiting Criteria for the Design of CRCP," by B. Frank McCullough, J. C. M. Ma, and C. S. Noble, August 1979. "Detection of Voids Underneath Continuously Reinforced Concrete Pavements," by John W. Birkhoff and B. Frank McCullough, August 1979. "Permanent Deformation Characteristics of Asphalt Mixtures by Repeated-Load Indirect Tensile Test," by Joaquin Vallejo, Thomas W. Kennedy, and Ralph Haas, June 1976.

(Continued inside back cover)

TECHNICAL REPORT STANDARD TITLE PAGE

r-::~:~~79 --1~~~~:~=-[~0'"'"~~ Am"•oo No.

~lo ood SobtHie

Recipient's Catalog No. 13.

I -+--:---::-----------·-------1 5. Report Date

I APPLICATION OF THE TEXAS MODEL FOR ANALYSIS OF INTERSECTION CAPACITY AND EVALUATION OF

July 1978 r6. Pedo.miog Q,gooi>otioo Code ·----

I TRAFFIC CONTROL WARRANTS f-----·---------------------1 7. Authorls) 8. Performing Orgcni z.ation Report No.

Clyde E. Lee, Vivek S. Savur, and Gl enn E. Grayson Research Report 184-4F

9. Performing Organization Name and Address 10. Work Unit No.

Center for Highway Research The University of Texas at Austin

l'i. Contract or Grant No.

1 Austin, Texas 78712 Study No. 3-18-72-184

13. Type of Repor~ and Period Covered h2. Sponsoring Agency Name and Addres~--·-·- -

Final 1 Texas State Department of Highways a 1 Transportation; Transportation

nd Public Planning Division

-· i P .. 0 .. Box 5051 14. Sponsoring Agency Code

78763

~Austin, Texas

15. Supplementary Notes

Study conducted in cooperation with the Ue s.

-----

Department of Transportation, Federal ils imu la tion I Highway Administration. Resear ch Study Title: of Traffic by a

I Step-Through Technique (Applicat 16. Abstract

i II ons) ----------------------------------------------~

I I I I

The TEXAS Model for Intersection Traffic is a microscopic simulation package describing the behavior of individual driver-vehicle units at isolated inter­sections. This report deals with two applications of this model, namely determin­ing the capacity of an intersection and analysis of warrants for traffic signal control. Service volume has been related quantitatively to five subjectively­defined levels of service by identifying suitable performance indicators, such as average queue delay, percent of vehicles required to stop, and percent of vehicles required to slow to below 16 kph (10 mph). These indicators are computed routinely during the simulation process and can be used for evaluating the performance of existing or proposed unsignalized intersections operating under various traffic volumes and different types of control. In the signal warrant analysis, effec­tiveness of various types of control is judged on the basis of total cost. This cost includes costs associated with user stopping and delay and costs related to providing, operating, and maintaining traffic control devices. It was concluded that peak-hour traffic volumes which result in unreasonable delay may be used as a criterion for judging the need to replace two-way stop control with signals, while total intersection costs should be considered when replacing all-way stop control with signals. Another finding indicated that fewer vehicles were delayed and that the total costs of controlling and using an intersection were lower under traffic­actuated signal control than under pretimed control.

17. KeyWords 18. Distribution Statement

microscopic traffic simulation, No restrictions. This document is computer simulation, levels of available to the public through the

l service, signal warrants, traffic National Technical Information Service, performance indicators, intersection Springfield, Virginia 22161.

Ll .19. Seco n ty Cl o,.il, (o I th" '~po,iJ- 120. SomHy C I oH• I. (of thi' poge) --21. No. of P og" 22. P 'i oe

Unclassified Unclassified 102 ________ .J..._ _____ _.J_ _______ ~

Form DOT F 1700.7 <a-69)

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APPLICATION OF THE TEXAS MODEL FOR ANALYSIS OF INTERSECTION CAPACITY

AND EVALUATION OF TRAFFIC CONTROL WARRANTS

by

Clyde E. Lee Vivek S. Savur

Glenn E. Grayson

Research Report Number 184-4F

Simulation of Traffic by a Step-Through Technique (Applications)

Research Project 3-18-72-184

conducted for

Texas State Department of Highways and Public Transportation

in cooperation with the U. S. Department of Transportation

Federal Highway Administration

by the

CENTER FOR HIGHWAY RESEARCH

THE UNIVERSITY OF TEXAS AT AUSTIN

July 1978

The contents of this report reflect the views of the authors, who are responsible for the facts and the accuracy of the data presented herein. The contents do not necessarily reflect the official views or policies of the Federal Highway Administration. This report does not constitute a standard, specification, or regulation.

There was no invention or discovery conceived or first actually reduced to practice in the course of or under this contract, including any art, method, process, machine, manufacture, design or composition of matter, or any new and useful improvement thereof, or any variety of plant which is or may be patentable under the patent laws of the United States of America or any foreign country.

ii

PREFACE

This is the fourth and final report in a series of four reports on

Research Study 3-18-72-184, "Simulation of Traffic by a Step-Through

Technique." This report describes the applications of the TEXAS Model for

Intersection Traffic. The model simulates the behavior of individual driver­

vehicle units at isolated intersections. The results of the simulation are

analyzed to determine the capacity at various levels of service and to inves­

tigate the validity of current warrants for signal control.

The four reports which deal with the development, use, and application of

the TEXAS Model are

Research Report No. 184-1, "The TEXAS Model for Intersection

Traffic - Development," Clyde E. Lee, Thomas W. Rioux, and

CharlieR. Copeland.

Research Report No. 184-2, "The TEXAS Model for Intersection

Traffic - Programmer's Guide," Clyde E. Lee, Thomas W. Rioux,

Vivek S. Savur, and CharlieR. Copeland.

Research Report No. 184-3, "The TEXAS Model for Intersection

Traffic- User's Guide," Clyde E. Lee, Glenn E. Grayson,

CharlieR. Copeland, Jeff W. Miller, Thomas W. Rioux, and

Vivek S. Savur.

Research Report No. 184-4F, '~pplication of the TEXAS Model

for Analysis of Intersection Capacity and Evaluation of

Traffic Control Warrants," Clyde E. Lee, Vivek s. Savur, and

Glenn E. Grayson.

Requests for copies of these reports should be directed to Mr. Phillip L.

Wilson, Engineer-Director, Planning and Research Division, File D-10, Texas

State Department of Highways and Public Transportation, P. 0. Box 5051,

Austin, Texas 78763.

iii

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ABSTRACT

The TEXAS Model for Intersection Traffic is a microscopic simulation

package describing the behavior of individual driver-vehicle units at isolated

intersections. This report deals with two applications of this model, namely

determining the capacity of an intersection and analysis of warrants for

traffic signal control.

Service volume, which is the maximum traffic volume that can be accommo­

dated at an intersection while maintaining a specified level of service, has

been related quantitatively to five subjectively-defined levels of service by

identifying suitable performance indicators, such as average queue delay,

percent of vehicles required to stop, and percent of vehicles required to slow

to below 16 kph (10 mph). These indicators are computed routinely during the

simulation process and can be used for evaluating the performance of existing

or proposed unsignalized intersections operating under various traffic volumes

and different types of control.

In the signal warrant analysis, effectiveness of various types of control

is judged on the basis of total cost. This cost includes costs associated

with user stopping and delay and costs related to providing, operating, and

maintaining traffic control devices. Representative values of one cent per

vehicle stop and three dollars per hour of vehicle delay are used. It was

concluded that peak-hour traffic volumes which result in unreasonable delay

may be used as a criterion for judging the need to replace two-way stop con­

trol with signals, while total intersection costs should be considered when

replacing all-way stop control with signals. Another finding indicated that

fewer vehicles were delayed and that the total costs of controlling and using

an intersection were lower under traffic-actuated signal control than under

pretimed control.

iv

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SUMMARY

This report describes practical application of the TEXAS Model for Inter­

section Traffic to determine capacity and analyze the warrants for signaliza­

tion of isolated intersections.

Hitherto, the manner of determining capacity has been based on empirical

formulae, probability of vehicle spacing, or observation of intersections.

The method described in this report utilizes a microscopic demand-response

simulation technique for evaluating the performance of intersections with any

form of traffic control. The relationship between capacity and level of

service is investigated. Performance indicators that can be used to define

levels of service at intersections are studied, and appropriate indicators are

selected. A relationship between these selected performance indicators and

each subjectively-defined level of service is established. Four cases in

which the TEXAS Model can be used to evaluate the behavior of an intersection

are then outlined.

The working of the TEXAS Model is explained briefly with an example using

actual input. The four cases previously mentioned are used to illustrate the

method. First, the level of service of a 2-lane by 2-lane uncontrolled inter­

section is determined to be E when it is accommodating 1600 veh/hr. Then, the

maximum volume that can be accommodated if that intersection is to operate

under a Level of Service B is determined to be 1000 veh/hr. Next, for that

intersection, the level of service for any volume and the service volume at

each level of service are analyzed with a graph and a table. Finally, the

optimum lane configuration and traffic control scheme to accommodate a desired

service volume are designed, and a summary table is constructed in the process.

In the last chapter of the report, an analysis of the traffic conditions

which must be met before signalization may be warranted at an intersection is

described. Traffic volume and delay statistics computed by the TEXAS Model

are analyzed for trends, relationships, and critical conditions and are used

to develop data for a cost analysis of various types of intersection control.

Warrants for traffic signals as recommended by the Manual on Uniform Traffic

v

vi

Control Devices and the Texas State Department of Highways and Public Transpor­

tation are then analyzed on the basis of cost effectiveness.

Conclusions forwarded as a result of the total investigation include the

following.

(1) Two-way stop control provides the least costly means of intersection

control over a wide range of traffic conditions when considering costs associ­

ated with stopping, delay, and traffic control devices.

(2) All-way stop control cannot be justified solely on the basis of

total intersection costs.

(3) For isolated intersections, traffic-actuated signal control is more

cost effective than fixed-time signal control.

(4) The decision to replace two-way stop control with signal control

should probably be based more on tolerable delay than on total intersection

costs.

IMPLEMENTATION STATEMENT

The TEXAS Model for Intersection Traffic is operational on both CDC 6600

and IBM 370 computers and can be used to analyze traffic performance at a

single intersection with any conventional form of sign or signal control, or

with no traffic control other than the basic rules of the road. This report

presents procedures for applying the simulation model to (1) determine inter­

section service volume at a specified level of service, (2) define the capaci­

ty of an intersection approach or of the whole intersection, and (3) evaluate

conditions which may warrant a specific form of sign or signal control on a

delay or on a cost-effectiveness basis.

It is recommended that traffic engineers and transportation planners

utilize the simulation technique and the procedures suggested to determine

optimum designs for specific intersection situations. Considerable refinement

over conventional analysis techniques is practical for both simple and com­

plex intersection configurations. Extended use of the simulation methodology

will lead to improvements in routine intersection design, analysis, and

operation.

The quantitative indicators for level of service that are presented in

Table 3 should be utilized in evaluating existing intersection performance and

in designing new intersectionso Required data can be obtained practically,

either by field survey or by simulation.

vii

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TABLE OF CONTENTS

PREFACE o•••••••••••••••••••eoaceeeoeoe

ABSTRACT • • • • • • • • • • • • • • • • o • • • e • • • • • • o o o a

SUM:MARY

IMPLEMENTATION STATEMENT

LIST OF TABLES

LIST OF FIGURES

CHAPTER 1. INTRODUCTION

CHAPTER 2. THE TEXAS MODEL FOR INTERSECTION TRAFFIC

Structure of the Model Output from the Model Computer Requirements

CHAPTER 3. INTERSECTION CAPACITY ANALYSIS USING THE TEXAS MODEL

Capacity and Level of Service Concept Indicators of Level of Service Relating Selected Performance Indicators

iii

iv

v

vii

X

xii

1

4 8 9

12 14

to Level of Service • • • . • • • • • • • . • • • • • • • • 16 Recommended Performance Indicators for

Unsignalized Intersections ........... . Capacity Analysis Procedure Using the TEXAS Model

Case I • • • • Case II Case III Case IV Example Traffic Data Analysis

Summary • • • •

viii

21 25 25 25 27 27 27 28 30 33

CHAPTER 4. EVALUATION OF TRAFFIC CONTROL WARRANTS

Application of the TEXAS Model Existing Warrants • • • ,. • • • • Scope of Warrant Investigation • • • . . . •••

Results of Simulation ••••.•• Evaluation of Existing Warrants Cost Concept • • • • . • • • •

Evaluating Existing MUTCD Warrants Least Cost Method • • • • • Proposed Warrants - Cost Basis

Cost Analysis of Texas MUTCD Actuated Signal Warrants S umm.ary • . . • • • . • • • • . • • • • • • • • • • •

CHAPTER 5. CONCLUSIONS AND RECOMMENDATIONS

Conclusions Recommendations

REFERENCES

APPENDIX

ix

39 39 40 46 48 52 57 57 62 62 66

67 68

70

72

Table

1

2

LIST OF TABLES

Interrelationships Among Levels of Service, Average Delay, and Volume Accommodated at All-Way Stop-Sign-Controlled Intersections •..•••••

Relationship Among Level of Service, Average Queue Delay, Percent Slowing to Below 10 mph, and Percent Required to Stop .•••••.•..•••

3 Recommended Indicators of Intersection

4

5

6

7

8

9

10

11

12

13

14

Levels of Service

Program-Supplied Values for Driver-Vehicle Characteristics •••••

Relationship Between Level of Service and Volume for a 2-Lane by 2-Lane Uncontrolled Intersection

Matrix of Lane Configuration and Type of Traffic Control Showing Level of Service for a Total Intersection Volume of 1600 veh/hr

Minimum Vehicular Volumes for Warrant 1

Minimum Vehicular Volumes for Warrant 2

Apparent Capacity Levels for 2-Way and 4-Way Stops

Total Intersection Volume When Average Queue Delay Per Queued Vehicle Reaches 60 Seconds

Annual Signal Costs

Computed Intersection User Cost to Meet MUTCD Warrant 1 • • • • • • • . .

Computed Intersection User Cost to Meet MUTCD Warrant 2 •.•.

Relationship Between Eighth High Hour and Higher Hour Volume . • ••••...

X

Page

20

24

26

31

36

37

41

41

49

51

56

58

59

60

xi

Table Page

15 Summary of Daily Costs Under Existing MUTCD Warrant Conditions 0 . . 61

16 Computed Intersection User Cost (2 X 2) 63

17 Computed Intersection User Cost (4 X 2) . . . . 64

18 Computed Intersection User Cost (4 X 4) 65

19 Proposed Warrant for Replacement of Two-Way Stop with Signalization . . . . . . . . . . . . . . . . 69

Figure

1

2

3

4

5

6

7

8

9

10

11

12

13

14

15

LIST OF FIGURES

Flow relationship among the programs in the TEXAS Model

Service volumes at various levels of service as indicated by average queue delay for an all-way stop-sign controlled intersection .

Levels of service at yield-sign-controlled intersections as indicated by average queue delay and percent of vehicles on signed approaches slowing below 10 mph •.••.•

Levels of service at yield-sign-controlled intersections as indicated by average queue delay and percent of vehicles on signed approaches required to stop • • •••

Intersection used for example Cases I, II, and III

Example of summary statistics

Service volume at Level of Service B for a 2-lane by 2-lane uncontrolled intersection

Analysis of a 2-lane by 2-lane uncontrolled intersection • • • 0 • • e • • •

Texas SDHPT actuated signal warrants, second high hour • • • . . • • • •

Pyramidal representation of 600 runs of the TEXAS Model using 6 levels

Detector configurations examined

Approach volume versus overall average delay

Total intersection volume versus average delay

Total user costs determined by simulation for various approach volumes • • • • • • • .

Total user costs determined by simulation for various total intersection volumes

xii

Page

5

19

22

23

29

32

34

35

42

43

45

47

50

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CHAPTER 1. INTRODUCTION

Traffic flow at street and highway intersections is a complex, time­

varying phenomenon that is affected by roadway geometry, driver and vehicle

characteristics, traffic controls, and many other less tangible factors.

Engineers are faced with the task of designing intersection configurations and

selecting appropriate controls which will simultaneously maximize safe traffic

throughput and minimize cost, delay, fuel consumption, pollution, vehicle wear

and tear, and driver frustration. Estimating the capacity of existing or

proposed intersections and deciding upon the most effective type of traffic

control for a given situation constitute a major portion of this job.

Practical, effective techniques for making these determinations are needed.

Historically, engineers either have relied on judgment developed through

experience with similar circumstances to guide their decisions or have applied

empirical or probabilistic methods of analysis. Other than direct observation,

no means has been available for studying the behavior of individually charac­

terized driver-vehicle units as they operate in the partly static, partly

dynamic intersection environment, but recent advances in digital computer

technology now make this possible through simulation.

The expected interaction among the four primary elements of intersection

traffic flow, (1) the driver, (2) the vehicle, (3) the roadway configuration,

and (4) the traffic control, can be evaluated in considerable detail and in a

highly-compressed time frame by computer simulation. Precedent reports

(Refs 1-3) in this series describe the TEXAS (1raffic EXperimental and ~na­

lytical ~imulation) Model for Intersection Traffic, a computer simulation

package that was developed specifically for analyzing traffic performance at

single, multi-leg, mixed-traffic intersections operating either without

control devices or with any conventional sign or signal control scheme. In

this model, each simulated driver of an individually-characterized vehicle is

provided every half second or so with information concerning his current

surroundings. Then, on the premise that the driver wants to maintain a

desired speed, obey applicable traffic laws, and maintain safety and comfort,

1

the priority choice to (1) continue at the same speed, (2) accelerate,

(3) decelerate, or (4) change lanes is made and implemented in the model.

Sequential application of this process steps each driver-vehicle unit through

the intersection on a microscopic space and time scale and allows performance

statistics to be gathered for subsequent analysis. A wide range of inter­

section configurations, traffic patterns, and control schemes can be examined

quickly without the time and expense of field studies or experimental instal­

lations.

2

This report describes an investigation in which the TEXAS Model was

applied for analyzing intersection capacity and for evaluating warrants for

various forms of traffic control. Pertinent features of the TEXAS Model which

make it uniquely suited for these purposes are presented in the next chapter,

and in succeeding chapters techniques for using the model as a practical aid

to engineering decision making are outlined.

Intersection capacity analysis involves two basic steps: (1) selecting

the criteria which define capacity, and (2) estimating the maximum amount of

traffic that can be accommodated without violating these criteria. The TEXAS

Model permits a wide range of geometric, traffic, and control conditions to be

specified, and then after simulating traffic flow for a selected period of

time, presents summary statistics concerning the behavior of traffic and of a

signal controller if one was used. Comparison of the resulting statistics with

the selected capacity criteria allows one to determine whether or not the

criteria were violated. Only a few runs of the model, using successive

approximations, are needed to find the capacity of an intersection operating

under a given set of circumstances. Examples of this technique are given in

Chapter 3, and easily-determined, quantitative indicators for intersection

levels of service are suggested.

Similarly, the geometric and traffic conditions which warrant a particu­

lar type of traffic control at an intersection can be evaluated by simulation.

Intersection traffic control can range from the basic rules-of-the-road, to

signs, and even to sophisticated signal schemes. Various criteria can be

selected to define the quality of traffic flow through an intersection, and if

a proposed scheme satisfies these criteria the geometric arrangement and

controls can be said to be warranted. Chapter 4 describes how the TEXAS Model

was used to study the cost effectiveness of (1) the minimum vehicular volume

warrant for signals, (2) the interruption of continuous traffic warrant for

3

signals as stated in the Manual on Uniform Traffic Control Devices, 1971

(Ref 4), and (3) the actuated signal warrant that is presented in the Texas

Manual on Uniform Traffic Control Devices, 1973 (Ref 5). A variety of inter­

section lane arrangements, types of control, and traffic patterns were simu­

lated in over 600 runs of the model. Conclusions are drawn concerning these

existing warrants, and a tolerable delay warrant is proposed for consideration

when two-way stop control is to be replaced with signalization.

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CHAPTER 2. THE TEXAS MODEL FOR INTERSECTION TRAFFIC

A model for simulating intersection traffic, the TEXAS (lraffic

EXperimental and ~nalytical ~imulation) Model, has been developed at the

Center for Highway Research at The University of Texas at Austin, as part of

Research Study No. 3-18-72-184, under the Cooperative Research Program with

the State Department of Highways and Public Transportation and the Federal

Highway Administration (see Refs 1-3). This computer model accomplishes a

microscopic, step-through simulation of traffic flow at a single intersection.

It is a deterministic model for the most part, in that none of the response

decisions is made on a probability basis. Rather, precise criteria for a

particular action are established, and when these criteria are met, a pro­

grammed action is carried out. Traffic input to the model is generated,

however, on a stochastic basis from descriptive information provided by the

user. Since the TEXAS Model was developed especially for isolated inter­

sections, headways in the entering traffic stream are considered to be random;

therefore, headways are generated as random variates of a user-selected prob­

ability distribution function.

Structure of the Model

The TEXAS Model is a package which consists of three main computer

programs. These are

(1) the geometry processor, GEOPRO;

(2) the driver-vehicle processor, DVPRO; and

(3) the simulation processor, SIMPRO.

Figure 1 shows the flow relationship among these programs.

The modular form of programming that was used provides for computational

efficiency by virtue of the fact that all data which require only one computa­

tion are processed by either the geometry processor or the driver-vehicle

processor and the results are stored for subsequent use. The simulation pro­

cessor then performs repetitious computations related to the behavior of each

vehicle.

4

Plotted Output

Fig 1.

Geometry Processor

Punched Output

Printed Output

Pre-Simu lotion Processor Card lnpuv

Simulation Processor

Card lnput

Simulation Processor

Printed Output

Driver Vehicle

Processor

Graphics Display

Printed Output

Flow relationship among the programs in the TEXAS Model.

5

6

The geometry processor, GEOPRO, accepts data concerning the physical

configuration of the intersection such as details of the approaches, lanes,

curb returns, and sight distance restrictions. Input information is coded by

the user in conventional Cartesian coordinates. The processor calculates the

vehicle paths on the approaches and within the intersection, the points of

conflict between intersection paths, and the minimum available sight distance

between approaches. GEOPRO uses straight line segments and arcs of circles to

describe paths that vehicles will follow in the intersection, and safe side

friction factors are used for computing the maximum speed at which a vehicle

may negotiate these paths. The minimum available sight distance between

inbound approaches is calculated for each 25-foot increment along the

approach. Computed information is written onto a tape for later use in the

simulation. A plot of the plan view of the intersection may be requested if

needed.

The driver-vehicle processor, DVPRO, takes user-supplied information

about the characteristics of up to 5 driver and 15 vehicle classes, generates

the required descriptive data for each individual driver-vehicle unit and

orders these units sequentially by queue-in time. The time headways of

vehicles which arrive on each inbound approach are calculated as random

variates of one of the following distributions: (1) Uniform, (2) Log Normal,

(3) Negative Exponential, (4) Shifted Negative Exponential, (5) Gamma,

(6) Erlang, or (7) Constant. The user chooses an appropriate distribution for

each inbound approach, specifies a traffic volume for that approach, and

defines an additional parameter, which indicates the expected variability in

headways. An auxiliary data processor, DISFIT, is contained in the simulation

package to aid the user in determining which mathematical distribution best

matches any empirical headway data that might be available. In DISFIT, a

value for Chi-Squared is calculated as a goodness of fit indicator for each

distribution that is fitted, and the maximum cumulative difference is found

for a Kolmogorov-Smirnov one-sample test. Histograms of the input headway

data and of each distribution that has been fitted are also plotted to assist

the user in selecting an appropriate mathematical description of the traffic

pattern under investigation. Each driver-vehicle unit is assigned a lane, a

turning movement, a driver class, and a vehicle class according to defined

percentages using a discrete empirical distribution. Arriving vehicles are

required to maintain a specified minimum safe headway, and speeds are assigned

using a discrete normal distribution with a specified mean and a standard

deviation calculated from the mean and the 85 percentile speed. All the

computer characteristics about each driver-vehicle unit such as its arrival

time, vehicle class, driver class, arrival speed, inbound approach, inbound

lane, and outbound destination are written on tape for use later by the simu­

lation processor.

The simulation processor, SIMPRO, accepts output from the geometry

processor, from the driver-vehicle processor, and by direct card input. The

card input specifies (a) the start-up and simulation time, (b) the time-step

increment for simulation, (c) speed for "delay below XX miles per hour,"

7

(d) the maximum clear distance for being in a queue, (e) lambda, mu, and alpha

values for use in the generalized car-following equations, (f) the type of

intersection control, (g) the desired summary statistics, (h) time for lead

and lag zones for intersection conflict checking, and (i) lane control for

each lane. Many of these values are supplied automatically by the program,

but the user may choose values of special interest. If the intersection is

signalized, signal indication information for each lane consists of card input

which models the cam stack found in most signal controllers plus the timing

scheme for displaying each interval. If the intersection operates under an

actuated controller, additional information about detector type and location

is required.

SIMPRO uses a specified, discrete time increment, usually in the range of

one-half second to one second, as the fixed time basis for scanning the inter­

section and updating each driver-vehicle unit. It has three types of links on

which to simulate driver-vehicle units: (1) inbound lanes, where there is

some form of control which regulates entry into the intersection; (2) inter­

section paths; and (3) outbound lanes, where there is no control at the far

end. The sequential flow of the program processes driver-vehicle units on the

outbound lanes, then on intersection paths, and next on inbound lanes; then

new driver-vehicle units are added to the system, and finally signal status is

processed. Driver-vehicle units, which are first on their link and have the

right to continue to the next link, look ahead and react to the last driver­

vehicle unit in the next link; thus, continuity between links is provided.

Flow through the system is assumed to attain a steady state condition

after a specified start-up time. During start-up time, all movements are

simulated but no performance statistics are gathered. After that, all traffic

and control activities are simulated and statistics are accumulated as each

vehicle logs out of the system at the end of the outbound lane. Summary

statistics are reported in a tabular form at the end of the specified simula­

tion time.

Output from the Model

8

Upon request, a large variety of information concerning the results of

simulation can be printed, punched on cards, or shown on a graphics display

screen. Summary statistics may be presented according to each inbound

approach, according to selected turning movements, and for the intersection as

a whole. The following statistics are included in the output:

(1) number of vehicle-seconds of delay;

(2) number and percent of driver-vehicle units delayed;

(3) average delay for delayed units;

(4) overall average delay for all units;

(5) number and percent of driver-vehicle units required to stop;

(6) total and average vehicle-miles of travel;

(7) total and average travel time;

(8) equivalent hourly volume of traffic;

(9) average desired speed;

(10) time and space mean speed;

(11) average maximum uniform acceleration and deceleration used;

(12) average and maximum length of queue on each inbound lane;

(13) average ratio of entry speed to desired speed;

(14) delay resulting from slowing below XX (specified value) miles per hour; and

(15) percent of vehicles required to slow below XX miles per hour.

Some of the statistics that are computed during simulation are difficult,

or nearly impossible, to obtain from field observations of traffic. The fact

that these values, along with all conventional descriptors of traffic

behavior, are incorporated in the output from the TEXAS Model makes applica­

tion of this simulation package a particularly powerful tool for analyzing

intersection performance.

As will be pointed out later in this report, the items of output that are

of significance in determining intersection capacity and level of service are

(1) total intersection volume, (2) percent of vehicles required to stop,

(3) percent of vehicles required to slow below 10 miles per hour, (4) average

queue delay, and (5) average stopped delay. In evaluating warrants for

traffic control at intersections, additional summary statistics relating to

(1) approach volume, (2) total queue delay, and (3) total stopped delay were

found to be valuable indicators of performance.

Computer Requirements

FORTRAN IV language has been used to implement the TEXAS Model on both

Control Data Corporatio.:1 (CDC6600) a:..1.d International Business Machines

(IBM370-155) computers.

The geometry processor, GEOPRO, requires 29,760 words (72,100 octal) of

storage on CDC computers and 176,000 bytes of storage on IBM computers.

Geometry computations for an average intersection (4 inbound and 4 outbound

approaches, 2 lanes per approach, 4 sight distance restriction coordinates,

and PRIMARY intersection paths) take 6.3 central processor seconds on CDC

computers and 9.2 central processor seconds (0.153 minutes) on IBM computers.

9

The driver-vehicle processor, DVPRO, requires 17,216 words (41,500 octal)

of storage on CDC computers and 102,000 bytes of storage on IBM computers.

The driver-vehicle processor requires approximately 3 seconds of computer time

on CDC computers and 4 seconds (0.067 minutes) on IBM computers to generate a

moderate flow of driver-vehicle units for an average intersection of 4 inbound

and 4 outbound approaches, 2 lanes per approach.

The simulation processor, SIMPRO, uses 32,704 words (77,700 octal) of

storage on CDC computers and 210,000 bytes of storage on IBM computers. The

computer time requirements for SIMPRO are difficult to reduce to a single

value. As an indication of the efficiency of the model, a simulation time to

computer time ratio for CDC computers has been calculated for each run of

SIMPRO. This ratio varies with the type of intersection control, the lane

lengths, the time increment, and the total number of driver-vehicle units

processed. For signalized intersections, 600-foot (182.88-meter) lanes, and a

time increment of one second, the lower limit of efficiency (worst case) is in

the general range from 30 at a total equivalent hourly volume of 1,000

vehicles per hour to 8 at a volume of 2,000 vehicles per hour. The upper

limit of efficiency (best case) is 45 and 15, respectively, for the same

10

volumes. For non-signalized intersections, 600-foot (182.88-meter) lanes, and

a time increment of 0.5 seconds, the lower limit of efficiency (worst case) is

in the general range from 40 at a volume of 750 vehicles per hour to 8 at a

volume of 1,250 vehicles per hour. These efficiencies may be different for

other computer systems.

This page intentionally left blank to facilitate printing on 2 sides.

CHAPTER 3a INTERSECTION CAPACITY ANALYSIS USING THE TEXAS MODEL

Traffic engineers and transportation planners are faced with the task of

designing road facilities and traffic control schemes which provide for safe

and efficient movement of people and freight. Intersections are critical com­

ponents of this system and a single intersection may be responsible for limit­

ing the capacity of an entire road network. An accurate and convenient method

for determining the capacity of an intersection is thus needed.

The methods currently available for analyzing the capacity of inter­

sectioGs are mostly empirical, probabilistic, or based on sample observations.

In the empirical methods, historical experience and analysis are usually

reduced to charts, tables, and adjustment factors. Probabilistic methods

utilize statistical distributions to represent traffic characteristics such as

headway, spacing, and speed. Expected interactions are computed and shown as

graphs or formulae for capacity. Observation methods involve field sampling

and forecasting. Time-lapse photography has sometimes been used to record

traffic movements at representative intersections; then data from the pictures

have been analyzed and reduced to formulae for capacity.

Since these methods are generally macroscopic and are intended to be

applicable over a wide range of situations, they usually do not consider

individual driver-vehicle movements. Most techniques for capacity analysis

are concerned with signalized intersections, and a method that can readily be

used to determine the capacity of unsignalized intersections is not currently

available. There is a need for a practical method of estimating the capacity

of intersections operating under any conventional form of control, or with no

control, whereby the behavior of each vehicle in the traffic system can be

accounted for.

11

Capacity and Level of Service Concept

Before 1965, three levels of intersection capacity were generally

recognized (Ref 6):

(1) basic capacity - the maximum number of vehicles that can be accommodated under the most nearly ideal traffic conditions which can possibly be attained;

(2) possible capacity - the maximum number of vehicles that can be accommodated under prevailing traffic conditions with a con­tinual backlog of waiting vehicles; and

(3) practical capacity - the maximum number of vehicles that can be accommodated under prevailing traffic conditions with no vehicle incurring undue delay.

12

Having identified only two categories for prevailing traffic conditions was

thought to be inadequate in practice, and it was felt that it would be more

definitive to describe intersection traffic flow in terms of a range of

values. Capacity is now defined (Ref 7) as the maximum traffic volume accom­

modated under a given set of conditions. Practical capacity has been replaced

by several service volumes representing any of several specific traffic vol­

umes related to a group of desirable operating conditions collectively termed

"level of service."

Level of service is the qualitative measure of the effect of a number of

factors, which include speed and travel time, traffic interruptions, freedom

to maneuver, safety, driving comfort and convenience, and operating costs.

Each level of service has associated with it a "service volume" which is the

maximum volume that can be accommodated while providing the specified level of

service. The service volume at level of service "E" is the maximum volume

that can be accommodated by the intersection under prevailing conditions and

is thus the capacity of the intersection. This definition corresponds to the

previously defined possible capacity. Six levels of service, identified

alphabetically from "A" to "F," have been selected for application in defining

the quality of intersection operating conditions.

13

Level of Service Flow Condition Description

A Free flow No waiting vehicles

B Stable flow Restricted within platoons

c Stable flow Back-ups develop behind turning vehicles

D Approaching unstable flow Substantial delays

E Unstable flow Capacity

F Forced flow No movement

One measure of intersection level of service is user satisfaction. A

facility can be said to provide a high level of service if the user is pleased

to drive through the intersection. This means that each driver may choose the

speed that he wants and pass through the intersection without unreasonable

hindrance.

In the case of uninterrupted flow on sections of roadway between inter­

sections, speed is generally used as a measure of level of service, and speed­

volume curves are used to describe the level of service under which the

section operates. However, at intersections, the inherent stop-go nature of

traffic makes such a relationship difficult to interpret. Speed is, therefore,

not considered to be a good indicator of performance in this situation, and a

different indicator of level of service is desired.

The level of service at intersections depends on the manner in which the

traffic flows through the intersection. At signalized intersections, load

factor is widely accepted as a performance indicator for level of service

(Ref 7). Load factor is defined as the ratio of the number of fully utilized

green phases in a series of signal cycles to the total number of green phases

in the same series. Load factor is easy to measure in the field, since all

that is required is a count of the green phases during which vehicles are

continually present and the total number of green phases displayed in the

selected time period. Load factor is the ratio of these two numbers. Numer­

ical limits of load factor for various levels of service are given as

14

Level of Service Traffic Flow DescriEtion Load Factor

A Free flow 0.0

B Stable flow <0.1

c Stable flow <0.3

D Approaching unstable flow <0. 7

E Unstable flow < 1.0

F Forced flow

Even though load factor is used extensively to identify intersection

levels of service, it is not an ideal descriptor. Its applicability is

limited to signalized intersections, and the break points between the various

levels of service have no strong rational basis. A better, and more widely

applicable, means for expressing the quality of intersection performance as

perceived by the user in quantitative terms is desired.

Indicators of Level of Service

Indicators that can be used at intersections with all forms of traffic

control are needed to identify the level of service that is provided. The

selection of appropriate indicators can be considered from two points of view.

The designer prefers indicators that can be measured easily in quantitative

terms, while the user perhaps comprehends more subjective measures of his

satisfaction. Indicators which relate to both these points of view should be

selected for evaluating the performance of intersections. The selected indi­

cators must be easy to measure quantitatively, and the user must be able to

relate them to his personal satisfaction. If simulation is to be used in

capacity analysis, any indicator of level of service should be readily

attainable from the simulation model.

The following indicators appear to be appropriate measures of level of

service at intersections in that they incorporate all the desired features

stated above.

(1) Queue delay: Queue delay is the delay experienced when a vehicle

is in a queue. A vehicle can be said to be in a queue if all the following

conditions are satisfied:

(a) The vehicle is at a virtual stop. A vehicle moving slower than, say, 2 mph is considered to be stopped.

(b) An object ahead, such as a stop sign, requires the vehicle to stop, or the vehicle immediately ahead is in a queue.

(c) The vehicle is less than a prescribed distance (e.g., 30 feet) from an object which requires a stop.

15

Once a vehicle is in a queue, it is considered to remain in the queue

until it enters the intersection, even if its speed exceeds 2 mph while moving

forward in the queue. Queue delay is thus measured from the time the vehicle

enters the queue until the time it enters the intersection and includes time

spent in moving up in the queue. Since vehicles at unsignalized intersections

experience this type of delay, queue delay is an appropriate criterion that

may be used to evaluate delay at unsignalized intersections. Queue delay is

readily identified by the user as an index of intersection performance since

the user prefers to travel through intersections under circumstances whereby

minimum time is spent waiting in a queue. As average queue delay is one of

the statistics compiled from simulation by the TEXAS Model, it is a readily

available quantitative factor that may be used as a level of service indicator.

In field studies, queue delay can be measured (1) by enumerating the

number of vehicles in the queue at fixed, periodic time intervals (point

sample), (2) by the input-output method, (3) by path trace based on a sample

of individual vehicles, and (4) by time-lapse photography. A special device

for recording queue delay by the point sample technique on a one-second time

basis is described in Ref 1.

A recent study by Sutaria and Haynes (Ref 8) utilized the opinions of

310 drivers with a wide variety of driving experience to evaluate intersection

levels of service. Each participant in the study was first asked to rank the

following factors according to their relative importance in defining the

quality of service provided by an intersection: (1) delay, (2) number of

stops, (3) traffic congestion, (4) number of trucks and buses in the traffic

stream, and (S) difficulty in lane changing. Then, each driver was shown a

series of photographs of a signalized intersection in Fort Worth, Texas,

operating under a variety of traffic conditions, or levels of service. A

majority of the drivers indicated both before and after viewing the pictures

that delay was the most important factor in their subjective evaluation of

intersection performance.

(2) Percent of vehicles that are required to stop: Percent of vehicles

that are required to stop is easy to measure in the field simply by counting

16

all the vehicles that stop and the total traffic volume for a selected period

of time. No special equipment is required for these measurements. It is

apparent to the driver that the intersection behaves more satisfactorily if

most vehicles can pass through without having to stop. This parameter is also

available in the summary statistics of the TEXAS Model. Since percentage

required to stop is easier to measure than average queue delay, this indicator

might be preferable to intersection designers as a level of service indicator.

It is applicable only at uncontrolled and yield-sign controlled intersections,

however, as at stop-sign controlled intersections, all vehicles on approaches

facing the stop signs are required to stop. An advantage of using this param­

eter is that the stage at which an uncontrolled or yield-sign controlled

intersection behaves similarly to a stop-sign controlled intersection can be

observed, since, at that point, a high percentage of vehicles will be required

to stop.

(3) Percent of vehicles required to slow to below 10 mph: This indica-

tor relates directly to driver satisfaction since no driver likes to slow to

below 10 mph. The percentage of vehicles that have to slow below 10 mph is

difficult to determine in field studies, however. This can possibly be

measured in the field using time-lapse photography. The TEXAS Model computes

this value from simulation and makes it available for comparing the perform­

ance of various types of unsignalized intersections. A further incentive for

considering this indicator is that the 1971 version of the Manual on Uniform

Traffic Control Devices (MUTCD) (Ref 4, p 34) states:

The Yield Sign may be warranted:

On a minor road at the entrance to an intersection where it is necessary to assign right-of-way to the major road, but where a stop is not necessary at all times, and where the safe approach speed on the minor road exceeds 10 miles per hour.

Relating Selected Performance Indicators to Level of Service

Since queue delay can feasibly be used as an indicator of level of

service for all types of intersection control, a quantitative relationship

between queue delay and level of service, similar to the one that has been

recognized between load factor and level of service, is desired. Once this

relationship is established, the maximum volume that cao1. be accommodated at

each level of service can be determined.

17

May and Pratt (Ref 9) established a relationship between average delay

and load factor for signalized intersections and then linked average delay to

level of service by using rec .. Jgnized relationships between load. factor and

level of service. They conducted simulation experiments to establish the

relationship between level of service and load factor. For their simulatLon

studies, May and Pratt generated arrival times for vehicles 0:1. each inter­

section approach by using a random headway distribution with a minimum input

headway of one second. The randomly generated numbers were multiplied by 3600

and arranged in a chronological order to obtain individual arrival times for

vehicles within a one-hour period. The simulated intersection was controlled

by a pre-timed signal with a 60-second cycle and equal red and green phases.

The minimum headway for discharging vehicles depended on the desired

specific capacity. For example, a capacity of 600 veh/hr meant that the

capacity per cycle was 600/60 10 . For 30 seconds of green, the uniform

discharge headway was 30/10 = 3 seconds Other discharge headways could

similarly be calculated by assuming other specific capacities. A vehicle was

not permitted to leave until the calculated discharge headway time had

elapsed. The load factor and the average delay incurred by each vehicle were

noted, and a graph (Fig 4, Ref 9, p 44) was drawn. From this graph and

Table 6.3 of the Highway Capacity Manual (Ref 7, p 131), a table relating

average delay to level of service (Table I, Ref 9, p 47) was constructed. May

and Pratt then utilized the relationship between load factor and level of

service developed in the Highway Capacity Manual and obtained a new relation­

ship in which level of service was based on approximately equivalent average

individual delay. This relationship is presented in Table II, Ref 9, p 47.

May and Pratt's analysis demonstrated that average delay could be used as

an indicator of level of service in place of load factor at signalized inter­

sections. Capacity analysis of unsignalized intersections would be facilitated

if a similar relationship between average queue delay and level of service

could be developed for unsignalized control.

Operational delays for a given level of service should be consistent

regardless of the type of control at the intersection. May and Pratt's

analysis defines reasonable and orderly relationships between average delay

and level of service at signalized intersections. These same values can be

used to describe levels of service at unsignalized intersections.

After making a large number of runs of the TEXAS Model for a 4-lane by

4-lane all-way stop-sign-controlled intersection for a wide range of traffic

demand, a graph of total intersection volume against average queue delay

18

(Fig 2) was drawn. A quite similar relationship was found for a 2-lane by

2-lane all-way stop-sign-controlled intersection. Horizontal lines represent­

ing average delay for the various levels of service shown in Table II, Ref 9,

p 47 (see also Col 2, Table 1), were superimposed on the graph. Column 3 in

Table 1 shows the volume of traffic accommodated at these levels of service as

read from Fig 2. For comparison, average delay as suggested by Sutaria and

Haynes (Ref 8) is shown in Col 4 of Table 1. Table 1, then, shows the inter­

relationships among level of service, average delay, and volume accommodated.

The volume at each level of service can be judged to be reasonable and can be

expected to result in the general flow conditions described in the Highway

Capacity Manual (Ref 7).

The Manual on Uniform Traffic Control Devices (Ref 4, p 33) states that

one of the conditions which might warrant a stop sign is an average delay of

at least 30 seconds per vehicle during the maximum hour. Since an average

delay of 30 seconds is the upper boundary suggested for level of service B

(see Table 1), this adds validity to the choice of 30 seconds as the boundary

between levels of service B and C at which intersections normally operate.

In Ref 10 this is further discussed, and a relationship was established

between volume warrants and 20, 30, and 35 seconds of average delay (Table 5.2,

Ref 10, p 84). This would correspond to levels B, B/C, and C, according to

Table 1.

Average queue delay can be used as a measure of level of service for all

intersections. However, for uncontrolled and yield-controlled intersections,

a more convenient indicator of level of service might be the percentage of

vehicles that are required to stop, since it is easier to measure the percent

stopped and these intersections operate as stop-controlled intersections if a

high percentage of vehicles are required to stop. For yield-controlled

intersections, another indicator is the percentage required to slow to below

10 mph, since a commonly accepted warrant for that control is that it may be

used if the approach speed exceeds 10 mph.

These two performance indicators, (1) percentage of vehicles required to

stop and (2) percentage of vehicles required to slow to below 10 mph, may also

be related to level of service. To establish these relationships, the TEXAS

90 ......-------------

- 80-0 Q)

~ 70- E

~

.s:! 60 --------------· Q) '· a 50- D I

~ -------------i I Q) 40 - C el I ~ • t•l Q) 30 ~------------•-; I I 0\ • : I I o 20 ~ B • •I I ~ • I 1 I > ~------------;_;~•! 1 I

<:t 10 ~ A • ••• I 1 I 1 •• •• •• • • I I

o~--_.·----~·----~~--~~~~~-~~~

Fig 3.

0 400 800 1200 1600 2000 Total Intersection Volume (veh/hr)

ALL-WAY STOP SIGN CONTROL 4-Lone by 4-Lone

Service volumes at various levels of service as indicated by aver­age queue delay for an all-way stop-sign controlled intersection.

19

TABLE 1. INTERRELATIONSHIPS AMONG LEVELS OF SERVICE, AVERAGE DElAY, AND VOLUME ACCOMMODATED AT ALL-WAY-STOP-SIGN-CONTROLLED INTERSECTIONS

Average Average Average Level of Delay, 7'" Volume, "'d.- Delay, "'d.-7.-

Service sec/veh veh/hr sec/veh

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

A ::; 15 s 1400 s 12.6

B ::; 30 s 1500 s 30.1

c ::; 45 ::;_ 1600 s 47.7

D ::; 60 :S. 1700 s_ 65.2

E > 60 > 1700 :S. 82.8

*Source: Table II on page 47 of Ref 9

"'d.-Source: Figure 2

***Source: Table 6-B, page 24, Ref 8

20

21

Model was run to examine traffic behavior at a representative yield-sign

controlled intersection under a wide range of demand volume; and the average

queue delay resulting from different percentages of vehicles slowing to below

10 mph and the average queue delay resulting from different percentages of

vehicles required to stop were obtained. Figure 3 is a graph of percent of

side-street vehicles slowing to below 10 mph against average queue delay, and

Fig 4 shows percent of vehicles required to stop against average queue delay.

On both these graphs, horizontal lines representing levels of service for

different values of average queue delay determined earlier (see Table 1) are

superimposed. From these graphs, the level of service for different percent­

ages of side-street vehicles slowing to below 10 mph (Table 2, Col 3) and the

level of service for different percentages of vehicles that were required to

stop (Table 2, Col 4) can be read. Table 2 shows the relationship among level

of service, average queue delay, percent slowing to below 10 mph, and percent

required to stop.

Recommended Performance Indicators for Unsignalized Intersections

For stop-sign controlled intersections, average queue delay is recommended

as the best indicator of level of service. Average queue delay can be measured

in the field by appropriate survey techniques, it can be comprehended by the

user, and it can be simulated by the TEXAS Model. Suggested relationships

between average queue delay and the various levels of service are presented in

Table 1.

For yield-sign controlled intersections, both the percentage of side­

street vehicles that have to slow below 10 mph and those that have to stop can

be considered as good indicators of level of service. The percentage of

vehicles that have to slow to below 10 mph can be determined from simulation

or it can be measured in the field using time-lapse photography; it can also

be understood by the.user. Too, this parameter has been recognized as the

basis of a warrant for yield-sign control of intersections. Suggested rela­

tionships between percent of vehicles slowing to below 10 mph and various

levels of service are presented in Table 2. The percentage of side-street

vehicles that have to stop can be measured easily in the field, it is easily

understood by the user, and it can be simulated by the TEXAS Model. Suggested

relationships between percent of vehicles that have to stop and levels of

service are also presented in Table 2.

Fig 2.

90---------------------------- 80-

Level of Service

E 0

~ 70->. ~ 60 !--------- ----·-, Q)

0 50 D • I •

- I • Q)

:::3 --------------, I Q) 40 :::3 ~ c : :

0 Q) 30 0\

------------... ~ ~ r • • •, , I

r- 8 .: I I I ~--------.-;. I I I

0 '­Q)

> <X

20

10 - A •. • ~ • I I 1 I I I I

0 ~----~·----·~-----·~-~·-~'·----J 0 20 40 60 80 100

o/o of Vehicles on Yield-Sign Approaches Slowing Below 10 mph

YIELD-SIGN CONTROL

Levels of service at yield-sign-controlled intersections as indicated by average queue delay and percent of vehicles on signed approaches slowing below 10 mph.

22

9 0 r----------------Level of Service

80 ~ ....... E 0

Q)

~ 701- • ~ 60 • -------------, Q)

a Q)

:::s 50 - D • I •

• • I ------- - - - -, I

~ 40 0

- C •I I • I I

Q)

0\ 30 ----------.-, r,

• • 1 I I ~<- B • I I • • I ~----- "J• • 1 I I

0 ~ .20 >

<(

Fig 4.

10- A • I I I I I I I jl I

o~--·~~-----~·----~·--~~~._·--~ 0 20 40 60 80

0/o of Vehicles on Yield-Sign Approaches Required to Stop

YIELD-SIGN CONTROL

100

Levels of service at yield-sign­controlled intersections as indicated by average queue delay and percent of vehicles on signed approaches required to stop.

23

Level of Service

(Column 1)

A

B

c

D

E

TABLE 2. RElATIONSHIP AMONG LEVEL OF SERVICE, AVERAGE QUEUE DELAY, PERCENT SLOWING TO BELOW 10 MPH, AND PERCENT REQUIRED TO STOP

Average Percent of Vehicles Percent of Vehicles Queue Delay Slowing to Below 10 mph Required to Stop

(Column 2) (Column 3) (Column 4)

< 15 sees < 60 percent < 40 percent

< 30 sees < 70 percent < 60 percent

< 45 sees < 80 percent < 70 percent

< 60 sees < 85 percent < 75 percent

> 60 sees > 85 percent > 75 percent

24

25

For uncontrolled intersections, percent of vehicles that are required to

stop is considered to be the most appropriate indicator of level of service,

since it can be measured very easily in field studies. The relationship

between percent of vehicles that are required to stop and level of service as

suggested in Table 2 can be used in evaluating uncontrolled intersections.

Table 3 is a summary tabulation of recommended performance indicators for

various levels of service at each type of unsignalized intersection. Sug­

gested values for signalized intersections (Ref 9) are also included in this

table for convenience.

Capacity Analysis Procedure Using the TEXAS Model

An intersection is characterized by its geometry, type of control, volume

accommodated, and level of service provided. Generally, if any three of these

factors are known, the fourth can be determined. To use the TEXAS Model, all

data regarding geometries, traffic characteristics, and volume conditions that

are known are collected and input to the geometry and driver-vehicle proces­

sors and to the simulation processor. The summary statistics that are re­

ported from the run are analyzed to provide the required information. Four

cases are now described in which the TEXAS Model can be used to evaluate the

performance of an unsignalized intersection.

Case I

Known: Lane configuration, type of control, and volume accommodated

Desired: Level of service

Method: The TEXAS Model is run with the known geometry and control at

the accommodated volume. The value of an appropriate performance indicator is

determined from the summary statistics, and then from Table 3 the level of

service is determined.

Case II

Known: Lane configuration, type of control, and level of service

Desired: Service volume that can be accommodated

Method: An estimate of the volume is made. Then the TEXAS Model is run

with the geometry, type of control, and estimated volume. The value of the

appropriate performance indicator is determined from the summary statistics.

The level of service that is provided is determined from Table 3. If this is

TABLE 3. RECOMMENDED INDICATORS OF INTERSECTION LEVELS OF SERVICE

Type of Two-Way All-Way Signal Intersection Uncontrolled Yield -Sign Control Stop Stop

Control Control Control Control

~ Percent of all Percent of Percent of Average Queue Average Queue Average Vehicles That Vehicles on Vehicles on Delay* to Delay* to Stopped-Delay**

r Must Stop Sign- Controlled Sign-Controlled Vehicles on Vehicles on to Vehicles on I Approaches That Approaches That Sign-Controlled A II Approaches All Approaches

f Must Slow Must Stop Approaches e Below IOmph

A < 40°/o < 60°/o < 40°/o < 15 sec < 15 sec < 15sec

8 < 60°/o < 70°/o < 60°/o < 30sec < 30sec < 30 sec

c < 70°/o < 80°/o < 70°/o < 45 sec < 45 sec· < 45 sec

D < 75°/o < 85°/o < 75°/o < 60 sec < 60 sec < 60 sec

E > 75°/o > 85°/o > 75°/o > 60 sec > 60 sec > 60 sec - _.._

-'---~ ----- --~- ----~- -*Queue delay is the time spent by a vehicle while at a virtual stop in a queue of vehicles on an intersection approach.

It is measured from the time the vehicle joins the queue unti I the vehicle enters the intersection, and thus includes

move-up time. **Stopped delay is the time spent by a vehicle while actually stopped on an intersection approach; it does not include

move-up time.

N Q"\

27

not the level desired, a fresh estimate of the volume is made and the process

is repeated until the intersection can be expected to operate at the desired

level of service. Usually two or three runs will be sufficient to estimate

the service volume.

Case III

Known: Lane configuration and type of intersection control

Desired: The level of service provided for different volumes, or the

maximum volume that can be accommodated at each level of service

Method: The TEXAS Model is run for the known geometry and control at a

range of volumes that could be expected to cover all the levels of service.

From summary statistics, a graph of volume against the specific indicator can

be drawn, and a table linking volume to level of service, using Table 3 as a

guide, can be constructed. This table is then used to determine the desired

information.

Case IV

Known:

Desired:

Volume to be accommodated and level of service to be provided

Optimum design (lane configuration and control)

Method: A lane configuration and a control scheme are chosen. Then the

TEXAS Model is run with the desired volume, and from summary statistics and

Table 3 the level of service that will be provided is determined. If this

level of service is not satisfactory, a fresh choice of geometry and control

is made, and the process is repeated until the desired level of service is

attained at that volume. Two or three runs should be sufficient to design the

intersection.

A working example using a step-by-step procedure is now described to

illustrate these four cases.

Example

For Case I, the level of service at which a 2-lane by 2-lane uncontrolled

intersection accommodating 1600 veh/hr will operated will be determined. For

Case II, the maximum volume that can be accommodated by a 2-lane by 2-lane

uncontrolled intersection operating at a level of service B will be determined.

For Case III, the levels of service at different volumes and the maximum

volume that can be accommodated at each level of service by a 2-lane by 2-lane

uncontrolled intersection will be analyzed using a graph and a table that will

be constructed. For Case IV, the optimum lane configuration and type of

intersection control to accommodate 1600 veh/hr while maintaining a level of

service A will be determined.

28

Geometry of the Intersection. The intersection is assumed to be a

right-angled intersection with four approaches and four exits. For the first

three cases, each leg of the intersection has one lane in each direction. The

number of lanes for the fourth case will be determined based on the volume to

be accommodated and the level of service to be maintained. Each lane is 10

feet wide. The influence of the intersection extends 800 feet in advance of

the intersection on each inbound lane and 400 feet beyond the intersection on

each outbound lane. The speed limit is 35 mph on all approaches. There are

no sight distance restrictions. A plot of the intersection used for the

example in Cases I, II, and III is shown in Fig 5.

Traffic Data

(1) The distribution of traffic on each approach was found to be

Approach

1

2

3

4

Direction

Northbound

Westbound

Southbound

Eastbound

Percentage of Total Volume

15

25

25

35

(2) On two inbound lanes, 45 percent of the vehicles were assumed to

be in the median lane, and 55 percent of the vehicles were in

the curb lane (Case IV).

(3) In every case, 15 percent of the vehicles turned right, 10 per­

cent of the vehicles turned left, and 75 percent of the vehicles

went straight through.

(4) On the minor (North-South) approaches, the mean speed was 25 mph,

and the 85 percentile speed was 30 mph. On the major (East-West)

approaches, the mean speed was 30 mph, and the 85 percentile

speed was 35 mph.

(5) The arrival headway pattern was described by the negative expon­

ential distribution.

29

19TH ~T A~ CHZC~N - 2 lANE MAJOR/2 lANE MlN~R - 800 FOOT R?PR~RCHES

+ +

+ + +

+ +

~CAlf fACTOR IS 15.0 FEET PER ZNCH

Fig 5. Intersection used for example Cases I, II, and III.

(6) The program-supplied values for the percentage of vehicles in

each vehicle class and the percentage of drivers in each driver

class were used. These values are presented in Table 4.

30

Simulation. Starting with no vehicles in the system, generated driver-

vehicle units were positioned at the start of the approach according to the

calculated arrival time. Then, depending on the desired speed, destination,

traffic condition, and relative position in the intersection area, each unit

responded logically to its surroundings. The system was scanned and updated

at fixed intervals of one-half second. Each unit was processed through the

approach. Flow through the system was assumed to attain a steady-state condi­

tion in two minutes of real time. Until then, all the movements were simu­

lated, but no statistics were gathered. After that, all movements were simu­

lated and statistics were accumulated as each vehicle logged out of the system

at the end of the exit. The duration of simulation for this example was 10

minutes of real time. Figure 6 shows the summary statistics for the inter­

section used in this example. The intersection was uncontrolled, in Cases I,

II, and III; therefore, the total intersection volume and the percent of

vehicles that were required to stop were used for capacity analysis.

Analysis

The four cases described earlier are evaluated here.

Case I. For a 2-lane by 2-lane uncontrolled intersection that accommo­

dates a volume of 1600 veh/hr, Fig 6 shows that the percent of vehicles re­

quired to stop is 79.5. From Table 3, the level of service provided is E.

Case II. For a 2-lane by 2-lane uncontrolled intersection that is to

operate at a level of service B, the first estimate of volume was 1300 veh/hr.

The percent delayed in this case after running the model in the manner

described above was 51.7. The level of service provided is B, but this is not

the maximum volume that can be accommodated. The model was next run with a

volume of 1500 veh/hr. The percentage stopping now was 68.4. The level of

service that is provided in this case is C. Next the model was run with a

volume of 1400 veh/hr. The percentage of vehicles that is now required to

stop is 59.3. This percentage is very close to the upper boundary of level of

service B. Thus, it can be stated that the capacity of a 2-lane by 2-lane

uncontrolled intersection operating under a level of service B is 1400 veh/hr.

TABLE 4. PROGRAM-SUPPLIED VALUES-'FOR DRIVER-VEHICLE CHARACTERISTICS

Vehicle Class and Type

1 2 3 4 5 6 7 8 9 10

Srna 11 Large Single- Full- Bus Car Car unit trailer

Medium Vans, Semi- Recrea- Sports Car Mini-bus trailer tional Car

Length 15 17 19 25 30 50 55 25 35 14

Operating Characteristic Factor 100 110 110 100 85 80 75 90 85 115

Maximum Deceleration 16 16 16 16 12 12 12 12 12 16

Maximum Acceleration 8 9 11 8 8 7 6 6 5 14

Maximum Velocity 150 192 200 150 160 160 150 150 125 205

Minimum Turning Radius 20 22 "24 28 42 40 45 28 28 20 '---

[: Percentage Aggressive Drivers 30 35 20 25 40 50 50 20 25 50

Percentage Average Drivers 40 35 40 50 30 40 40 30 50 40

Percentage Slow Drivers 30 30 40 25 30 10 10 50 25 10

c= Percentage in Traffic Stream 20 32 30 15 .5 .2 . 1 .2 .5 1.5

1 2 3 Driver Class and Type Aggressive Average Slow

Driver Characteristic 110 100 85

Perception Reaction Time 0.5 1.0 1.5 w 1-'

32

TfXAS TRAFFIC AND INTERSE'CTION SIMUL.ATION PAC~<AGE .. SIMUl.ATION PROCESSOR

N8tM58U • HIGHLAND HILLS • DRIVE AT CTRCLE * UNCONTROLLED

SU~MARV STATYSTICS FOR ALL APPROACHES

TOTAL OELAV CVF.HICLE•SECONOS' •••••••••••••••••·~·· : NUMBER OF VEHIClES INCURRING TOTAL DELAV •••••••••• : PERCENT OF VEHICLES INCURRING TOTAL DELAV •••·•·••• : AVERAGf TOTAL DELAY CSECONOS' ••••••••~••••~·-••••• : AVERAGE TOTAL OELAV/AVERAGE T~AVEL TIME ••••••••••• =

QUEUE OELAV (VeHIClE•SECONOS' ••••••••~••·•~••••••• : NUMBER OF VEHICLES INCURRING QUEUE DELAY •••••••••• : PERCENT OF VEHICLES t~CURRING QUfUE OE~AV ••••••••~ 8

AVERAG~ QUfUE DELAV (SECONDS) ••••••••••••••••••••• : AVERAGE QUEUE DELAY/AVERAGE TRAVEL TIME ••••••••••• :

STOPPED DELAV CVfHICLE•SECONOS) ••••••••••·~~·•••·~ a NUMSE~ OF VEHIC~ES INCURRING STOPPED DElAY ···~···~ : PERCENT OF V~HICLES !NCURRING STOPPED ~ELAV •••••·~ : AVERAGE STOPPEn DELAY (SECONDS' •••••••••••••••~•·• : AVERAGE STOPPED DELAY/AVERAGE TRAVEl TtME ·~··••••• :

DELAY BELOW t0:0 MPH CVEHICLE.SECONDSl •••••••••••~ : NU~RER OF VEHICLES INCUR~ING OELAY BELOW 10~~ MpH • : PERCFNT OF VEHICLES INCURRING DELAV 8ELO~ t~:~ MP~ : AVERAGE DELAY 8ELOW t0.~ MPH CSECONOS) •••••••••••• : AVfRAGE DELAV RELOW 1~ 0 0 ~PH/AVER4~E TRAVEL TIMF •• ~

VEHICLE•MILES OF TRAVEL •••••·•••••••••••··~··••••• : AVfRAGE VEHICLE~MILES OF TRAV~L e••••===•==·=~=~=·= : lRAVEL TI~f CVEHICLE•SECONDS) •••••••••••••••••·••••= AVER~G~ TQAVEL TT.ME fSfCONOS' ••••••••·~~··===••••= ~ NUMBER OF VEHlCLfS PROCESSF.O ~····••••••••••••••••• = VOLUME PROCESS~D CVEHICLES/HOURl ••••-~•••••·•••••• : TIME MEAN SPEED C~PH' c MEAN QF ALL VEHICLE SPEf05 : SPACf MEA~ SPEED (MP~) a TnT DIST I TOT TRAV~L T!~E = AVERAGE DESIRED SPEEn (MPHl ••••••••••••••••••••••• : AV~RAGE MAXIMUM ACCELERATION cFTISEC/SEC1 ••••••••• • AVF.RAGE MAXJMU~ DECELERATION tFT/SECISECl ••••••••• :

OVERALl AVERAGE TOTAL OELAV tSF.CONOS) •••••••·•·••• : OVERALL AVF-RAG~ QUEUE DELAV tsECONDSl ••••••••••••• 8

OVERALl AVERAGE STOPPED D~LAV CSECONDS) ••••••••••• : OVERALL AVERAGE DELAY BELO~ 1~~0 MPH CSECON~Sl •••• :

NU~8ER OF VEHICLES ELIMINATED (LANE FULL) ••••••••• m

AVERAGE OF LOGIN SPf~D/DESIRED SP~ED (PERCENT, -~·• :

Fig 6. Example of summary statistics.

1f,"03,3 25/J 100.1{1 39.4 55 8 5 PfRCENT

7441,0 2A2 .,q,s lb,8 51,9 PERCENT

1b14,~

202 79~5 ~.3

11,7 PERCENT

9921,0 23.,

CJ2o9 42.0 5 9 I 3 p E' R c E f\! T

b1.487 .21J?

18017,1 7~,9

254 t524.1?1

14.q 12,3 28,3 4.5 4.3

3q,l.4 2q,3 b,b

3Q,1

7

Figure 7 is a graph of total intersection volume against percent of vehicles

that are required to stop for these three runs.

33

Case III. An analysis of a 2-lane by 2-lane uncontrolled intersection

was conducted by running the TEXAS Model with a wide range of volumes. From

the summary statistics reported, a graph of total intersection volume against

the percentage of vehicles that are required to stop was drawn (Fig 8).

Horizontal lines representing levels of service, obtained from Table 3, were

superimposed, and a table relating level of service to total intersection

volume was constructed (Table 5). Table 5 can be used to find the level of

service provided at any volume and the maximum volume that can be accommodated

at each level of service for a 2-lane by 2-lane uncontrolled intersection.

Similar graphs and tables can be constructed for other traffic controls and

lane arrangements.

Case IV. To design the intersection so that 1600 veh/hr can be accommo­

dated while a level of service A is maintained, different lane arrangements and

traffic control schemes were tried. The TEXAS Model was run with these geo­

metries and controls with a volume of 1600 veh/hr until the desired level of

service was attained. An efficient and economical way would be to try the

arrangement most likely. For a first trial, a 2-lane by 2-lane stop-sign

controlled intersection was tried. The level of service that was provided

was D, so a 4-lane by 4-lane two-way stop-sign controlled intersection was

tried. The level of service that was now provided was A. Other combinations

were tried, but no other lane arrangement and traffic control scheme gave a

level of service of A. Table 6 is a matrix of lane arrangements and control

schemes that were run showing the level of service that will be provided under

each scheme. This table can be used in two ways. It can be used to determine

the level of service of an existing or proposed intersection, or it can be

used to design an intersection to provide any desired level of service. This

table is to be used when the total intersection volume is 1600 veh/hr.

Similar tables can be constructed for different intersection volumes.

Summary

A method for determining the capacity and level of service of unsignal­

ized intersections using the TEXAS Model for Intersection Traffic has been

described in this chapter. Hitherto, the manner of determining capacity has

_a. 0 0 .c:-1-U)

(I).E ~~ 0 <J.) ·- '-.c: ·­Q) ::J >o-

<J.)

'QO:

~~ 0 0

Fig 7.

100 ------------..........

80

60

40

F

1------------------:~===~~~~~=~~~~~~== c ~------------,-----

8 • I I I

~-----------~------1 I

20""" A I I I

I I I ' I 0 ~--~~---d--------L--------0 400 BOO 1200 1600 2000 Total Intersection Volume (veh per hr}

Service volume at Level of Service B for a 2-lane by 2-lane uncontrolled intersection.

34

-Q. o-2 .ccn t-

o (1)-

~"t:J OQ) ·- '-.c: ·­Q) ::::s ::>o-

Q)

'QCl:

~~ 0 0

100 ,.------------......

F 80- ___________ .__ __

_ 'E:_---- ----- _.__,_ --· -~-----------~----c •

60 ------------.----·

8 •• • 40 _________ __._, ..... ----

A 20 -

• • • • •

•• , . • • •

• • • • • • I • 8 I I 0 ~----~------~-------~-----._ __ __

0 400 800 1200 1600 2000 Total Intersection Volume (veh per hr)

Fig 8. Analysis of a 2-lane by 2-lane uncontrolled intersection.

35

TABLE 5.

Level of Service

A

B

c

D

E

RELATIONSHIP BETWEEN LEVEL OF SERVICE AND VOLUME FOR A 2-LANE BY 2-LANE UNCONTROLLED INTERSECTION

Percentage of Vehicles Total Intersection Required to Stop Capacity

40 1200 veh/hr

60 1400 veh/hr

70 1500 veh/hr

75 1600 veh/hr

>75 >1600 veh/hr

36

TABLE 6.

Type of Control

Uncontrolled

Yield-sign

Two-way stop

All-way stop

MATRIX OF LANE CONFIGURATION AND TYPE OF TRAFFIC CONTROL SHOWING LEVEL OF SERVICE FOR A TOTAL INTERSECTION VOLUME OF 1600 VEH/HR

2-Lane Major 2-Lane Major 4-Lane Major 4-Lane Major

2-Lane Minor 4-Lane Minor 2-Lane Minor 4-Lane Minor

D - - -D or E - E -

D B B A

E E c or D c

LoJ -.....!

been based on empirical formulae, probability of vehicle spacing, or obser­

vation of intersections. The method described here uses a microscopic,

demand-responsive simulation model for evaluating the behavior of traffic at

intersections with any form of control.

38

Capacity is the maximum volume that can be accommodated while maintaining

a desired level of service. The relationship between capacity and level of

service was investigated. Subjectively-defined levels of service were estab­

lished and qualified by relating them to specified values of selected perform­

ance indicators. Performance indicators that were best suited for the various

types of intersection control were identified, and the levels of service that

can be expected for different values of these performance indicators were

determined. Table 3 presents a summary of recommended indicators, and quanti­

tative values, for each level of service and for the various types of traffic

control that may be used at unsignalized intersections. Four cases in which

the TEXAS Model can be used for determining intersection capacity and level of

service are presented as examples. In the first case, the level of service

was determined knowing the geometry and type of intersection control. For the

second case, the maximum value that can be accommodated at a specified level

of service for a given intersection geometry was determined. For the third

case, a given intersection geometry was assumed and the maximum volume that

can be accommodated at each level of service was determined. In the fourth

case, an intersection was designed to accommodate a given volume of traffic

while maintaining a specified level of service.

CHAPTER 4. EVALUATION OF TRAFFIC CONTROL WARRANTS

Five basic types of traffic control are generally available for use at

intersections: (1) two-way yield, (2) two-way stop, (3) all-way stop,

(4) fixed-time signal, and (5) traffic-actuated control. Each of these has

its best application under certain conditions of traffic flow. The less

restrictive sign control is usually associated with lower traffic volumes;

higher volumes usually mandate some type of signal control. The criteria by

which intersection control should be selected have long been recognized as an

important element of traffic engineering. In recognition of the need for

nationwide uniformity of traffic control, an updated version of the Manual on

Uniform Traffic Control Devices (Ref 4) was published in 1971, and a new

revision is due in 1978. This manual, along with several other publications,

suggests warrants for various forms of intersection control.

Application of the TEXAS Model

The TEXAS Model provides a convenient and practical method for investi­

gating the validity of existing traffic-based warrants for intersection

control and for examining existing and proposed warrants. In the final phase

of Research Study 3-18-72-184, more than 600 simulation runs were made for

different types of intersections handling a wide range of traffic volumes

under different forms of control. The resulting relationships between

geometry, volume, and delay were thoroughly analyzed. These relationships

were then used to appraise the validity of several existing warrants and to

suggest new traffic signal warrants.

Existing Warrants

Warrants are presented in the Manual on Uniform Traffic Control Devices

(MUTCD) (Ref 4) for yield-sign control, stop-sign control, and signal control.

Provisions of the signal warrants, which are of most importance in this inves­

tigation, are summarized here.

Warrant 1, Minimum Vehicular Volume. This warrant specifies major street

and higher-volume minor street approach vehicular volumes for the eighth

39

40

highest hour of an average day. When these volumes are met or exceeded, a

traffic signal may be considered under this warrant. These volumes are shown

in Table 7.

Warrant 2, Interruption of Continuous Traffic. This warrant specifies a

different set of volumes for the eighth highest hour, as shown in Table 8, and

implies conditions under which two-way stop control might be replaced by

signa 1 con tro 1.

Other warrants for signals are included in the MUTCD, but these two are

the only ones which deal with actual traffic volume parameters. Warrant 3,

Minimum Pedestrian Volume; Warrant 4, Progressive Movement; Warrant 5, Acci­

dent Experience; and Warrant 6, Combination of Warrants, are the other

warrants.

TEXAS utilizes MUTCD (Ref 4) warrants for pretimed signals, but also

considers traffic actuated signal installations where peak period volumes

exceed certain values (Ref 5). The 2-hour graphical warrant appears in

Fig 9. Studies by the State Department of Highways and Public Transportation

at twenty permanent count stations revealed that the hourly volumes for the

fourth and second high hours were approximately 25 percent and 50 percent

larger, respectively, than the eighth high hour volumes. In developing the

Texas warrants, factors of 1.25, 1.50, and 1.75 were applied to the MUTCD war­

rant volumes for the fourth, second, and first high hour, respectively. The

factor of 1.75 was chosen for use when heavy traffic volumes exist during only

one hour of an average day.

Scope of Warrant Investigation

In order to evaluate the volume-based signal warrants, simulation runs

using a range of traffic volume from well below to well above those included

in the warrants were made. The variety of runs that were made is shown

schematically in Fig 10.

There are three basic inputs to the TEXAS Model: (1) geometry, (2) inter­

section control, and (3) traffic pattern. Each of these inputs was varied one

at a time while the other two were held constant. In this way, a match-up of

all the input was included.

41

TABLE 7. MINIMUM VEHICULAR VOLUMES FOR WARRANT 1 (MUTCD, 1971, p 236)

Number of Lanes for Vehicles Per Moving Traffic on Each Vehicles Per Hour on Minor

Street Hour on Major Street ( Higher Street ( Total Volume Approach

Major Minor of Both Approaches ) Only ) Street Street

2 2 500 150

4 or more 2 600 150

2 4 or more 500 200

4 or more 4 or more 600 200

TABLE 8. MINIMUM VEHICULAR VOLUMES FOR WARRANT 2 (MUTCD , 19 71, p 2 3 7 )

Number of Lanes for Vehicles Per Moving Traffic on Each Vehicles Per Hour on Minor

Street Hour on Major Street ( Higher Street ( Total Volume Approach

Major Minor of Both Approaches ) Only )

Street Street

2 2 750 75

4 or more 2 900 75

2 4 or more 750 100

4 or more 4 or more 900 100

j....j,-..... Q),..C:

...c: p... oo:>

·r-1........., ::c

...c: I C)

(1j +-1 0 Q) l-l Cl) p... H p... +-1~ C/)

Cl) H S 0 ;j ~r-l

·r-1 0 ~>

700

600

500

400

300

200

100

3b

*

URBAN CONDITIONS

Major Street - Total of Both Directions (vph)

[Source: Reference 5 ]

See page 62 for reference to points

Fig 9. Texas SDHPT actuated signal warrants, 2nd high hour.

42

VARIABLE

Major Street Volume ( vph)

Major Street Directional Distribution

Minor Street Volume ( vph)

Intersection Control

Number of Major Street Lanes

Number of Minor Street Lanes

Fig 10.

VALUE

eeee e ~ ~

8 8 8 Two-way All--.;,·Jay Pre timed Semi-stop stop signal actuated

signal

8 8

8 8

Pyramidal representation of 600 runs of the TEXAS Model using 6 levels.

43

Full-actuated signal

(1) Geometry: Since four geometric configurations, or lane configura­

tions, are contained in the MUTCD warrants, the same four were chosen for

simulation:

Number of Lanes for Moving Traffic on Each Street Shorthand

Notation of Major Street Minor Street Configuration

2 lanes 2 lanes 2 X 2

2 lanes 4 lanes 2 X 4

4 lanes 2 lanes 4 X 2

4 lanes 4 lanes 4 X 4

44

(2) Intersection control: Five basic types of control were used in the

investigation - two-way stop on minor street, four-way stop, pretimed signal,

semi-actuated signal, and full-actuated signal.

A sixty-second cycle was used for the pretimed controller. An even split

of 27 seconds green on each approach was used for most runs. However, when

traffic volume became greatly uneven, the split was altered so that the main

street would receive 32 seconds of green ..

In the case of traffic-actuated control, several loop detector config­

urations were investigated. These arrangements are shown in Fig 11. Pressure

pad detectors were compared with 20-foot, 40-foot, and 80-foot loop detectors.

Detectors were placed at the stop line and 40 feet back from the intersection.

Almost no difference in signal operation could be seen between 40-foot-long

detectors and pressure pad detectors. More max-outs and longer phase time

occurred with 80-foot loops when compared to 40-foot loops. As a result of

longer phase times, total lost time at the intersection was increased in the

range of 25 to 100 percent. Although it appears that shorter loops would have

yielded lower delays, later analysis will show that actuated signals gave

lower delays than other types of control. Therefore, these higher delays can

be viewed as conservative estimates of the best operation of traffic actuated

controllers. To be conservative, 80-foot detectors were simulated, leaving

about two car lengths for storage. Controller dial settings used for actuated

control were 8 seconds initial interval, 2 seconds vehicle interval, and 3

seconds amber clearance. For the semi-actuated controller, the minimum

assured green time for the main street was set at 35 seconds. Maximum

extension after demand on red was 25 seconds for the minor street, and (for

Direction of .. Travel

80ft.

40ft.

20. ft.

40ft. -....

40ft.

20ft.

~ ... 30ft.

Fig 11. Detector configurations examined.

--

~ ...

45

Q) c: _J

c. 0 +-(/)

Q) c: _j

0. 0 +-(f)

46

the full-actuated controller), 45 seconds for the major street. Right turns

on red were allowed for all simulation runs.

(3) Traffic demand: A wide range of traffic volumes around those speci­

fied in the MUTCD warrants was used. Volumes of 500, 700, 900, 1100, and 1300

vehicles per hour were simulated for the major street. Minor street volumes

of 200, 400, and 600 vph were observed. Directional distributions of both 60

percent and 75 percent were used on the major street, and 60 percent alone on

the minor street.

(4) Other assumptions:

(a) Turning movements in each approach were held at 10 percent left and 15 percent right.

(b) The distribution used to generate vehicle headways was the Negative Exponential. A further stipulation was that no two vehicles could enter the system on the same lane less than one second apart. In such cases, the trailing vehicle was eliminated.

(c) Two minutes of start-up time and ten minutes of simulation time were used in all cases.

(d) A time-step increment of one second was used for all signalized simulations, but, for non-signalized simulation runs, a time­step of one-half second was used.

(e) Desired speeds for all vehicles entering the system were set as a random variate of the normal distribution.

(f) A mean speed of 30 mph was used and the 85 percentile speed corresponded to the speed limit on all approaches of 35 mph.

The following parameters were varied systematically:

(1) cycle length,

(2) cycle split,

(3) de tee tor design and type,

(4) percent of left-turners, and

(5) right turn on red.

Results of Simulation

Figure 12 shows the relationship between volume and the overall average

queue or stopped delay occurring in each approach. When the minor street ap­

proach volumes reach about 500 vph under two-way stop control, overall average

delays begin to increase rapidly. At approach volumes near 600 vph, all-way

47

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0 0 0 0 0 0

0 .....) 0 0 tC 0 (1) z Q;l

C> ::I: G.. en

Q...

0 ::::> ...... 0 0

0 ~~

./f) 0 Lt.! ot.&J

>- (.0 1- tP-z: a: )C tC :::> :::. :::> ..J ,_.

0 -I t) o> -I 0 a: a: 0 I O:r:

;- ......J -ru -I a: :;:, 0 ...__ a::

0 a...

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09 09 Oir 0€ 06 OI 0 09 Oir OS oa OI 0 (:J3S) J.l::ll30 3fl3flV 3tJI:ICI~AI:f lli:ICI3AO 0 (JJS) J..l:ilJO OJddOlS Jt)I::J~)I\tl lli::J~)I\{J 0

0 ....... 0

0 0

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(l} _J (()

a: l: z a.. C'J >

0 (/'"1 0~

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CL. Lt.! :::> ..... -I

0 a: 0 ..... ~ o> (T) 0 .....

7-0 ~ O::t: ;- ""<.J

tC I a: :::a. 0

0 X: 1%:

""" Q~ :3' 0

{/') 1-

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(\1

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09 09 017 06 oa OI 0 09 Ot- 0€ oa OI 0

{J35) .un3a 31'l3fllJ 3VI:Iti3J\I:I lll:lti3A0 (.J3S) .ll:/130 03cldOJ.S 3tJI:fCI3AI:I lli:ICI3AO

48

stop control begins to show the same tendencies. Table 9 shows the apparent

capacity levels for two-way and four-way stops.

Figure 13 relates volume and average delay per delayed vehicle for the

total intersections. Figures 12 and 13 consider the 4 X 4 case. Similar

figures for the other three cases have been drawn (see Appendix, pp 73-78).

An implied criterion is that no one driver is more important than another and

that any delay which is incurred should be apportioned fairly among all users.

In other words, no driver should find himself being "unreasonably" delayed

simply because he is on the minor street. Many traffic engineers and re­

searchers have tacitly adopted a 60-second value as the basis for unreasonable

delay. In the case of a 4 X 4 lane configuration, this point is reached at

approximately 2000 vph for the two-way stop and 1500 vph for the all-way stop.

Table 10 summarizes the corresponding volumes for each of the lane config­

urations.

Evaluation of Existing Warrants

An examination of the MUTCD signal warrants with respect to the prelim­

inary volume-delay relationships from simulation has shown no obvious inade­

quacy in the warrants. Volume warrants for a particular type of traffic

control are meant to identify the approximate traffic conditions at which a

less restrictive means of traffic control should be replaced by a more restric­

tive means. The reason for the change may be for safety, intersection effi­

ciency and capacity, vehicular delay, or some combination of these. For

example, a logical reason to specify yield-sign control is to more safely

assign the right-of-way to one of the traffic streams. On the other hand, a

traffic signal would probably be specified for reasons of additional capacity

or lowered delay.

The most frequently-applied warrants for traffic signals are volume

based; that is, the approximate traffic conditions above which a traffic

signal is better are specified in terms of the vehicular volume which uses the

street. Such warrants are probably utilized because of the fact that volumes

are easily measured in the field and apparently serve as an independent vari­

able which measures intersection performance.

More important from the standpoint of justification or evaluation of the

warrants, though, is the philosophy which was followed in developing the

warrant. Some of the points of view which must be kept in mind are

49

TABLE 9. APPARENT CAPACITY LEVELS FOR 2-WAY AND 4-WAY STOPS

Lane 2-Way Stop 4-Way Stop Arrangement Control Control

Major Minor Minor Approach Major Minor Volume Approach Approach

Volume Volume

4 X 4 500 vph 600 vph 600 vph

4 X 2 150 600 300

* 2 X 4 600 300 600

2 X 2 200 300 300

J'(

All-way stop on a 2 X 4 configuration is comparable to an

all-way stop on a 4 X 2 configuration, with volumes swapped.

so

0 0 II> s:: (\) 0

•...-! -1-.1

:I: O(L tr. C,) . 0> 0 (!) rJl :>-. o......, z rJl :,j tU (\)

I: 1-l Ulr-1 w (!) 1-l (!) c u.J -1-.1 (I)'"C'J

..J ::::>

O..J z s:: :> a:: 0~

a: ·...-! (!) z ..J C!? II>> (!) bO

:z '<r ........ § tU (f)

~ tU 1-l

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CD 0 0 :> 'C ow ~ E-1 :> tU

ow 0 1-

..... if)

a: I u.J LU

a: a::. I: CL

1- ("(')

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a:; _) •...-! 1- .r f::t.l ~ 1-

0

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0 0

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II> (\)

(\7

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tlE@ j.Q 0 II>:::>-

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d) 0 1-Ql-

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II) II>_J

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r-------,-

09 0~ Ot? Oe 02 or 0 09 Ot> 06 0?; 01 0

(J~Sl ~lJIH~A O~O~~V ~~d Al:ll~O JnJ~V ':311.1:1 0 ~lJIH~A 0Jdd01S ~Jd .U:Il]O 0Jdd01S • 3,\!:1 0

Q 0

1.0

[~~ <"

<1-

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(\1 _)

f :~ q:; z

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0 (n 00 LO L/.) ::>

c::J .... a.. 4.1 z b 1- 0 1-

£:(

(n 0 :::::::, Ql-

0 ....... o<.> >- 0 ~

ow a: _, (/")

,. I tr.

i: 4J

b 1-,. 0 4.1 o;:

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0 If.> Ll)_~

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--r- 0 ---.--- 0

09 OS Otr OS oa or 0 09 Ot< 06: 06 Ot 0 (J3Sl 31JIH~A O~n3nV ~3d .L.tll30 3n3nv ·3Atl ~IJIH~A O~dd91S ~~d Al:ll~O O~dd9lS '3M/

51

TABLE 10. 10TAL INTERSECTION VOLUME WHEN AVERAGE QUEUE DELAY PER QUEUED VEHICLE REACHES 60 SECONDS

Lane Arrangement T'~"J!O-~"Tay Stop All~Way Stop

1\~ajor Hi nor Control Control

4 X 4 2000 vph 1500 vph

4 X 2 1600 1400

2 X 4 1500+ 1000

2 X 2 1400 900

·--

(1) least total delay at the intersection,

(2) a balanced delay among approaches,

(3) no unreasonable delays, and

(4) least total cost.

52

The basis chosen for evaluation of signal warrants in this investigation

is least cost.

Cost Concept

The overall cost associated with traffic operations at intersections may

be logically considered in terms of user cost and traffic control device (TCD)

costs. Each of these two costs may be stated in terms of daily operational

costs. Representative values of both user cost and TCD cost may be found in

the literature. The development of these costs will now be considered.

User Cost. User costs, or costs borne by the traffic stream, may be

divided into stopping costs and delay costs. Researchers have found that in a

single stop-and-go cycle, a vehicle incurs costs in the terms of excess gaso­

line and lubrication consumption, additional tire wear, increased engine and

brake maintenance, and additional depreciation due to wear. Winfrey (Ref 11),

in 1952, reported a cost of 0.696 cents per stop from an initial speed of

25 mph. Claffey (Ref 12), in 1971, reported itemized costs of 0.097 gallons

of gasoline (0.54 cents if gasoline costs 56 cents per gallon), and between

0.3 cents and 0.6 cents for the other factors for a total of between 0.8 cents

and 1.1 cents. These costs were for initial speeds of 25 mph. For purposes

of this signal warrant analysis, a cost of one cent is assigned to each

vehicle which has to stop.

In additional to actual costs arising from vehicular operation, the value

of travel time must be considered. Time saving for commercial vehicles is a

direct function of the driver wage and the value of time associated with that

particular commercial activity. As such, current estimates of the value of

this particular type of time on delay range between $4.00 and $10.00 per hour.

In an economic sense, reduction in passenger car travel time is not a saving

but certainly is a factor which must be considered. Money is not left unspent,

as would occur if gasoline, oil, and tires were not purchased, but time is

made available for other purposes. The intersection improvement resulting in

travel time reduction would have to be financed by the user spending less

money on other commodities rather than the savings realized from commodities

53

he did not have to buy. While some question remains as to the actual value of

this time, there is general agreement that drivers are willing to pay for

facilities which result in a savings in time. Thomas (Ref 13) cites costs of

$2.80 per hour, and Lisco (Ref 14) reports $2.50 per hour. Both of these

researchers studied the peak hour trip of middle to upper-middle class urban­

ities in 1966. Winfrey (Ref 11) states that "reasonable values (of time) lie

within the range of $1.00 and $4.00 per hour, depending on prevailing local

factors." At least one researcher has put forward the theory that 10 cars

waiting 80 seconds do not have the same economic value associated with waiting

that 400 cars waiting 2 seconds would have. Thomas and Thompson (Ref 15) say

that the value of time increases faster than the unit of time, so that 2

minutes is worth considerably more than 60 times the value of 2 seconds, the

latter being practically valueless. For this signal warrant analysis, a value

of $3.00 per hour will be utilized.

User costs determined by simulation are shown in Figs 14 and 15. The first

shows costs experienced in each approach and the second costs for the total

intersection. These relationships are for 4 X 4 lane configurations. Similar

costs for other lane configurations have been drawn (see Appendix, pp 79-84).

Traffic Control Device Costs. A 1964 study of the economics of signals

by Stanford University (Ref 16) reported initial costs of $8,418 and annual

maintenance and operational expenditures (M.O.E.) of $960 for a typical

traffic actuated controller. More recent publications (Ref 17) identify

initial construction costs ranging between $15,000 and $30,000, depending on

the complexity of the intersection, and M.O.E. of $500 per year. For this

warrant analysis, first costs of $15,000 and M.O.E. of $1,000 per year will be

used for traffic actuated controllers. Pretimed controllers, being less

complex, and therefore somewhat less costly, will be assumed to have first

costs of $14,000 and M.O.E. costs of $800. If the first costs are amortized

over a 10-year period using a 7 percent interest rate, a capital recovery

factor of 0.1424 results. Therefore, the first costs may be turned into

annual costs. A summary of the total annual signal control cost is found in

Table 11. Annual costs for sign controlled intersections were ignored since

their magnitude is small compared to signal control.

In an economic analysis of signal control, the cost of the control should

be "paid for" only during the hours of operation under which it is warranted.

Signal control may not be justified during weekend operation, so only 250 days

.,. ""'

.,.. cv_

'/v" cvl I' ftni'IPI'!'I'fiM' (\)l t

.. i'3l 0

~~ ~ ;x (\J ~

......... X

,....

~.; 9 ~LL VAY STOP (9

-- ~ I PRET1MEO ~1GNRL I 'It a:::.m 0:::.<0

X '>i< a:::. co ~ ..... j_, g .... -0 co I: l: I:

~ X a::. a::.

~ cv ~ ~ v •• X ltJ u.s )( CLC\J a..(\) ~-....., .......... ...... ...... v xx C/2 TWO WA.Y StOP lJ) (/) 0 co 0 m X u (!) f..) <..-a::. a::. a:. '~(P (!I ~co ~co

::::> :::> ::::> ..J ..J ..J 0:. a: CI: t- t- t-0 co 0 t-.,. "'<Y I-"'" ~ .,..

0 0 0

0 '200 400 ~00 $00 1000 0 '200 ·+00 '600 soo 1000 0 200 A.QO 600 eoo 1000 ~PPR0ACH VOLUME (VPH}

I

i;: 1 SEMI -ACTUATED SIGNAL

0 (\)

.........

9 ® ~ )( e - (!) 0:::.<£)

(!) 0:::.<0

FULL-RCTURTEO SZGNRL ::::>....,

I ::::>_,

0 0 I:

')( l:

a::. a::. ~ 4 LAN£ MAJOR BY ~ LAN£ MINOR u.s

X~ (

IJJ )( Cl.cv a..(\) (!)

........... :t ........... (!) (!) ')( ')(

(!)')( (/)

xx I X (/) ~

(x rt1fU N !HR£! t J 0 0 ~ f..) f..) ~ ')( (l!l I t1 I NOR $ tR££ T) (!))( /

~ (!) xx/x a::. a::.

(!) ® ')( ~

~co /)( ')( ~co (!) (!) 'X ')(

::::> :::::> ~..--< ')( )( .....J

')( -~ .....J '* ')( a: : xx/x xI ct:

~~ ')(

t- t- ')( Fig 14. Total user costs 0 0 t-""' x*/.; t-<t-

determined by ')( ')(

J/~~xxxx simulation for X X

various approach 01 o, ----..,

volumes. 0 '200 100 600 soo 1000 0 200 400 600 eoo 1000 lJl

~PPROACH VOLUME (VPH) RPPRORCH VOLUME (VPHl +:--

0 \0,

0 I.J)

~ .......

~0 0.,..

r11o I(RY sroP I:

a::. ~ a...

0 t-('1) Vl I!) u

~OJ Vl(.\) :::;:)

_) (!) CI.

(!) (!)I!> t- all oo I- .... ..JrJ

0

. J .. 0 r..p

I 0 \.0

.......

I &

a::. ::>0 C/Y I:

a::. UJ Q..

0 t--(1) lf) C/ (..)

a::. UJo lf>C\.1 ::>

I!) _J 0:: I-oo t- ...

0

ALL

/

m' Jft

(!)I!>

l!l

0 500 1000 1500 '2000 '2500 0 500 2000 1500 2000 2500

- ~~ (!)

I SENI-RCTURTED- StGNRL

: I ::>0 O""" I:

a::. UJ a..

0 t--(1) (f) 0 (..)

cr. (!)

UJQ l!l (./)C\.1 (!)I!)

::> _J (!)(!) 0:: t- I

oo .1!1 t- ..... /

0 -t------r --, 0 500 1 000 1 soo '2000 '2500

TOTRL INTERSECTION ~OLUNE £VPH)

0 lD

,...... &

a::. ::>0 0..,... I:

a::. UJ Q..

a t-(T) lf)

C/ (..)

a::. IJ.JO lf>C\.1 ::> _J

0: I-oo 1--.-.

(!)

FULL-ACTUATED SIGNA:/

mm~rn m"lll<P

/~

a +--- - --,--·---.-- ,---------.---, 0 500 1 000 1 500 2000 2500

TOTAL INTERSECTION VOLUME (VPH>

$>

0 lD

0 l.f.l•

a::. ::>0 C/ ~­I:

a::. \LJ a..

0 t- ('I) Cl) 0 u a::. lUO Cl)cu "::;)

J IX. t­Oo t- ..... -

PRETIMEO SIGNAL

(!)

(!)

0 I I •

0 500 1000 1500 2000 2500 TOTAL INTERSECTION VOLU~E CVPHJ

4 LAN£ MAJOR BY 4 LAN£ MlNOR

Fig 15. Total user costs determined by simulation for various total intersection volumes.

Vl Vl

56

TABLE llo ANNUAL SIGNAL COSTS

-.-~~at· 7% ·interest :over 10 ye·ars

Equivalent Total Uniform Total

S~gnal E'irst Annual Annual Daily Type co·s·t cRF· First Cost 110E Cost Cost

Fixed $11,000 0.1424 $1,566 $800 $2,366 $9.04 Time

Actuated 15,000 0.1424 2,136 1,000 3,136 12.54

---at 10% interest over 10 years

Fixed 11,000 0.1627 1,790 800 2,590 10.36 Time

Actuated 15,000 0.1627 2,440 1,000 3,440 13.76

57

of the year (weekdays with two peak hours) will be considered. Therefore, the

daily costs of signal operation are as shown in Table 11. For a signal to be

economically justified then, the user cost associated with signal control must

be $9.00 to $12.00 per day less than the user cost associated with stop

control.

Evaluating Existing MUTCD Warrants

Least Cost Method

Table 12 shows the tabulated results of the total intersection costs for

volumes which just meet MUTCD Warrant 1 (minimum vehicular volume) conditions

for the 4 x 4 lane configuration (see Appendix, pp 85-87, for other config­

urations). Table 13 shows similar costs for Warrant 2 (interruption of contin­

uous traffic) conditions (see Appendix, pp 88-90, for other configurations).

Costs shown in these tables were obtained in the following manner. Eighth hour

volumes were taken directly from the MUTCD Warrants. A slightly uneven direc­

tional distibution was assumed for each street, and four volumes, each repre­

senting an approach volume, were determined. Using the multiplying factors

shown in Table 14 (from Box and Alroth, Ref 18), volumes for the higher hours

were obtained. Then, entering the correct graph in Fig 14 with each volume, a

user cost was obtained. Similar tables for other lane configurations have been

prepared (see Appendix). A summary of all costs for the existing MUTCD Warrants

is shown in Table 15.

Several observations concerning the cost results in Table 15 may be made:

(1)

(2)

(3)

Two-way stop control is the least costly for each condition.

All-way stop control is the most costly for each condition.

Traffic actuated each condition.

Two-way stop

control

signal control is less costly

Increasing Cost )~~!~rae

Actuated signal control

Pre timed signal control

than pretimed

All-way stop

control

for

It appears that, strictly on the basis of cost, the volume levels speci­

fied in the MUTCD signal warrants might need adjustment. When considering

the replacement of a two-way stop with a signal, warrant volumes should be

Hour

8

7

6

5

4

3

2

Peak

Sum

TABLE 12 • COMPUTED INTERSECTION USER COST W MEET MUTCD WARRANT 1

Major Minor Major Street User Cost Approach Approach

Fixed-Volumes Volumes * 2-Way 4-Way Time SA EB WB NB SB Stop Stop Signal Signal

325 200 0.75 7.10 5.00 3.00 275 150 0.50 5.10 4.30 2.25

335 226 0.75 7.25 5.25 3.00 283 170 0.55 5.80 4.75 2.25

365 230 0.80 7.45 5.75 3.25 308 172 0.60 6.15 5.00 2.60

365 254 0.85 7.45 5.75 3.25 308 190 0.60 6. 15 5.00 2.60

367 288 0.85 7. 50 5.80 3.30 310 216 0.70 6.20 5.05 2.70

390 330 0.90 8.00 6.25 3.50 330 247 0.75 6.80 5.30 3.00

432 370 1.00 8.80 7.00 4.10 365 277 0.80 7.50 6.00 3.25

432 408 1.00 8.80 7.00 4.10 365 306 0.80 7.50 6.00 3.25

12.90 113.60 89.20 49.40

Fixed-* 2-Way 4-Way Time SA

Total Intersection Stop Stop Signal Signal User Cost,

8-Hour Totals 109.50 204.00 153.10 143.40

** FA 2-Way Signal Stop

3.50 4.25 2.90 3.00 3.55 5.25 2.90 3.80 3.70 5.30 3.00 3.80 3.70 5.90 3.00 4.20 3.70 7.00 3.00 4.50 4.00 8.50 3.50 5.40 4.50 10.00 3.70 6.50 4.50 11.75 3.70 7.50

56.80 96.60

** FA Signal

126.50

Minor Street User Cost

Fixed-* 4-Way Time SA

Stop Signal Signal

3.50 3.25 4.40 2.50 2.30 3.25 4.30 3.50 4.80 2.90 2.50 3.55 4.50 3.55 4.85 3.00 2.60 3.60 4.80 4.00 5.30 3.40 3.00 4.10 5.70 4.60 6.00 4.25 3.30 4.50 6.90 5.30 7.50 5.00 4.00 5.30 8.00 6.00 8.00 5.60 4.50 5.80 8.75 6.50 9.00 6.20 5.00 6.70

90.40 63.90 86.60

4 x 4 Geometry

Warrant 1 Conditions

*SA = Semi-actuated **FA = Full-actuated

** FA Signal

3.70 2.60 4.10 3.00 4.15 3.00 4.25 3.35 5.00 3.90 5.50 4.30 6.00 4.70 7.00 5.15

69.70

\.Jl (X)

Hour

8

7

6

5

4

3

2

Peak

Sum

TABLE 13. COMPUTED INTERSECTION USER COST TO MEET MUTCD WARRANT 2

Maj0r Minor Major Street User Cost Approach Approach

Fixed-Volumes Volumes * ** 2-Way 4-Way Time SA FA EB WB NB SB Stop Stop Signal Signal Signal

500 100 0.80 11.25 8.20 5.00 5.40 400 75 0.60 8.50 6.50 3.90 4.25

515 113 1.00 12.00 8.50 5.25 5.70 412 85 0.70 8.75 6.80 4.00 4.50

560 115 1.05 13.00 9.10 5.90 6.00 448 86 0.75 9.70 7.25 4.50 4.75

560 127 1.05 13.00 9.10 5.90 6.00 448 95 0.75 9.70 7.25 4.50 4.75

565 144 1.10 13.25 9.25 6.00 6.00 452 108 0.75 9.80 7.30 4.50 4.80

600 165 1.25 14.50 10.25 6.75 6.50 480 124 0.85 10.25 7.75 5.00 5.00

665 185 1. 50 18.00 11.25 8.20 7.70 532 135 1.05 12.50 8.60 5.75 5.60

665 204 1.50 18.00 11.25 8.20 7.70 532 153 1. 05 12.50 8.60 5.75 5.60

15.75 194.70 136.95 89.10 90.25

Fixed-* ** 2-Way 4-Way Time SA FA

Total Intersection Stop Stop Signal Signal Signal User Cost,

8-Hour Totals 54.65 229.25 172.55 132.40 128.05

Minor Street User Cost

Fixed-* 2-Way 4-Way Time SA

Stop Stop Signal Signal

2.00 1.75 2.00 2.10 1.30 1.25 1.60 1.70 2.30 2.00 2.10 2.40 1.50 1.30 1.60 1.80 2.35 2.00 2.10 2.40 1.50 1. 30 1.65 1. 80 2.50 2.10 2.20 2.70 1.60 1.50 1.80 2.00 2.70 2.50 2.30 3.10 1.90 1.70 2.10 2.25 3.00 2.80 2.70 3.80 2.25 2.00 2.25 2.75 4.00 3.00 3.00 4.00 2.50 2.40 2.30 3.00 4.50 4.00 3.30 4.25 3.00 2.95 2.60 3.25

38.90 34.55 35.60 43.30

4 x 4 Geometry

Warrant 2 Conditions

*SA = Semi-actuated **FA = Full-actuated

** FA Signal

2.00 1.60 2.20 1.75 2 . .20 1.75 2.35 2.00 2.60 2.10 2.90 2.20 3.10 2.30 3.95 2.80

37.80

Vl \.0

TABLE 14. RElATIONSHIP BE'IWEEN EIGHTH HIGH HOUR AND HIGHER HOUR VOLUME

High Hour

Peak

2nd

3rd

4th

5th

6th

7th

Multiplying Factor

Major Street

1.33

1.33

1.20

1.13

1.12

1.12

Minor Street

2.04

1.85

1.65

1.44

1.27

1.15

1.13

, ___ s_t_h ___ -'-j ___ l_._o_o ___ -~----- _l_._o_o_" __ _

60

..1-J 0

..1-J m 0 H Q) H s m Q) ::s: bO H 0 A Q)

aJ m U,.c 0 H H S m 1-1 ~~ H<G

4 X 4 1

2

4 X 2 1

2

2 X 4 1

2

2 X 2 1

2

TABLE 15. SUMMARY OF DAILY COSTS UNDER EXISTING MUTCD WARRANT CONDIT IONS

0 0

·r-1 ..1-J cJ User Costs Traffic Q) cJ r-1 (/) •r-1 0 Control H 4-! H Total Q) 4-! ..1-J Major Minor Device Intersection +-~ m o Total 0 H 0 Street Street Cost Cost HHU

2W 12.90 96.90 109.50 0.00 109.50 4W 113.60 90.40 204.00 0.00 204.00 PT 89.20 63.90 153.10 9.04 162.14 SA 49.40 86.60 143.40 12.54 155.94 FA 56.80 69.70 126.50 12.54 139.04 2W 15.75 38.90 54.65 0.00 54.65 4W 194.70 34.55 229.25 0.00 229.25 PT 136.95 35.60 172.55 9.04 181.59 SA 89.10 43.30 132.40 12.54 132.40 FA 90.25 37.80 128.05 12.54 128.05

2W 16.50 113.65 130.15 0.00 130.15 4W 122.70 95.80 218.50 0.00 218.50 PT 95.25 67.75 163.00 9.04 172.04 SA 51.60 83.25 134.85 12.54 147.39 FA 65.45 56.05 121.50 12.54 134.04 2W 23.10 36.80 59.90 0.00 59.90 4W 206.10 34.40 240.50 0.00 240.50 PT 154.50 24.10 178.60 9.04 187.64 SA 87.00 39.20 126.20 12.54 138.74 FA 103.80 27.00 130.80 12.54 143.34

2W 12.70 90.65 103.35 0.00 103.35 4W 103.80 85.65 189.45 0.00 189.45 PT 75.05 65.75 140.80 9.04 149.84 SA 45.00 98.90 143.90 12.54 156.44 FA 54.60 79.70 134.30 12.54 146.84 2W 19.75 38.80 58.85 0.00 58.85 4W 437.00 40.10 477.10 0.00 477.10 I

PT 223.40 27.55 250.95 9.04 259.99 SA 78.70 44.95 123.65 12.54 136.19 FA 87.35 34.60 121.'95 12.54 134.49

2W 16.55 110.60 127.15 0.00 127.15 4W 179.25 79.15 258.40 0.00 258.40 PT 109.05 62.70 171.75 9.04 180.79 SA 53.85 89.75 143.60 12.54 156.14 FA 67.35 97.15 164.50 12.54 177.04 2W 25.70 34.40 60.10 0.00 60.10 4W 462.00 34.80 496.80 0.00 496.80 PT 219.95 25.60 245.55 9.04 254.59 SA 95.55 34.10 129.65 12.54 142.19 FA 116.50 38.00 154.50 12.54 167.04

61

62

considerably higher than those specified. When, on the other hand, considering

the replacement of an all-way stop with a signal, warrant volumes should be

considerably lower than those specified.

Proposed Warrants - Cost Basis

The cost associated with all-way stop control (Fig 14) seems to be fairly

close to the cost associated with signal control, up to about 200 vehicles per

lane per hour. Beyond the volume, four-way stop control costs increase

dramatically, and signal control obviously becomes the more cost effective

type of intersection control. Under these circumstances, 200 vehicles per

lane per hour can be considered to be a critical volume. The following

traffic volumes were investigated as possible warrant volumes for the replace­

ment of four-way stop control with signal control.

Cost Analysis of Texas MJJTCD Actuated Signal Warrants

The Texas State Department of Highways and Public Transportation supple­

ments the MUTCD signal warrants with a set of graphical warrants for actuated

signal control. Four graphs, corresponding to peak hour, second, fourth, and

eighth highest hourly volumes, are used. Figure 9 shows a graph for the

second high hour. Insofar as the warrant is specified as a continuous func­

tion between major street volume and higher-minor-approach minor street volume

for various lane arrangements, two points were chosen to represent each lane

configuration in the evaluation. The cost associated with each type of

control for each of the six traffic conditions are shown in Tables 16, 17,

and 18.

Two-way stop control results in the least costly control and four-way stop

control is most costly in terms of total intersection costs for each of the

six traffic conditions. As concluded in the previous section, a single signal

warrant specifying the replacement of either two-way stop or all-way stop

control cannot be stated when the basis for the warrant is cost. Rather,

signal control is cost warranted over four-way stop control for most traffic

conditions. Two-way stop control, while being the most cost effective over a

wide range of conditions, must be replaced by signal control when side street

delays become excessive.

The concept of having separate or enumerated warrants for signal control

has merit. For every traffic condition studied in this report, actuated

Hajor Minor Approach Approach

Volumes Volumes

Hour EB WB NB SB

POINT A 2 450 225

300 150 Peak 450 225

300 150

Sum

POINT B 2 650 113

475 75 Peak 650 113

475 75

Sum

Total Intersection User Cost,

2-Hour Totals

POINT A

POINT B

TABLE 16. COMPUTED INTERSECTION USER COST

Major Street User Cost

Fixed-* 2-Way 4-Way Time SA

Stop Stop Signal Signal

1.90 50.00 14.50 6.80 1.10 18.00 7.50 3.50 1.90 50.00 14.50 6.80 1.10 18.00 7.50 3.50

6.00 136.00 44.00 20.60

3.10 90.00 50.00 11.50 1.95 90.00 16.00 7.30 3.10 90.00 50.00 11.50 1.95 90.00 16.00 7.30

10.10 360.00 132.00 37.60

Fixed-* 2-Way 4-Way Time SA

Stop Stop Signal Signal

27.40 154.40 57.60 40.80

17.10 367.80 136~ 45.80 - -----~ ------~- -~----

** FA 2-Way Signal Stop

7.60 7.20 4.80 3.50 7.60 7.20 4.80 3.50

24.80 21.40

13.00 2.10 8.20 1.40

13.00 2.10 8.20 1. 40

42.40 7.00

** FA Signal

47.40

50.40

Minor Street User Cost

Fixed...: * ** 4-Way Time SA FA

Stop Signal Signal Signal

5.90 4.30 6.30 7.30 3.30 2.50 3.80 4.00 5.90 4.30 6.30 7.30 3.30 2.50 3.80 4.00

18.40 13.60 20.20 22.60

2.40 1.60 2.80 2.60 1.50 0.80 1. 30 1.40 2.40 1.60 2.80 2.60 1.50 0.80 1.30 1.40

7.80 4.80 8.20 8.00

2 x 2 Geometry

Points A and B on Figure 9

*SA = Semi-actuated **FA = Full-actuated

I .

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TABLE 17. COMPUTED INTERSECTION USER COST

Major Minor Hajor Street User Cost Minor Street User Cost Approach Approach

Fixed-Volumes Volumes 2-Way 4-Way Time

Hour EB WB NB SB Stop Stop Signal

POINT C 2 550 225 1.60 13.60 9.40

350 150 0.90 7.50 6.00 Peak 550 225 1.60 13.60 9.40

350 150 0.90 7.50 6.00

Sum 5.00 42.20 30.80

POINT D 2 750 113 3.30 25.00 15.10

600 75 1.80 15.50 11.70 Peak 750 113 3.30 25.00 15.10

600 75 1.80 15.50 11.70

Sum 10.20 81.00 53.60

Fixed-Total Intersection 2-Way 4-Way Time

User Cost, Stop Stop Signal 2-Hour Totals

POINT C 29.00 62.20 46.80

POINT D 18.60 88.60 58.70

* ** SA FA 2-Way Signal Signal Stop

6.20 7.20 8.00 3.30 4.10 4.00 6.20 7.20 8.00 3.30 4.10 4.00

19.00 22.60 24.00

9.30 10.30 2.60 7.00 8.00 1.60 9.30 10.30 2.60 7.00 8.00 1.60

32.60 36.60 8.40

* ** SA FA Signal Signal

38.80 36.20

41.20 42.20

Fixed-* ** 4-Way Time SA FA

Stop Signal Signal Signal

6.50 5.00 6.10 4.20 3.50 3.00 3.80 2.60 6.50 5.00 6.10 4.20 3.50 3.00 3.80 2.60

20.00 16.00 19.80 13.60

2.20 1. 60 2.40 1.70 1.60 0.95 1.90 1.10 2.20 1.60 2.40 1.70 1.60 0.95 1.90 1.10

7.60 5.10 8.60 5.60

4 x 2 Geometry

Points C and D on Figure 9

*SA = Semi-actuated **FA = Full-actuated

I

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Major Minor Approach Approach

Volumes Volumes

Hour EB WB NB SB

POINT E 2 550 300

350 200 Peak 550 300

350 200

Sum

POINT F 2 750 150

600 100 Peak 750 150

600 100

Sum

Total Intersection User Cost,

2-Hour Totals

POINT E

POINT F

TABLE 18. COMPUTED INTERSECTION USER COST

Major Street User Cost

Fixed-* 2-Way 4-Way Time SA

Stop Stop Signal Signal

1.30 12.70 9.30 5.80 0.60 7.20 6.00 3.30 1.30 12.70 9.30 5.80 0.60 7.20 6.00 3.30

3.80 39.80 30.60 18.20

2.00 30.00 13.50 10.20 1.40 14.90 10.30 6.70 2.00 30.00 13.50 10.20 1.40 14.90 10.30 6.70

6.80 89.80 47.60 33.80

Fixed-2-Way 4-Way Time * SA Stop Stop Signal Signal

26.80 60.10 38.40 41.20

16.80 99.60 57.40 44.80

** FA 2-Way Signal Stop

6.20 7.30 3.60 4.20 6.20 7.30 3.60 4.20

19.60 23.00

8.90 3.00 6.90 2.00 8.90 3.00 6.90 2.00

31.60 10.00

** FA Signal

38.00

34.00

Minor Street User Cost

Fixed-* ** 4-Way Time SA FA

Stop Signal Signal Signal

6.10 5.30 7.00 5.40 4.05 3.60 4.50 3.80 6.10 5.30 7.00 5.40 4.05 3.60 4.50 3.80

20.30 17.80 23.00 18.40

3.00 3.00 3.40 4.00 1.90 1.90 2.10 2.20 3.00 3.00 3.40 4.00 1.90 1.90 2.10 2.20

9.80 9.80 11.00 12.40

4 x 4 Geometry

Points E and F on Figure 9

*SA = Semi-actuated **FA = Full-actuated

0'\ Vl

66

control yielded significantly lower costs than pretimed signal control. Even

though the investigation in this report used several assumptions regarding

signal timings, traffic-actuated signal control seems to be more cost effec­

tive than fixed-time signal control at isolated intersections.

Summary

An evaluation of volume-delay relationships was determined by simulation.

After reviewing the philosophy of signal warrants, total intersection cost was

chosen as the basis for judging the effectiveness of intersection control.

Comprised of costs associated with user delay, vehicular stop-start cycles, and

traffic control devices, total intersection costs were derived for the range

of conditions simulated. Texas SDHPT actuated signal warrants and MUTCD

signal warrants were studied. At traffic levels corresponding to each, a cost

analysis of the effectiveness of signal control was made. Based solely on

cost and delay, two general conclusions may be drawn from the analysis.

(1) Two-way stop control was the least costly control for all conditions

evaluated, but intolerable delays to side street traffic, rather than overall

cost efficiency, should be the criteria for signalization in this case.

(2) All-way stop control was the most costly control for all conditions

evaluated. Even at very light traffic conditions (350 vph major, 250 vph

minor, eighth high hour, 4-lane by 4-lane intersection), signal control proved

to be more cost effective. All-way stop control is not justified on the basis

of cost.

CHAPTER 5. CONCLUSIONS AND RECOMMENDATIONS

This report describes a method of employing the TEXAS Model for Inter­

section Traffic to determine the capacity of isolated intersections operating

under different forms of unsignalized control at various subjectively-defined

levels of service and to analyze warrants for traffic signals as recommended

by the Manual on Uniform Traffic Control Devices and the Texas State Depart­

ment of Highways and Public Transportation on the basis of cost effectiveness.

Conclusions

The TEXAS Model can be used to (1) determine the capacity of inter­

sections, (2) evaluate the performance of an intersection, and (3) design an

intersection, that is, determine the optimum lane combination and traffic

control scheme.

Several other conclusions reached as a result of the total investigation

include the following.

(1) Two-way stop control provides the least costly means of intersection

control over a wide range of traffic conditions when considering the costs

associated with stopping, delay, and traffic control devices.

(2) All-way stop control cannot be justified on the basis of total

intersection costs. For all traffic conditions included in this investigation,

ranging from well below 100 to over 500 vehicles per hour per lane, signal

control consistently yielded lower costs than all-way stop-sign control ..

(3) Total delay time experienced at an intersection is approximately 75

percent greater than stopped time delay at the intersection. This relation­

ship may be used to estimate total delay when measurements of stopped-time

delay are available from field observations.

(4) For isolated intersections, traffic-actuated signal control is more

cost effective than fixed-time signal control. Full-actuated control is

generally better than semi-actuated, but semi-actuated signals may be appro­

priate where relatively steady traffic flow is present on the major street.

67

68

Traffic-actuated control, in general, causes a lower percentage of vehicles to

stop at the intersection when compared with pretimed control.

(5) The decision to replace two-way stop control with signal control

should probably be based on tolerable delay rather than on total intersection

costs. The following traffic volumes result in about 60 seconds of average

stopped-time delay to traffic on the minor street, and are recommended as

peak-hour volume warrants for signals (see Table 19).

(6) The TEXAS traffic simulation model has been shown to be a useful

tool for studying intersection performance under a wide range of traffic

demands and under various types of intersection control. More than 200 hours

of real-time intersection operation were simulated during the course of this

investigation.

Recommendations

User costs associated with stopping and delay should be considered when

selecting a particular type of intersection control. Even at light traffic

volumes (e.g., 600 vph, total of all approaches during the eighth high hour),

user costs far outweigh the amortized costs of traffic control devices.

Computer simulation models provide a practical means for evaluating, on a cost

basis, existing or proposed signal warrants. These models can be used to

simulate a wide variety of traffic conditions and summary performance statis­

tics can be produced rapidly at a fraction of the cost of field observation.

The scope of the analysis given in this report is somewhat limited, and

further study should be undertaken to strengthen and broaden the basis for the

conclusions that are drawn. Parameters which need more study include (1) dif­

ferent detector locations and configurations, (2) different signal controller

settings, (3) more geometric arrangements, and (4) one-way streets. The

variety of intersection configurations and traffic conditions that can be

evaluated is quite broad.

69

TABLE 19. PROPOSED WARRANT FOR REPLACE-MENT OF TWO-WAY STOP WITH SIGNALIZATION

Lane Arrangement Minor Approach

Major Minor Volume

4 X 4 550 vph 4 X 2 250 vph 2 X 4 700 vph 2 X 2 250 vph

This page intentionally left blank to facilitate printing on 2 sides.

REFERENCES

1. Lee, Clyde E., Thomas W. Rioux, and Charlie Re Copeland, "The TEXAS Model for Intersection Traffic -Development," Research Report No. 184-1, Center for Highway Research, The University of Texas at Austin, December 1977.

2. Lee, Clyde E., Thomas W. Rioux, Vivek s. Savur, and CharlieR. Copeland, "The TEXAS Model for Intersection Traffic - Progrannner's Guide," Research Report No. 184-2, Center for Highway Research, The Univer­sity of Texas at Austin, December 1977.

3. Lee, Clyde E., Glenn E. Grayson, CharlieR. Copeland, Jeff W. Miller, Thomas W. Rioux, and Vivek s. Savur, "The TEXAS Model for Inter­section Traffic -User's Guide," Research Report No. 184-3, Center for Highway Research, The University of Texas at Austin, July 1977.

4. Manual on Uniform Traffic Control Devices for Streets and Highways, U. S. Department of Transportation, Federal Highway Administration, Washington, D. C., 1971.

5. Texas State Department of Highways and Public Transportation, Manual on Uniform Traffic Control Devices for Streets and Highways, Vol 2, Appendix D-2, Division of Maintenance Operations, Austin, Texas, 1973.

6. Highway Capacity Manual, Highway Research Board, 1950.

7. "Highway Capacity Manual," Special Report 87, Highway Research Board, 1965.

8. Sutaria, T. C., and J. J. Haynes, '~Study of Level of Service at Signal­ized Intersections," a paper presented at the 56th Annual Meeting of the Transportation Research Board, January 1977.

9. May, Adolf D., Jr., and David Pratt, "A Simulation Study of Load Factor at Signalized Intersections," Traffic Engineering, Institute o£ Traffic Engineers, February 1968, pp 44-49.

10. Lee, Clyde E., and Walter C. Vodrazka, "Evaluation of Traffic Control at Highway Intersections," Research Report No. 78-lF, Center for Highway Research, The University of Texas at Austin, March 1970.

11. Winfrey, Robley, Economic Analysis for Highways, International Textbook Company, Scranton, Pennsylvania, 1969, p 688.

70

12. Claffey, Paul J., "Running Costs of Vehicles as Affected by Road Design and Traffic," NCHRP Report No. 111, 1971.

13. Thomas, T. C., "The Value of Time for Passenger Cars: An Experimental Study," Vol II of a report by Stanford Research Institute for the U. S. Bureau of Public Roads, May 1967.

14Q Jisco, T. E., "The Value of Connnuters' Travel Time- A Study in Urban Transportation," unpublished Ph.D. dissertation, University of Chicago, June 1967.

71

15. Thomas, T. c., and G. E. Thompson, "Value of Time Saved by Trip Purpose," Highway Research Record 369, pp 104-117.

16. '~pplication of the Principles of Engineering Economy to Highway Improve­ments," Report REP-8, Institute of Engineering Economic Systems, Stanford University, 1964.

17. Wilbur Smith and Associates, "Traffic Signal Warrants for Heavy Traffic Volumes Occurring During Short Periods of Time (A Tentative Peak Hour Delay Warrant)," West Virginia Department of Highways, NTIS Publication Number PB-245-612, April 1975.

18. Box, Paul C., and Willard A. Alroth, "Assembly, Analysis, and Application of Data on Warrants for Traffic Control Signals," Traffic Engineering, November 1967, pp 32-41, December 1967, pp 22-29, and January 1968, pp 14-21, 56.

APPENDIX

73

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Hour EB WB NB SB Stop Stop Signal Signal

8 325 150 1.00 7.00 5.40 3.00 275 125 1.00 6.25 4.50 2.40

7 335 170 1.00 7.25 5.70 3.05 283 141 1.00 6.50 4.75 2.55

6 365 173 1.00 7.95 6.25 3.40 308 144 1.00 7.00 5. 15 2.80

5 365 190 1.00 7.95 6.25 3.40 308 151 1.00 7.00 5.15 2.80

4 367 216 1.00 8.00 6.25 3.40 310 180 1.00 7.00 5.15 2.80

3 390 248 1.10 8.50 7.00 3.70 330 206 1.00 7.40 5.70 3.00

2 432 278 1.20 9.50 7.75 4.25 365 231 1.00 7.95 6.25 3.40

Peak 432 306 1.20 9.50 7.75 4.25 365 255 1.00 7.95 6.25 3.40

Sum 16.50 122.70 95.25 51.60

Fixed-* Total Intersection 2-Way 4-Way Time SA

User Cost, Stop Stop Signal Signal 8-Hour Totals 130.15 218.50 163.00 134.85

** FA 2-Way Signal Stop

3.80 3.80 3.00 3.00 4.00 4.30 3.00 3.40 4.50 4.35 3.25 3.50 4.50 5.40 3.25 4.00 4.50 6.80 3.25 5.20 5.00 9.40 3.60 6.50 5.40 13.50 4.50 8.00 5.40 22.00 4.50 10.50

65.45 113.65

** FA Signal

121.50

Minor Street User Cost

Fixed-* 4-Way Time SA

Stop Signal Signal

3.50 2.70 3.80 3.00 2.00 3.00 4.20 3.20 4.20 3.25 3.60 3.60 4.25 3.25 4.30 3.40 2.70 3.65 5.00 3.80 5.00 3.90 3.20 4.00 6.25 4.50 5.70 4.75 3.50 4.40 8.00 5.80 6.70 6.00 4.00 5.50

10.30 6.80 7.80 7.75 5.10 6.00

13.00 8.80 8.90 9.25 5.80 6.70

95.80 67.75 83.25

4 x 2 Geometry

Warrant 1 Conditions

*SA = Semi-actuated **FA = Full-actuated

** FA Signal

2.40 1.90 2.60 2.05 2.65 2.10 3.00 2.40 3.50 2.80 4.50 3.20 6.10 4.25 7.80 4.80

56.05

00 L11

Major Minor Major Street User Cost Approach Approach Fixed-

Volumes Volumes * 2-Way 4-Way Time SA Hour EB WB NB SB Stop Stop Signal Signal

8 300 200 0.80 6.50 5.00 2.60 200 150 0.50 4.50 3.25 1.90

7 309 226 1.00 6.70 5.10 2.80 206 170 0.50 4.60 3.30 2.00

6 336 230 1.05 7.40 5.60 3.40 224 172 0.50 5.00 3.50 2.20

5 336 254 1.05 7.40 5.60 3.40 224 190 0.50 5.00 3.50 2.20

4 339 280 1.05 7.50 5.60 3.40 226 216 0.50 5.00 3.50 2.20

3 360 330 1.10 8.10 6.10 3.60 240 247 0.55 5.10 3.50 2.30

2 400 370 1.20 10.00 6.75 4.00 266 277 0.60 5.50 4.00 2.50

Peak 400 408 1.20 10.00 6.75 4.00 266 306 0.60 5.50 4.00 2.50

Sum 12.70 103.80 75.05 45.00

Fixed-* Total Intersection 2-Way 4-Way Time SA

User Cost, Stop Stop Signal Signal 8-Hour Totals 103.35 189.45 140.80 143.90

L_

** FA 2-Way Signal Stop

3.60 4.50 2.20 3.00 3.75 5.00 2.30 3.40 4.00 5.20 2.50 3.50 4.00 5.70 2.50 4.00 4.00 6.50 2.50 L~. 80 4.25 7.95 2.80 5.50 5.10 8.50 3.00 6.20 5.10 9.90 3.00 7.00

54.60 90.65

** FA Signal

134.30

Minor Street User Cost

Fixed-* 4-Way Time SA

Stop Signal Signal

4.10 3.20 5.00 3.00 2.20 3.40 4.95 3.50 5.30 3.40 2.70 4.00 5.00 3.60 5.50 3.50 2.75 4.20 5.20 4.00 6.20 3.80 3.00 4.80 5.80 4.80 7.20 4.10 3.25 5.50 7.10 5.60 8.10 5.00 4.00 6.00 8.50 6.25 9.00 5.80 4. 70 7.00

10.00 7.00 10.00 6.40 5.20 7.70

85.65 65.75 98.90

2 x 4 Geometry

Warrant 1 Conditions

*SA = Semi-actuated **FA = Full-actuated

** I FA Signal

3.80 3.00 4.20 3.40 4.50 3.50 4.80 4.00 5.60 4.20 6.70 5.00 7.30 5.50 8.20 6.00

79.70

00 0'\

Major Minor Major Street User Cost Approach Approach

Fixed-Volumes Volumes * 2-Way 4-Way Time SA Hour EB WB NB SB Stop Stop Signal Signal

8 300 150 1.00 9.40 7.00 3.50 200 125 0.60 4.50 3.75 1.80

7 309 170 1.10 10.10 7.40 3.60 206 144 0.60 4.75 4.00 2.00

6 336 173 1.30 11.90 8.20 4.00 224 144 0.65 5.50 4.50 2.10

5 336 190 1.30 11.90 8.20 4.00 224 159 0.65 5.50 4.50 2.10

4 339 216 1.30 12.10 9.00 4.10 226 180 0.65 5.50 4.60 2.15

3 360 248 1.50 18.40 9.50 4.80 240 206 0.70 6.10 5.00 2.50

2 400 278 1.80 30.00 11.00 5.70 266 231 0.80 6.80 5.70 2.90

Peak 400 306 1.80 30.00 10.00 5.70 266 255 0.80 6.80 5.70 2.90

Sum 16.55 179.25 109.05 53.85

Fixed-* 2-Way 4-Way Time SA

Total Intersection Stop Stop Signal Signal User Cost,

8-Hour Totals 127~15 258.40 171.75 143.60

** FA Signal

4.80 2.20 4.90 2.25 5.20 3.00 5.20 3.00 5.40 3.00 5.80 3.10 6.20 3.50 6.20 3.50

67.35

** FA Signal

164.50

Minor Street User Cost

Fixed-* 2-Way 4-Way Time SA

Stop Stop Signal Signal

3.80 3.50 2.60 4.00 3.00 2.20 1.85 3.00 4.20 3.80 2.90 4.25 2.50 2.80 2.40 4.00 4.50 4.00 3.00 4.30 3.50 2.90 2.50 4.20 5.50 4.60 3.50 5.50 4.00 3.60 3.00 4.50 7.00 5.15 4.00 6.10 5.00 4.20 3.60 5.20 9.50 6.10 5.20 7.10 6.00 5.00 4.10 5.80

13.50 8.50 6.25 8.20 8.00 6.00 5.00 6.40

20.00 10.00 7.20 10.00 9.60 6.80 5.60 7.20

110.60 79.15 62.70 89.75

"2 x 2 Geometry

Warrant 1 Conditions

*SA = Semi-actuated **FA = Full-actuated

** FA Signal

4.10 2.80 4.60 3.60 4.80 3.75 5.50 4.10 6.80 5.10 7.80 6.00

10.10 7.10

12.50 8.50

97.15

00 -.....)

Major Minor Major Street User Cost Approach Approach Fixed-

Volumes Volumes * 2-Way 4-Way Time SA Hour EB WB NB SB Stop Stop Signal Signal

8 500 75 1.40 12.00 9.00 5.20 400 75 1.00 8.90 7.10 3.60

7 515 85 1.45 12.50 9.20 5.50 412 85 1.10 9.20 7.50 4.00

6 560 86 1.60 13.80 10.50 5.80 448 86 1.20 10.40 8.00 4.25

5 560 95 1.60 13.80 10.50 5.80 448 95 1.20 10.40 8.00 4.25

4 565 108 1.60 13.90 10.65 5.90 452 108 1.25 10.60 8.05 4.40

3 600 124 1. 70 15.40 11.20 6.70 480 124 1.30 11.10 9.00 4.80

2 665 139 1.85 18.80 12.90 7.60 532 139 1.50 13.25 10.00 5.80

Peak 665 153 1.85 18.80 12.90 7.60 532 153 1.50 13.25 10.00 5.80

Sum 23.10 206.10 154.50 87.00

Fixed-* Total Intersection 2-Way 4-Way Time SA

User Cost, Stop Stop Signal Signal 8-Hour Totals 59.90 240.50 178.60 126.20

** FA 2-Way Signal Stop

6.20 1.50 4.90 1.50 6.50 1.60 5.20 1.60 7.00 1.60 5.40 1.60 7.00 2.00 5.40 2.00 7.10 2.40 5.50 2.40 7.80 2.70 5.80 2.70 8.40 3.00 6.60 3.00 8.40 3.60 6.60 3.60

103.80 36.80

** FA Signal

130.80

Minor Street User Cost

Fixed-* 4-Way Time SA

Stop Signal Signal

1.50 1.00 1.50 1.50 1.00 1.50 1.80 1.00 1.80 1.80 1.00 1.80 1.80 1.00 1.80 1.80 1.00 1.80 2.00 1.05 2.20 2.00 1.05 2.20 2.20 1.20 2.40 2.20 1.20 2.40 2.40 2.00 2.80 2.40 2.00 2.80 2.60 2.20 3.50 2.60 2.20 3.50 2.90 2.60 3.60 2.90 2.60 3.60

34.40 24.10 39.20

4 x 2 Geometry

Warrant 2 Conditions

*SA = Semi-actuated **FA = Full-actuated

** FA Signal

1.10 1.10 1.20 1.20 1. 20 1.20 1.50 1.50 1.70 1.70 2.10 2.10 2.20 2.20 2.50 2.50

27.00

I

00 00

Major Minor Major Street User Cost Approach Approach Fixed-

Volumes Volumes ~~

2-Way 4-Way Time SA Hour EB WB NB SB Stop Stop Signal Signal

8 400 100 1.10 30.00~ 12.00 4.40 350 75 1.00 13.00 10.10 3.60

7 412 113 1.15 30.00 12.50 4.60 360 85 1.05 14.00 10.40 3.80

6 448 115 1.25 30.00 13.80 5.00 392 86 1.10 25.00 11.50 4.30

5 448 127 1.25 30.00 13.80 5.00 392 95 1.10 25.00 11.50 4.30

4 452 144 1.30 30.00 14.00 5.10 396 108 1.10 30.00 11.70 3.40

3 480 165 1.40 30.00 16.00 5.60 420 124 1.15 30.00 13.10 4.80

2 532 185 1.60 30.00 21.50 6.70 465 139 1.30 30.00 15.00 5.20

Peak 532 204 1.60 30.00 21.50 6.70 465 153 1.30 30.00 15.00 5.20

Sum 19.75 437.00 223.40 78.70

Fixed-* Total Intersection 2-Way 4-Way Time SA

User Cost, Stop Stop Signal Signal 8-Hour Totals 58.55 477.10 250.95 123.65

** FA 2-Way Signal Stop

5.10 1.80 4.40 1.30 5.20 2.10 4.50 1.55 5.60 2.15 5.00 1.55 5.60 2.40 5.00 1.60 5.65 2.90 5.10 2.00 6.00 3.25 5.20 2.30 6.70 3.90 5.80 2.70 6.70 4.30 5.80 3.00

87.35 38.80

** FA Signal

121.95

Minor Street User Cost

Fixed-* 4-Way Time SA

Stop Signal Signal

2.00 1.30 2.10 1.50 1.05 1.50 2.10 1.40 2.30 1.80 1.15 1.80 2.15 1.45 2.35 1.80 1.20 1.85 2.50 1.60 2.70 1.95 1.25 2.00 2.80 1.90 3.30 2.10 1.35 2.20 3.10 2.20 4.00 2.50 1.55 2.65 3.90 3.10 ·4. 60 2.75 1.75 3.10 4.20 3.25 5.00 2.95 2.05 3.50

40.10 27.55 44.95

2 x 4 Geometry

Harrant 2 Conditions

*SA = Semi-actuated **FA = Full-actuated

Q = Estimated

** FA Signal

1.50 1.10 1.60 1.30 1.70 1.35 2.05 1.40 2.80 1.55 3.10 2.00 3.60 2.60 4.00 2.95

34.60

00 \.0

Major Minor Major Street User Cost Approach Approach Fixed-

Volumes Volumes * 2-Way 4-Way Time SA Hour EB WB NB SB Stop Stop Signal Signal

8 400 75 1.50 30.00r2 12.00 5.30 350 75 1.20 18.00 9.00 4.40

7 412 85 1.60 30.00 12.10 5.50 360 85 1.30 24.00 1.30 4.50

6 448 86 1.85 30.00 14.00 6.00 392 86 1.45 30.00 11.20 5.10

5 448 95 1.85 30.00 14.00 6.00 392 95 1.45 30.00 11.20 5.10

4 452 108 1. 90 30.00 14.20 6.20 396 108 1. 50 30.00 11.25 5.15

3 480 124 2.05 30.00 16.50 7.20 420 124 1.65 30.00 12.40 5.50

2 532 139 2.05 30.00 20.70 8.20 465 139 1.95 30.00 15.70 6.60

Peak 532 153 1. 95 30.00 20.70 8.20 465 153 1. 95 30.00 15.70 6.60

Sum 25.70 462.00 219.95 95.55

Fixed- * Total Intersection 2-Way 4-Way Time SA

User Cost, Stop Stop Signal Signal 8-Hour Totals 60.10 496.80 245.55 129.65

** FA 2-Way Signal Stop

6.60 1.30 5.40 1.30 7.00 1.50 5.50 1.50 7.50 1.50 6.50 1.50 7.50 1.80 6.50 1.80 7.70 2.10 6.60 2.10 8.40 2.50 7.00 2.50 9.20 3.00 8.00 3.00 9.20 3.50 8.00 3.50

116.50 34.40

** FA Signal

154.50

Minor Street User Cost

Fixed-*

4-Way Time SA Stop Signal Signal

1.50 0.80 1.20 1.50 0.80 1.20 1.70 1.00 1.60 1.70 1.00 1.50 1.70 1.00 1.50 1.70 1.00 1.50 1.90 1.20 1.90 1.90 1.20 1.90 2.10 1.50 2.10 2.10 1.50 2.10 2.60 1.90 2.60 2.60 1.90 2.60 2.80 2.40 2.75 2.80 2.40 2.75 3.10 3.00 3.50 3.10 3.00 3.50

34~80 25.60 34.10

2 x 2 Geometry

Warrant 2 Conditions

*SA = Semi-actuated **FA = Full-actuated

r2 = Estimated

** FA Signal

1.50 1.50 1.70 1.70 1.90 1.90 2.00 2.00 2.10 2.10 2.70 2.70 3.10 3.10 4.00 4.00

38.00

\0 0

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183-8

183-9

183-10

183-11

183-12 184-1

184-2

184-3

184-4F

188-1 188-2F 196-1F

198-1F 209-1F

212-1F 244-1 245-1F 514-1F l053-1F

RR 16

RR35

RR36

RR 37

RR38

RR 39

RR40 RR43

RR45 RR46

RR47 RR48 RR49 RR 50 RR51 RR 52 RR 53 RR 54 RR55 RR 56

RR60

RR61

RR 62 RR63 RR64

(Continued from inside front cover)

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"An Evaluation of Promotional Tactics and Utility Measurement Methods for Public Transportation Systems," by Mark Alpert, Linda Golden, John Betak, James Story, and C. Shane Davies, March 1977. "A Survey of Longitudinal Acceleration Comfort Studies in Ground Transportation Vehicles," by L. L. Hoberock, July 1976. "A Pavement Design and Management System for Forest Service Roads - A Working Model," by Freddy L. Roberts, B. Frank McCullough, Hugh J. Williamson, and William R. Wallin, February 1977. "Characteristics of Local Passenger Transportation Providers in Texas," by Ronald Briggs, January 1977. "The Influence on Rural Communities of Interurban Transportation Systems, Volume I: The Influence on Rural Communities of Interurban Transportation Systems," by C. Michael Walton, Richard Dodge, John Huddleston, John Betak, Ron Linehan, and Charles Heimsath, August 1977. "Effects of Visual Distraction on Reaction Time in a Simulated Traffic Environment," by C. Josh Holahan, March 1977. "Personality Factors in Accident Causation," by Deborah Valentine, Martha Williams, and Robert K. Young, March 1977. "Alcohol and Accidents," by Robert K. Young, Deborah Valentine, and Martha S. Williams, March 1977. "Alcohol Countermeasures," by Gary D. Hales, Martha S. Williams, and Robert K. Young, July 1977. "Drugs and Their Effect on Driving Performance," by Deborah Valentine, Martha S. Williams, and Robert K. Young, May 1977. "Seat Belts: Safety Ignored," by Gary D. Hales, Robert K. Young, and Martha S. Williams, June 1978. "Age-Related Factors in Driving Safety," by Deborah Valentine, Martha Williams, and Robert K. Young, February 1978. "Relationships Between Roadside Signs and Traffic Accidents: A Field Investigation," by Charles J. Holahan, November 1977. "Demographic Variables and Accidents," by Deborah Valentine, Martha Williams, and Robert K. Young, January 1978. "Feasibility of Multidisciplinary Accident Investigation in Texas," by Hal L. Fitzpatrick, Craig C. Smith, and Walter S. Reed, September 1977.

"A Pavement Design and Management System for Forest Service Roads- Implementation," by B. Frank McCullough and David R. Luhr, January 1979. "Multidisciplinary Accident Investigation," by Deborah Valentine, Gary D. Hales, Martha S. Williams, and Robert K. Young, October 1978. "Psychological Analysis of Degree of Safety in Traffic Environment Design," by Charles J. Holahan, February 1979. "Automobile Collision Reconstruction: A Literature Survey," by Barry D. Olson ar.d Craig C. Smith, December 1979. "An Evaluation of the Utilization of Psychological Knowledge Concerning Potential Roadside Distractors," by Charles J. Holahan, December 1979.