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This is to certify that the

thesis entitled

OPTIMIZATION TECHNIQUES FOR

,URBAN HIGHWAY TRAFFIC $IGNALIZATION

presented by

Sugeng Setyawan

has been accepted towards fulfillment
of the requirements for

Masters degree inCivil Engineering

 

 

fléz-céém cs 731/4}:

Major professor

Date 4/3/89
/ /

0-7639 MS U is an Affirmative Action/Equal Opportunity Institution

 

MSU RETURNING MATERIALS:
Place in 550E drop to
LIBRARIES remove this checkout from
“—- your record. FINES will

be charged if booE is
returned after the date
stamped below.

 

 

 

 

' .
JAN 1 1 19‘2—

was;

 

 

OPTIMIZATION’ IECEWIOUFS
FOR

UTWZN' 5705”]? IRAFTTC SIGNZIIZATIQN

BY

SUGENG SETYZMAN

A IRESRS

SUBMITIED T0

‘HTCHTUZN' STZZE UNIVERSITY

in partial fulfilllent of the require-eats

for the Degree of

MMSIER OF SCIENCE

Departnent of Civil and Environnental Engineering

1988

’“Uh’/;j)

ABSIRACT

OPTIMIZATION’ ZEQENTOUES
F05

”5355' 5105!]? ZRAFTIC SIGNZIIZZTTON

By

Sugeng' Setyauan

Increasing construction costs which exceed revenues
have forced traffic engineers to more closely fine tune
the existing roadway facilities using various transporta-
tion system management strategies. Among these stra-
tegies, traffic signal coordination and optimization is
recognized as one of the most cost effective and easi-
est to implement strategies.

Numerous computer packages are available to optimize
and/or simulate existing or expected traffic flow condi-
tions. However, few of these models have been introduc-
ed to the developing countries where the need for op-
timization is strong as financial constraints are one of
their major problems.

Techniques for using two traffic signal models were
introduced in this study and the consistency between
the models tested. Furthermore, the impacts of signal

timing optimization were evaluated. Delays, stops and

fuel consumptions were estimated for before and after
optimization of signal timing plans, and the results
were converted into highway user costs, so that the
benefit of optimization could be determined.

This study also identified the level of saturation
in the traffic flow which limits the value to be gain-

ed from the use of optimization models on a network.

If

10 NY mum's

1'1'1'

J!(9JKJVZ7JVHEAEI7(ZAIIZAVJ"

I am deeply indebted to Dr. William 0. Taylor,
Professor and Chairperson of the Department of Civil
and Environmental Engineering, for his immeasurable
guidance and assistance during this study.

A sincere appreciation is expressed to the Petra
Christian university in Indonesia which provided the
possibility for my program of study.

Special thanks also to the other members of my
committee, Dr. Tho-as L. .Maleck, and Dr. Richard W.
Lyles, for their enthusiasm and assistance.

Finally, the support and understanding of my wife,
Ellyana, and our children, Renata and Karina, in pro-
viding the impetus and strength to complete this work

are admired.

Sugeng Setyawan

TABLE 01' CONTENTS

LIST OF TEBLES

LIST’ OF .FTGEEES

CHAPTER ONE : INTRODUCTION

(II-FOONr-I

HHHHH

OEEPTER TWO :

11.1.

11.2.

Background

Traffic Signal Timing Optimization

Models Available
Study Objectives
Outline Of The Study

ENGINEERING

Transportation And Traffic
In The Developed Countries

11.1.1. U.S. Signal Timing
Project

Traffic Engineering In The
Countries

OEEPTER THREE : .MUDEI OVERVIEN

III.1.

TRANSYT-7F

III.l.l. Model Description
III.l.2. Input Required
III.l.3. The Operation
III.l.4.
III.l.5.

vi

TEE STATE-OFrTEE-ART IN TEAEFIC -

Engineering -

Optimization -

Developing

Computational Algorithms
Limitation and Other

Features

Page

viii

ix

r—u-a
OOHODNH

14

17

20

25

25
26
26
27
33

111.2.

SOAP84

III.2.1. Model Description

III.2.2. Input Required

III.2.3. The Operation

III.2.4. Computational Algorithms
III.2.5. Limitation and Other Features

34

35
35
36
37
43

CHAPTER FOUR : TRANSIT-TP' AND SOAPBA CONSISTEMCY - TEST

IV.l.
1V.2.
IV.3.

IV.4.

OF THE .NDE’S

Description of The Study Site

Study Approach

Results and Analysis of Performance -
Measures

Consistency Test of The Performance -
Measures

CHAPTER FIVE : EXAMTNINC THE IMPACTS OF SIGNAL -

<<<<
booms-

OPTIMIZATION'

Description of The Study Site
Study Approach

Results and Analysis

Energy and Cost Evaluation

CHAPTER SI! : CONCZUSIONS

V1.1.
V1.2.
V1.3.

APTTWDICES

Appendix-1

Summary

Future Development

Transferability of U.S. Experience to -
Indonesia

TRANSYT-7F Optimization Run for Study -

vii

45
46

48
51

56
58
59
70

73
75

76

Case-1, in Michigan Avenue, Lansing,
Michigan

Appendix-2 SOAP84 Simulation Run .of TRANSYT-7F -

Optimal Timings for Study Case-I, in
Michigan Avenue, Lansing, Michigan

Appendix-3 Regression Analysis - Program in Basic

Appendix-4 TRANSYT-7F Simulation Runs for The

Study Case-II, in Cirebon, Indonesia

Appendix-5 TRANSYT-7F Optimization Runs for The

Study Case-II, in Cirebon, Indonesia

'RITERENCES
LIST OF TMBLES
Table
111.1. Reduction of Stops as a Function of Delay
1V.l. Relationship Between TRANSYT-7F and SOAP84 -
Results
1V.2. The Effect of The Ratio of External to -
Internal Link Volumes
v.1 Benefit Estimated for Volumes of .308

viii

79

99

111

115

126

140

Page

32

52

54

71

Figure

111.1.
111.2.
1V.1.
1V.2.

1V.3.

LIST OF FIGURES

TRANSYT-7F Estimate of Delay

Webster’s Model Delay

Section of Arterial Under Study

Traffic Flow Diagram for The Case Study
Comparison of Performance Measures

Network System of The Case Study
Link-Node Diagram for The Case Study

Network-wide Traffic Performance

ix

Page

32
39

46

50
57
60

61

(CJPQIJDUTIEUE’ (9JVHTHr .120f1!£?€2£7(7(71PJFCZAV'

I. l . BACKGROUND

Currently, the emphasis in transportation planning
has been shifted from long term, capital intensive -
construction projects, to shorter term, relatively low
cost projects, which are designed to optimize the use
of existing facilities. Such a trend places heavy con-
sideration on ‘gransportation system Aganagement [tsm] as

a part of the planning process and as a prerequisite
for improvements to increase Vthe capacity and efficiency
of transportation systems, in particular for urban traffic
operations.

The provision of improved traffic signal systems

for control at heavily trafficked intersections and corr-

idors is ‘by far the most common form of tam. In-
efficient use of the transportation system results when
traffic signals are installed without sufficient study.

while the U.S. Manual on Uniform Traffic Control De-

vices for Streets and Highways [25] discusses several
warrants to justify traffic signal installations, the
manual does not specify the operation of such signals.

The by-products of inefficient use of traffic sig-
nals include greater energy consumption, an increase in
certain environmental impacts such as vehicle noise and

emission levels, increased travel time and delay, higher

accident rates, and less reliable service.

The Federal Highway Administration forecasted that
energy consumption could be conserved by 100,000 barrels
of crude oil per day by optimizing the timing of the
130,000 coordinated, signalized intersections that current-
ly exist in the U.S. urban streets. (211(2‘3 Thus, it
is obvious that a signal optimization program could be
one of the most cost effective strategies that can be

implemented under tsm.
I. 2. TRAFFIC SIGNAL TIMING OPTIIIIZATION

In general, signalized intersections can be classi-
fied into two major systems : (a) isolated signals,
and (b) coordinated signal systems which consist of two
or more intersections and streets that link those inter
sections. For the analysis of isolated signal timing,
Webster’s model represents one of the major advances in
the development of optimizing signal timing. [‘1 [71 ‘31
Other analytical methods include the U.S. Highway Capacity
Manual method [TRB Special-Report 209; ch.9], the Canadian
Manual on Uniform Traffic Control Devices method, the
Australian Road Capacity Guide method, the Average Loaded
Phase Expanded [ALE] method, Bellis’s method, Failure-rate
method, and the use of certain British and Swedish mo-
dels. For coordinated signals, various manual and com-

puter aided progressive signal system designs have been

used with reasonable success on single arterial streets.
In the case of signal network design, simplification was
traditionally made by providing preferential treatment to
one or more major arterials within the network, and
after assigning favorable splits and offsets to these ar-
terials, the remaining signals were forced to conform
with the various restraints imposed by those major arte-
rials.
The manual solutions are subject to more human

error, and are often cumbersome and time consuming. With

the availability of the computer as a versatile ana-

lytical tool, complex algorithms for signal timing
design were developed, which represent significant pro-
gress in the current state of the art.

I. 3. MODELS A VA I LADLE

A number of computer based optimization models have
been demonstrated to be effective and reliable. Some of

those are

SOAP

SOAP stands for the .QIGNML .QPEHATIONS and-‘ANZLYSIS
EMCKAGES, developed by the University of Florida, for
the Florida Department of Transportation, and the-Fede-

ral Highway Administration. SOAP is a macroscopic ana-

lysis program, which provides a method of evaluating

and developing a wide-range of signal design alterna-

tives for isolated intersections. SOAP is an optimization
model which determines the solution for optimal cycle

lengths, splits, phasing patterns, and left turn con-
figurations for three or four legged intersections.

Inputs include traffic flow per-approach, truck and bus
composition, left turn data, signal related data,
saturation flow rates, and progression related data. Basic
outputs include delays, percent stops, percent saturation,
maximum queue, left turn conflicts, and excess fuel con-

sumption. The program is well written and easy to use.

MMIBAND

The .MMXIMUM’ BANDNIDTH, is a bandwidth optimization

program which calculates signal settings on arterials
and triangular networks. This program can handle as
many as twelve signals efficiently. Inputs include the
range of cycle lengths, the network geometry, traffic
flows and their capacities, left turn patterns, queue
clearance. times, and the allowable range of speeds.

The output include a data summary report and the so-
lution report of cycle time and bandwidths, selected
phase sequencing splits, the offsets, travel time and

speed on links.

TEIAS

The- .TRAFTIC lggPERLMENTAL and .ANZLYTICAL .§LMULATION,
was developed by the University of Texas Austin Center
for Highway Research, for the Texas Department of High-
ways and Public Transportation. This program has the
ability to evaluate existing and proposed intersection
designs for both geometric and traffic operations. TEXAS
is a simulation model which provides quantifiable measures

of changes in traffic operations from roadway geometry,

driver and vehicle characteristics, intersection and lane
control, flow conditions, and signal timing plans.
PMSSER

PROGRESS] ON ANAL YSI S an d §IGJVAL .5; YSTKM _L_' VAL (IA TION
,gpuriua, was developed by the Texas A and M University’s
Texas Transportation Institute for the Texas Department
of Highways and Public Transportation. PASSER provides
a valuable tool for determining optimal splits, phases,
and offsets, primarily for coordinating traffic signals
along arterial highways. Basic inputs include the range
of the cycle lengths, movement flows, saturation flows,
left turn patterns, queue clearence times, the desired
speeds, minimum green time, allocation of bandwidth by
direction, cross street phase sequences, and link dis-

tances. Outputs include cycle length, bandwidths, band

speeds, a time-space diagram, delay, probability of queue
clearances, offsets, splits, phase sequences, and volume

over capacity ratios.

SUE

ISLMULATION' 0F .QRBAN’.§USES, is a special purpose
model which has been developed by the Federal Highway
Administration for evaluating the benefits of alternative
bus stop location [near side, farside or midblock], and
physical characteristics such as protected or unprotected
lanes. This model was developed to provide transit
operators with a tool for evaluating bus operations a-
long an arterial as well as the effect of various bus

stop strategies on their performances.

TRANSIT

The .QEAEFIC ‘QETWORK .STUDZ .ZOOL. The original TRAN—
SYT was developed by Mr. Dennis I. Robertson of the
Iransport and :fload lgesearch .Laboratory [TRRL], Crawthorne
in the United Kingdom. TRANSYT is a major tool avail-
able to traffic engineers for analysis and evaluation of
alternative traffic control strategies. It is primarily
used for optimizing the signalization on arterial and
grid networks. The model has a hill climb optimization

algorithm that varies the offsets and phase-lengths at

each signal to locate the particular set of signal
timings that minimize a Performance Index, which is a
weighted -linear combination of stops and delays. Basic
inputs include cycle lengths, phasing, performance index
weights, lost time value, link lengths, either link
travel times or speeds, link flows, turning movements

and saturation flows. Basic link outputs include percent

saturation, total travel, travel times, delays, rate of
stops, maximum queue length, offsets and splits, plus
the value of the performance index. Since the

original model was introduced in 1968, numerous improve-

ments have been made and a number of versions issued,

some examples are

- TRANSIT-6C

TRANSYT-GC includes fuel consumption, the es-

timation of emissions, demand response, a
provision for priority links, and a more
comprehensive measure of effectiveness. Users
may determine the basis of optimization by

weighting various variables.

- TRANSIT-7F

This is one of the recent versions avail-

able to day with the North American no-

menclature on input and output. ‘ It also
produces a time space diagram and the es-

timation of fuel consumption. A new
revision will optimize the cycle length, and

identify potential intersection blockages.

- TWMNSYT‘E

TRANSYT-B, the newest version which includes
gap acceptance functions for left turns and
a cycle search routine. The British govern-
ment charges a fee, limiting the use of

the program.
SIGOP

SIGOP stands for the traffic SIGNAL ‘QPTIMIZATIONe
model. It is a powerful analysis and design tool. Con-
ditions, such as the existing conditions, might be ana-

lyzed in terms of a number of useful traffic engineer-

ing measures. The signal timing may be optimized
for cycle length, splits and offsets to minimize the
’disutility’ function. Comparison of the results of

several alternatives enables the traffic engineer to eva-
luate the relative effectiveness of the designs. The
current version of SIGOP was developed by KLD Assoc.,

Inc. for the Office of Research, Federal Highway Ad-

ministration. It can handle up to 150 intersections,
multi-phase signals can be modeled as well..

Input includes arrival flows and saturation flows, the
minimum green times, yellow times, special phase times,
passenger car equivalent factors for trucks, buses, and
turning vehicles, while the output include time-space dia-

grams along selected arterials and links.

NETSIM

NETSIM is an abbreviation of the name of a model
for traffic ‘ggzwonr .SLQWLATIONZ It was developed by KLD
and Associates for the Federal Highway Administration.
NETSIM was designed primarily to provide a powerful ana-
lysis tool to test complex network problems. It is
particularly useful for the analysis of dynamically con-
trolled traffic signal systems with the highly variable
nature of their operation. This simulation model can
also evaluate several alternatives which are being con-

sidered and provides a basis for a comprehensive analysis

and identification of potential problems which could
occur that would not show up in other models. The
inputs include : the network geometry, arrival flows,
:saturation flows, turning counts, traffic composition, and
signal setting. Outputs include a variety of measures
such as delay and stops, cycle failures for pretimed

Signals, fuel consumption and level of’emissions. NETSIM.

10

simulates the performance of a network by using a
microscopic, probabilistic model which incorporates car
following, queue discharge, and lane switching algorithms.
It has the capacity to handle 99 intersections, 160

links, and 1600 vehicles at a time.

PRIERE

PRIFRE is a reverse acronym for the fififlEflAYfiEEIORITY
LANE model. This model was developed by the
University of California Institute of Transportation Stu-
dies at Berkeley, to improve the efficiency of freeway
systems. The physical system considered by PRIFRE is
a directional freeway with a priority lane reserved for
high occupancy vehicles [HOV’s] and the on and off ramps
to the freeway. PRIFRE can be used to ,evaluate various
types of priority treatment of high occupancy vehicles,
but its primary use is for the evaluation of freeway

rather than signalized intersections.

FWTOEP

FREQ3P is an acronym for the gggranr OPTIMIZATION
with .QUEUFINC, version q; control and IERIOPITY treatment.
This model has been used frequently to evaluate alter-
native priority entry control strategies at any or all

entrance ramps to optimize freeway operations. It can

ll

be used to maximize an objective function such as passenger
input or miles of travel. The physical system considered
by this -model is a directional, urban freeway section
and the associated ramps. The freeway section is
described as a series of contiguous sections which are
internally operationally homogenous. It was developed by
the University of California Institute of Transportation
Studies at Berkeley, and it is not proposed for signal-

ized intersections.

OTHER .NDDELS

Recently, a number of advanced computer models for
analyzing transportation corridors have been introduced.
Models like ; EREOOPL, EFFOOPE, TRESCOT, TRANSFT—SC, and

SLNTOL provide the capability for investigating demand,

supply and control interaction for transportation cor-
ridors. Such models are still in the process of
development, testing and refinement, and won’t be con-

sidered more in this study.

I. 4. STUDY ODJECTIVES

These computer models have been developed and cal-
ibrated according to the conditions of the developed
countries. Many of these factors are significantly

different in developing countries. Thus, the models can

12

not readily be used by practicing engineers for solving

many of the transportation management problems in the
developing countries. The lack of use in these countries
is also caused by many other reasons, for example

- lack of computer hardware to run the models,

- difficulties of obtaining the software program
and model documentation,

- non-familiarity with the existing models and
their uses,

- perception that use of models requires an
expertise in traffic flow and higher mathe-
matical theory,

— a belief that computer models will not give

practical results,

Considering the beneficial use of such models in
the U.S. and other developed countries, as well as
remembering the ’optimization’ policy introduced by the
Indonesian Directorat General of Highway, in 1979, this
study was performed to determine the feasibility of
using such models in Indonesia. Hence, the purpose
of this study is primarily to demonstrate optimization
techniques and analyze the possible impacts of using

signal optimization models in Indonesia.

13‘

1.5. OUTLINE OF THE STUDY

Two models were selected for more detailed study,
TRANSYT-7F and SOAP84 versions, and their consistency
was tested on an arterial street in the city of
Lansing, Michigan. The performance measures of
the models were compared statistically to examine the
differences, if any. Furthermore, the effectiveness
of TRANSYT-7F was tested in an Indonesian network. The

’existing network was loaded with volumes equal to .105,
.205, .305 and .405, where S is the street saturation
flow. Then the improvements of signal timing
optimization were measured, so that the benefits of the

optimization could be quantified.

(CZHQIJDUTHTUR' EPTVZ’:' EPITIE' Agdrhlfir1?-(217-ZE£Z£?-<AL£?1"
LIJV' JTUTUIJFJFUFZ7 .ATJVTTDIJVUTJT}?JKAVCF

A brief insight of traffic engineering experiences
in the developed countries and the developing countries

are presented in this chapter. The greater population

density that is commonly found in the developing coun-

tries, especially in urban areas, is associated with a
lower level of traffic engineering service than in the

developed countries. Many other factors also contribute
to differences in traffic conditions, including nature,
culture, government regulations, technology of public trans-
portation systems, communication systems, alternate trans-
portation facilities, pedestrian behaviors, etc. This
chapter concludes briefly by examining what benefits.

are transferable, and what ’lessons’ could be learned

from the success experiences of the developed countries.

II.l. TWANEPORTATION’ AND TRAFTTC.ENCINEERINC PRACTICES IN

TEE DEVELOPED COUNTRIES

"The inherent need of highly developed and indus-
trialized nations is a sophisticated and widespread trans-

portation system". [123

This statement is certainly true for the developed

countries, which is evidenced with their intricate

l4

15

urban, regional, and national transportation systems.
The adequate mobility broadens the perspective of the
individual as well as the nation. Mobility links
the activities from different locations and facilitates
the movement of ideas, people, and goods. A strong
transportation system is the principal component of eco-
nomic, social, cultural, and political structures of
modern societies, which is an important factor in the
national development. Nations that have strong and stable
economics are generally those with more than adequate
transportation systems.

Although Transportation Engineering has been practic-
ed for many centuries, it was not until the last two
decades that this study received recognition as a pro-
fessional subdiscipline within civil engineering. For the
developed countries, transportation today‘ has benefited
from centuries of experiences accumulated from across
the globe, and has recently been crystalized as an

interdiciplinary study involving

- engineering;
- operation research; and

- the social sciences.

It can be defined as the science and art of
planning, designing, implementing, operating, monitoring,

and maintaining any medium for facilitating the movement

16

of people and goods.

The° planning stage involves a deliberate investiga-
tive study for identifying and evaluating needs and op-
tions. It is in this stage where the tools of system

engineering and the social sciences receive great empha-

sis. The policy or a standard system of transportation
planning for urban, state, regional or rural settings
is always based on scientific, analytical design

techniques such as trip generation, trip distribution,

modal split and traffic assignment.

The designing of transportation facilities involves
adherence to engineering science, design standards and an
assortment of specifications. The science of engineering

has a predominant *role in facility design.

Implementation refers to construction and the final

opening of transportation facilities to the public. The
implementation process is one of the key successes of
developed countries, especially for projects which are

designed to encourage a particular human behavior. It is
very uncommon to find the opening of modern facilities
without parallel activities in the area of public edu-
cation such that proper use is encouraged and negative

impacts will be minimized.

17

Operation is usually the direct function of govern-
ment, though the operation by quasi-governmental and
private agencies is not uncommon. Good management is a

key component of an effective operation.

Monitoring functions are keyed to the evaluation of
the primary transportation objectives and the performance
of the physical components. Monitoring is a data collec-
tion and analysis mechanism which generates an information
base useful for future designs, service improvements, and
detecting new needs. An example of monitoring activity
is the maintenance of accident record systems, which is
important for improvements to design or other policies

on vehicle operation.

Maintenance is just emerging as an activity which

must be deliberately planned. In the U.S., thousands
of miles of interstate highway have been built since
1956. However, neglecting maintenance in the planning

process caused the maintenance cost to be significantly

higher than what was estimated.

II. 1 . l . U. S. SIGNAL TIMING OPTIMIZATION PROJECT

As stated before, one of the current tsm targets

is to provide systematic control to the traffic operation

over the existing highway network so as to achieve a

18

comprehensive set of mobility, safety, energy, environ-
mental and efficiency objectives.

The' National Signal Timing Optimization Project was

initiated by the Federal Highway Administration as a
fuel conservation effort in response to the high cost
of imported oil. About 35 percent of the U.S.’ total
daily oil consumption is consumed by vehicles traveling
in urban areas throughout signalized intersections. ‘10]
A significant portion of this is wasted due to poor
[traffic signal timing. In the networks with poorly
timed traffic signals, the fuel consumed by vehicles
stopping and idling at traffic signals accounts for
approximately 40 percent of the network—wide vehicular
fuel consumption. By improving traffic signaI timing,

the quality of traffic flow will be improved, and
driving will be made faster and easier 'for all traffic
using the street system.

There are an estimated 240,000 signalized intersec-

tions in the U.S.; of these, an estimated 130,000 are
coordinated. (211(2‘3 Just optimizing the signal

timing at those intersections nationwide, it has been
estimated, could conserve about two million gallons of
gasoline per day. Therefore the FHHA’s main target is
the development of optimal signal timing plans for all
of the coordinated signals and most of the non-coor-
dinated signals within the U.S. As an initial part of

the overall effort, the National Signal Timing Optimiza-

19

tion Project was intended to satisfy the following ob-

jectives

- establishing credible data on the effective-
ness of signal timing optimization;

- making signal timing optimization projects
easy to accomplish;

- defining cost, level of staff, computer,
and other resources necessary to undertake
a signal timing optimization project, so
that such an optimization project can be

effectively budgeted.

To accomplish these objectives, the TRANSYT-7F pro-
gram was first developed, then applied to programs in

11 cities nationwide to evaluate the effectiveness of the

model. The 11 cities participating in the project
were : Charleston, SC ; Denver, CO ; Des Moines, IA ;
Fort Wayne, IN ; Gainesville, FL ; Milwaukee, WI ;

Nashville, TN ; Portland, OR ; Pawtucket, RI ; San-
Francisco, CA ; and Syracuse, NY. By evaluating the

results, .it was concluded that a signal timing optimiza-
tion program could significantly reduce vehicle delays,

stops, and particularly fuel consumption which is a va-
lid national objective that can be realized through the
actions of state and local governments. TRANSYT~7F has

proven to be a very valuable tool for signal timing

20

optimization projects. Its success for design depends
largely on the accuracy of the data used in the
model.

II. 2 . TRAFFIC ENGINEERING IN THE DE VEL OPING COUNTRIES

Most of the third world countries are experiencing
rapid growth in motorization, as their urban centers are

growing much faster than rural areas. However, such rapid

developing motorized societies exist without A adequately
expanding the roadway infra-structure or transportation
policies. As a result, urban centers are experiencing a

major growth in the need for personal mobility, and con-
sequently in increased traffic volumes and congestion.

Traffic control practices are not keeping pace with this

rapid growth. Economic resources for investment have
become increasingly scarce, and this trend seems likely
to continue. Traffic engineering problems are usually

approached by managerial solutions rather than capital

intensive ones to meet the rising mobility demands in urban
centers. There are vast variations in traffic engineering
characteristics, standards, and management techniques among

the countries.

A study was performed by the ITE Technical Council
Committee 4A - 20, in order to understand the specific

types of traffic engineering practices in the developing

21

countries. (20] The study included

DATA COLLECTION' AND INEENTORIES

The study was designed to assess in a comprehensive

manner the collection techniques and their application in

design, as well as to provide some insight into the
state of the art in traffic engineering practices. The
information gathered, can be summarized as follows

- most of the countries have some method of

traffic volume counting;
- accident reports are not regularly recorded;

— the study of pedestrian behavior, particularly

at intersection locations, are not routinely
conducted; and
- parking studies are not done regularly,

especially with respect to duration and off-

street parking facilities.

STANTARDS ANT PRACTICES

Many countries have some form of highway capacity
manual. Some of them use the U.S. Highway Capacity
Manual [221 as well as their own manuals which were

developed to take account of the different traffic be-

havior. Some specific differences in traffic behavior

22

are a large percentage of heavy trucks, traffic with

slow moving vehicles, mixed traffic problems, etc.

TRAETIC CONTROL

Most of the countries use their own standards, which
have been developed based on local conditions and re-
present modifications of U.S. or European manuals. Local

languages are used for signs, and some warrants for the

installation of traffic signals are modified. Certain
countries, especially in Latin America, use the U.S.
manual markings as well as their own markings. A lot

of the countries do not incorporate the pedestrian phasing

in traffic signal designs. With regard to having an
inventory system for signs and markings, most countries
maintain the drawings of the location record, and quite

a few are using computerized maintenance systems.

TRAFTIC CONTROL .PRACTICES ON' SPECIAL .EEENTS

Developing countries face serious traffic problems,
particularly during special events due to the concen-
tration of automobiles on the road networks within the
urban centers. Few countries do trip-generation analysis,
and parking demand studies. However, nearly all of the
countries practice some form to control for the added

traffic during special events. Those countries implement

23

one way systems, detour by signs, and manned detours.
In case of deficiency and or incidents on the roadway,
usually no restrictions are provided, which could create

a hazard to traffic.

THAEPIC ENGINEERING PROBLEMS

In the surveys used to identify typical problems
in the developing countries, most of those countries
laddressed nearly similar problems, which generally include

the following :

- limited financial resources;

- poor geometric design of the roadway;

- deficiency . of traffic control devices;
especially signs and signals;

- insufficient roadway lighting;

- inability to manage parking;

- inadequate traffic law enforcement;

- difficulties in safely accomodating slow moving
vehicles, and mixed traffic problems;

- inefficient traffic police forces; and

- the operation of unsafe vehicles.

Recognizing such problems, particularly the financial
constraint, it would be reasonable if a signal timing

optimization program which became the state of the art in

24

transportation engineering in the developed countries,
could be considered in setting policy in . the developing
countries: The benefits of such programs are obvious,

and have been proven in the developed countries. However,
care must be taken in implementing the models to include
such specific behavior as previously mentioned. The
differences cannot be neglected and good judgement is

always necessary.

(CJPDIJDZTHTUP’ LNIZZZ£R£?:' .flf(2£l£?13 C’lZ£R£?l71K£?flV

As previously described, the models selected in
this study were TRANSYT-7F and SOAP84, for the reasons
that they are easy to use and their use in the U.S.
has demonstrated their reliability. Another consideration
is that both models place the emphasis on various impact

evaluations for their objective functions.

III.l. TRANSYT-Tr

TRANSYT-7F stands for the lzngic .fletwork A§tudz .flool,
version 15, where ’F’ refers to the fact that this is
the FHWA’s version of TRANSYT-7, the TRRL’s model.
The newest version, TRANSYT-8, is now available under a

licensing agreement.

III.l.]. .MGDEL .DESCRIPTION'

The TRANSYT model is a macroscopic, deterministic
simulation and optimization program with independent time
scan. The original program was written in machine
language for use on the MARCONI MYRIAD Computer, and
later rewritten in Fortran IV for more universal use.
The model has been executed successfully on the IBM-360,
370, and 3033, AMDAHL-470, CDC—7700, digital VAX-ll/780,

BURROUGHS-7700, and HONEYWELL-6220. It requires 288k bytes

25

26

of cpu addressable memory in unoverlayed format or 172k
bytes if the program is overlayed. The physical charac-
teristics' of a system considered by TRANSYT-7F is co-
ordinated signalization on arterials and networks of up

to 50 intersections with about 250 links.

III.l.2. INPUT .REOUIHED

The TRANSYT program requires as input, the des-
cription of : traffic volumes and flow patterns, signal
timing parameters [cycle lengths, phasing, minimum pedes-
trian timing if any, and the offsets], network geometry

[link sections and lengths, intersections, the saturation

flows, and average free speeds], and control data which
indicates what the user desires to take into account,
e.g. ; simulate or optimize, read English or metric
unit.

III.l.3. THE OPERATION

TRANSYT’s optimization procedure uses a ’hillclimbing’
process that begins with the calculation of the per-
formance index [PI] of the network for an individual
set of signal timings. The next stage is to alter the
offset of one of the signals by the number of time
units in the specified step size, and recalculate the

network’s PI. If the index is reduced, then the

27

offset is altered successively in the same direction

until a minimum value of the PI is obtained. If the
first alteration increased the PI, the search is made
in the opposite direction. Each signal is adjusted in

a similar manner in a specified order until the minimum
value of P1 is reached. The process of optimizing the

offset of each signal in turn is repeated to obtain the

final signal settings. TRANSYT-7F also optimizes splits
by altering the start of each phase and recalculating
the PI as before. The current version has the capa-

bility to determine the optimal cycle length 'for a
given range specified by the user. A number of exe-
cutions will be done for every step size 'increment and
the cycle with the lowest PI will then be selected.
Therefore, optimization no longer requires multiple runs

by varying input for cycle lengths as the earlier ver-

sions. Other features of the current version are the
capability to provide a time-space diagram, the esti-
mation of fuel consumption, and reduced control inputs
by internally generating certain parameters.

III. I . 4 . COHPUTA TI ONAL ALGORITHMS

The major algorithms in TRANSYT-7F are the calcu-
lation of traffic characteristics and minimizing the
objective function which is called the performance index

[PI]. The index is a linear combination of delay and

28

stops, and is expressed as

n
P1 = SUM [ W(D)i.di + k W(S)i.51 ],
i
where
W = the weighting factors for delay (D), and
stops (8) respectively, for every link i,
di = delay on the 1“1 link of the network,

in [veh-hr/hr],

Si = average number of stops per-second on
link i,
k = a user input coefficient to express the

importance of stops relative to delay.

TRANSYT simulates traffic flow macroscopically, by
considering vehicles as platoons rather than individually.
There are three traffic flow patterns ; the ’IN’, ’GO’,

and ’OUT’ patterns considered.

The ’IN’ pattern is the arrival pattern and is expressed

mathematically as

n
INit = SUM F15 [ P15 * OUTjt]

J

where

The

29

INit = the ’IN’ pattern on link i for step
t [the cycle is divided into time
increments called steps],
Flj = a smoothing factor for flow from link j
to link i,
Pij = the proportion of OUTJt that feeds link i,
OUTjt= the out pattern of link j for step t, and
n = the number of links j that feed link i.
smoothing function [Flj] represents the dispersion

of vehicles, which is expressed as

where

that

F13 = 1/[1+(Sp*Ce*t)]
Sp = the smoothing parameter [usually assumed
to be .35, but it might be varied],
Ce = a coefficient which ’shifts’ the effective
travel time [set to .8],
t = link travel time.

The ’GO’ pattern is the flow rate at each step

would leave the stopline if there were enough

traffic to saturate the green.

The ’OUT’ pattern is the periodic traffic flow

rate leaving a link,
pattern as long as
queue dissipates, it
for the duration of
the ’OUT’ pattern, the
stopline during time
mined by
It = max
where
m: = the number
time interv
milarly for
q: = number of
t, given b
St = number of
interval t,
Thus, the ’OUT’ patte
interval t is
OUTit =
TRANSYT estimates
element, du; a random

oversaturation, ds.

30

which would be equal to the ’GO’

there is a queue, and after the
would be equal to the ’IN’ pattern
the effective green. To determine

number of vehicles held at the
interval t, must first be deter-
{ [mt-1 + gt. - St ]; 0}
of vehicles in the queue in
a1 t, on a given link [si—

mt-il,
vehicles arriving in interval
Y ’IN’ pattern,
vehicles allowed to leave in

given by the ’OUT’ pattern.
rn given for link i- during time
mi.t-1 ‘+ Qit - lit

a delay as composed of a uniform
element, dr, and the delay due to
The uniform delay is determined by

everaging

where

du

It

TRANSYT

31

the queue length over the cycle, or

N
du = [C/(3600/N2)]* SUM mt

t

uniform delay in [veh-hr/hr],
cycle length in seconds,
queue length during step t,

number of steps in the cycle.

computes the combined effect of random delay and

saturation

where
drs
Bn

Do

The total

delay [drs] using an algorithm as follows

drs = [(Bn/Bd)2 + (Xz/Bd)l°'5 "' [BU/Dd]

random, and saturation delay,
2 t [l-x] + [x t z],

4 t z - 23,

[2x/v] * [SO/T].

the degree of saturation,
volume of the link,

simulation time, normally 60 minutes.

delay, then is computed as D = [du + drs].

32

 

SECONDS OF.DELAY : l. 2 3 4 5 6 7

PERCENT OF STOPS : 20 50 65 76 83 88 93 9

8 9

5 97

10 >10

99 100

 

Table [11.]. Reduction of stops as a inaction of delay.

The number

number

such

 

Delay - seconds per vehicle

 

 

/| /
ITransyt model

  

 

Degree of saturation ,

(Khnifbrm delay

 

 

 

Figure III.l.

of

of vehicles stopped is simply equal

vehicles delayed. However, if

vehicles is small, only partial stops

the

are

TRANSYT-7F estimate of delay

to the
delay to

counted.

33

The recommended adjustment of these stops, based on an
empirical study suggested by TRRL are shown in Table
III.l.

III.l.5. LIMITATIONS AND OTHER EEATURES

TRANSYT-7F is sufficiently realistic, and extremely

useful in designing the optimal signalization of many
network configurations. However, care should be taken in
order to use this model. TRANSYT-7F assumes all major
'intersections in the network are signalized, even though
mid-block bottlenecks or other sign controlled inter-

sections can be modelled. TRANSYT does not adequately

model unprotected left turnning [movements. The fact that
vehicles must wait for an acceptable gap in traffic in
opposing link must be considered since this could reduce
the rates of saturation flow, and cause increasing -
delays and' stops in the traffic streams. Tanner’s curve

and the approach introduced in the user’s manual [29]

do not adequately represent the real world. TRANSYT—7F
calculates average speed in the network by excluding
links having zero distance [e.g. external links] and

links that have been assigned zero delay and stop -
weights [e.g. non-vehicular links]. This could of course
significantly influence the results of optimization,
since average speed is an important factor in estimating
total travel time which is an independent variable' in

the estimation of fuel consumption. The entering traffic

34

for any network, the dispersion, volumes, and the pro-
portion of turns are considered to be uniform and
constant,‘ which are not realistic over the entire period
of analysis.

Despite those several limitations, TRANSYT-7F is an
extremely powerful tool for the practicing traffic engi-
neer. It can be used to design larger networks by
subdividing those into sections handled by the present
program. It also uses a fairly realistic flow model

without requiring outrageous run times.

III.2. SOAPRU

SOAP84, released by the Federal Highway Administra-

tion in June 1985, is one of several versions of the
.gignal .Qperation Apalysis .flackage. It developes signal
control plans for any three or four legged isolated
intersection. This program can evaluate a wide range

of control alternatives including pretimed or multiphase
actual control. SOAP determines the optimal cycle length
and phasing, and provides several measures of effective-
ness including delay, stops, fuel consumption, and volume
over capacity ratio. Left turn configurations might also
be programmed with seperate capacity calculation made for
protected phases, unprotected phases and the clearance

intervals.

35

III.2.l. NUDEI DESCRIPTION

The SOAP model, designed and written by the Univ.
of Florida Transportation Research Center, is a deter-
ministic, macroscopic, optimization program. It was written
in Fortran IV on an IBM 370/165 computer system.

The program requires 202 k bytes of computer memory.
During its development phase, the program had‘ been run
using IBM Fortran G, H-extended and WATF IV computers.

The current version is ready to run on most IBM systems

with some changes required for other systems. A version
is also available for the BORROUGH computer. For the
microcomputer version, the computational methodology is

similar, but not identical to the methodology used in the

original IBM version. SOAP84 reconciles only one set of
design volumes, saturation flows, phase sequences, etc.
This version deals with a maximum of 48 contiguous
time periods, each with its own characteristics. Phasing
optimization is accomplished by a multiple run, trial
and error procedure. The complete phase sequence must

be specified for SOAP84.

III.2.2. INPUT REGUIRED

'The input data required include the traffic volumes,

which are adjusted to reflect trucks and buses if any,

36

saturation flows per hour of green time given to each
movement, the headway for each movement; the existing
signal timing which includes minimum green time, cycle
length, phasing, green time by movement, and all red

time; the loss time due to starting and stopping of

every movement; the growth factor to project future
conditions at the intersection; left turns per cycle on
clearance; peak-hour factor; speed; type of controller,

pretimed or actuated control.

III. 2. 3. THE OPERATION

SOAP has the capability for design, analysis and
evaluation. All of which can be accomplished by providing
the input data previously described. To design signal
timing, it is necessary to configure the intersection
and input the appropriate data. SOAP then produces all
legitimate phasing patterns. It internally analyzes each
pattern and selects the one which can be executed using
the minimum amount of green time. Cycle length
is the most difficult design element to be determined,
particularly when several control periods are being con-
sidered. However, SOAP determines this quickly based on
the traffic volumes, capacity and other parameters. A
trial and error optimization procedure is done to find
the cycle length which produces the minimum total delay,

subject to constraints which govern the tolerable length

37

of the queue. To analyze the effects of various control
strategies, a number of measures of effectiveness [MOE],
are computed, including delay, stops, excess fuel con-
sumption, degree of saturation, and left turn conflicts.
Evaluation is done by comparing several alternative

schemes. Comparisons can be produced automatically by SOAP

or manually by the user.

III.2.4. COMPUTATIONAL ALGORITHMS

The algorithms used by SOAP for the calculation of

the values of the MOE’s identified above are

DELAY

To estimate delay, SOAP utilizes Webster’s delay

model for unsaturated flow under fixed time operations.
The Webster’s model has three components, which are ex-
pressed as the delay due to uniform arrivals, D1;
random arrival, D2; and an adjustment factor, Da.

The delay due to uniform vehicle arrivals, is

D1 = C[ l - L ]2/2/[ 1 - L t X ]

where

cycle length [sec.],

C
II

L = the proportion of green time given to

38

the movement [effective green time/cycle
length],

X 5 the degree of saturation of the movement
or : approach flow [veh./sec.]/saturation-

flow [veh./sec.]

The component due to random arrivals, is

D

N

=[le/[2*q}/[1-X]

where
q = approach flow [veh./sec.], and the other
notations are the same as previously

described.

Then the adjustment factor is

n. = [ - .65][C/q2]1’3 . XI2*5LJ

which was derived empirically to provide a better
mathematical fit to the field data. Webster’s delay
increases infinitely as the degree of saturation X,
approach 100 X, and reenters the finite realm’ from the
negative side at values above 100 8. This is due to
the [ l-X ] factor in the denominator of the second
term. The upper limit on the useful range of ’X is

generally in the neighborhood of 97.50 8. For the

39

 

 

 

 

 

 

region where the saturation is between 97.50 x to 100 X,
delay is assumed to be constant at the value for X =
97.50 X ; I or 2.0 min./veh., whichever value is less.

0)

3+ I

.~ '

'5 Useful range I

r l

K I

” I

a. l /

{g0 1&0 2&0

g .Degree of saturatipn

g l

W I

l I

a I

Q l

N l

g-

Q

Figure III.2. Rebater’s model delay
Great care must be taken in applying Webster’s equation
under conditions of near or oversaturation. Webster’s
delay model is plotted in Figure 111.2. For saturation
in excess of capacity, the following formula is used
Qr = T[q-L * S]
where
Q: = the number of vehicles not accomodated

40

during the green,

T = time period [sec.],

8 '= saturation flow [veh./sec.], while the
queue length at the end of the phase,
00, is calculated as the sum of 0b,
the queue length at the beginning of

the period, and Or.

Therefore with these values,“ the total delay is

D = T/2/[ 0b + 0r ].

In the case of actuated control, the problem is

quite complex, and no reliable delay model exists. The
approximation used in SOAP simulates a ’well timed’
actuated controller. The actuated control strategy is

assumed to

- distribute green time available in proportion
to the demand on the critical approach;

- minimize ’wasted’ time by terminating each
green interval soon after the queue has

been served.
1!? 67015 LEWUIE

Cycle length is calculated by using Webster’s -

41

method as well. For fixe timed operation, the optimal

cycle length is

Co = [(1-5*1)+5]/(1 - y)

where‘:
1 = total lost time due to starting and
stopping critical movements, and
y = the overall degree of saturation [i.e.
the proportion of green time required

for the traffic movement].

For actuated control, the cycle calculated is the ave-

rage cycle length, which is determined as

Ca = [ l.l*1 ]/[ 1- y ]

In the low to moderate demand range, this value will
always be smaller than Co. As the intersection appro-
aches saturation, actuated control approaches fixed time
control.

EICRSS FUEL CONSUMPTION

Fuel consumption is determined from the total of

the percentages of stops and delay i.e

42

E=Es+Ed
The excess fuel consumption due to stops is calculated
as
Es=fs*q*Ps
where
Es = gallons of fuel consumed due to stops,
f. = fuel consumption rate [gal/stop],
,q = traffic volume [veh/hr],
Ps = percent of stops, which is equal to
the number of vehicles joining the queue
while it is still discharging, all
divided by the number of arrivals per-
cycle, or
95 = [r*S]/C/[S ‘ V].
where
r = red time [sec],
S = saturation flow during green [veh/sec],
Then, the excess fuel consumption associated with delay
is
Ea = fi* qt d/3600

43

where
fl = fuel consumption rate per veh-hr of
idling,
d = average vehicle delay [sec/veh].

Llff THRN' CONFLICZS

A conflict can occur when left turns are permissive,

or not exclusively protected. The measure of effective-
ness is described as the number of left turns which
cannot be accomodated safely. The turning vehicles
may cross traffic, if sufficient gaps in the oncoming
traffic exist. Tanner’s model is used to calculate the
effective left turning saturation flow. This model re-

lates the opposing flow to left turn traffic. Given the
opposing flow, the left turn saturation flow is taken from
a curve and compared to the left turn demand. Excess

demand is the number of left turn conflicts.

III.2.5. LLHTZATIONS AND OIHRR ERATURES

As described before, SOAP has the capability of
design and analysis for any traffic control strategy,
either pretimed or actuated operations. However, several
limitations warrant notice. The optimization and analysis

are obviously based on mathematical models which often

44

cannot take human behavior into consideration. The SOAP
program does not exactly simulate the traffic in real
world events. For instance, the combining of right turns
with thru traffic presents a problem with the accurate
estimation of the capacity. Some other problems include

the incapability of analyzing closed loops, lack of wide-
spread testing, and lack of validation of the platoon

dispersion algorithm.

(ZLZELI’Jfilflfl? 17(9l2£?: JWEZALAflSYJ71"-FKIP Ia; £9¢2£ll3£?47
C7¢9JV29LIESUTU§DRflCYJr .JTERSVZP I611? ifilil? .fl!Z2£?"£?

TRANSYT-7F and SOAP84 are well accepted as produc-
ing realistic results with nearly similar computational
bases. Both are deterministic, macroscopic, time scan,
simulation and optimization models based on simple sets
of equations. They offer practical methods of signal
timing which are easy to use. TRANSYT-7F is generally
used for the traffic signals along an arterial or net-
work of up to 50 nodes with approximately 250 di-
rectional links, while SOAP84 provides a method of de—
veloping signal control plans at isolated intersections.
This would of course raise an intriguing question: can

TRANSYT-7F and SOAP84 produce consistent results under

the same traffic condition?. A positive answer could
reflect favorably on both models. Therefore, it is the
objective of this study to reveal the answer to this
question.

17L]. DESCRIPTION' or IE? STUDY' SIZE

In .the downtown area of Lansing, the capitol of
the state of MICHIGAN, a section of Michigan Avenue was
selected as the case study. Michigan Avenue carries two
way traffic, two lanes in each direction, 12 ft width

each, with a left turning lane between directions.

45

46

Parking is permitted on both sides of the road.

I 5&1. | - I
l. ‘fi [.9qu

Eulern
.HIglI School

Hun!!!
Put

L—

 

Fjgure IV.1. Section of arterial under study

The section under study consists of seven coordinat-
ed signalized intersections with 60 second cycle length,

all are pretimed and operated in two phases.
17.2. STUDY' APPROACH
The TRANSYT-7F program was first run to determine

the optimal cycle length, splits, and systemwide per—

formance with optimal settings corresponding to the

47

F

“a
'0

 

f"

 

.ka

‘0
01

 

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48

traffic flows at the observation period of 16.00 - 17.00
hours. The optimal setting times resulting from the
TRANSYT-7F run then were specified‘ as inputs for the
SOAP84 evaluation. The outputs generated by TRANSYT-7F
and SOAP84 program are provided in the Appendix-l, and

Appendix-2 respectively.

Total delays, stops and fuel consumptions predicted
by both models were selected as performance measures
for testing of their consistency. Scatter plots and

linear regression equations were established to determine
the relationship patterns of performance measures esti-

mated by both models.

IV.3. RRSUZTS ANT ANZLYSIS 0F .RKRFORHMNCF .MTZSURFS

Delay and stops are well recognized as very use-

ful measures of effectiveness in a traffic control sys-

tem.
BIIAY

SOAP utilizes Webster’s model to estimate the ave-
rage delay per-vehicle. SOAP defines delay as the

difference in average travel time through the intersection
and the travel time for a vehicle which is not stopped

or slowed down by a signal. Webster’s delay model was

49

modified by Mr. Robertson for use in the TRANSYT program

to give more reasonable results, particularly for traffic
volumes beyond the saturation point. TRANSYT and SOAP
consider delay mostly as a waiting time in the queue
caused by the red phase. Total delay is then defined

by both models as the product of the average delays

and the total intersection volumes.
SIDES

The proportion of vehicles stopped by the signal
is also important. Stops are very significant factors

in the estimation of both fuel consumption and potential

accidents at a traffic signal. SOAP describes the pro-
portion of vehicles stopped at a signal as equal to
the number of vehicles in the queue at the beginning
of the green time plus the number of vehicles which
join the queue while the queue is still discharging,
divided by the average number of arrivals per cycle.

TRANSYT assumes, that vehicles which are delayed are also
stopped, though this is not always the case in, the
actual traffic flow. The problem of modelling this
arises when vehicles do not actually stop. . TRRL con-
siders that the short periods of delay can be expressed
as a fraction of stops for vehicles affected. [see
table III.l.] The total delay, stops, and fuel' con-

sumption performances predicted by TRANSYT-7F and SOAP84

FUEL CONSUMP. - -[gaI/l)r]

STOPS— ~ [percen t]

URL! Y——[ veh “hr/hr]

50

 

 

 

 

 

 

   
 

 

 

 

  
   

 

50
40 1
30 .
20 1
SOAP84
10 .
e—us : TRANSYT-7F
0 v v v v v fir
16' 57 87 89 92 91 90
NODE NUMBER
20
16 1
1.?
8 4
SOAP84
4 ‘
—. : TRANSYT-7F
0 . . . T . r f
16' 6'7 87 89 92 91 90
NODE NUMBER
100
80 ‘
6'0 .
40 <
0—0 SOAP84
20
0 V v r v v
16 67 87 89 92 91 90

N005 NUMBER

Figure IV.3. Comparison of performance measures

 

 

 

51

programs are shown in Figure IV.3.

[7.4. CONSISIENCY IE5! or IE3 .RERFORMMNUF’ MTZSURES

As stated earlier, TRANSYT-7F and SOAP84 were de-

veloped for different purposes. TRANSYT-7F is primarily

used for analyzing traffic signals along an arterial or

a network, while SOAP84 is a model for analyzing iso-
lated intersections. Therefore, it would be 'reasonable
if in some cases their estimation of the performance
measures would be different. However, their reliability
will be enhanced if they generate consistent results

under similar traffic conditions.
In this case, the regression equations were first

established to determine the relationship patterns for

the performance measures generated by both models un-
der similar traffic conditions. The linear regression
equations presented in Table IV.1. indicate that the

results for total delay and stops generated by both
models were strongly correlated.

Within the conditions investigated in this study,
TRANSYT-7F and SOAP84 produced compatible results in terms
of the estimation of delay and staps. However, if we
consider the fuel consumption performances predicted in
this study, they seem significantly different. The bases
of computing fuel consumption are obviously different

between these models.

52

 

N. 0. E. .' - REGRESSION EQUATION CORREL. S. S. E.

COEF., [R].

 

Tot. del. STDEL = .69640 + .95 TTDEL .97 1.52
Stops SSTOP = 30.66364 + .59 TSTOP .96 3.64
Fuel cons. SFCON = 3.69637 + .60 TFCON .62 7.70

 

Table IV.l. Relationship between TRANSYT-7F and SOAP84 results

NOTE

STDEI = SOAP84 total delay.

TIDEL = TRANSYT-7F total delay.

SSTOP = SOAP84 total uniform stops.

TSTOP = TRANSYT-7F total uniform stops.
SFCON = SOAP84 total fuel consumption.
TFCON'= TRANSYT-7F total fuel consumption.

TRANSYT-7F generates the total gallons of fuel
consumed by all vehicles based on exprimental studies.

A stepwise multiple regression analysis was used which

53

resulted in the following equation : [41(291

F = kl * TT + k2 * TD + k3 t TS

where ;
F = gallons of fuel consumption per-hour.
TT = total travel per-hour.
TD = total delay.
T8 = total stops.
k1, k2, k3, are coefficients of regression.

SOAP84 on the other hand, estimates only the
total fuel consumption due to idling delays and accele-
rations from stopped positions. Therefore, it would be

reasonable if the estimation from SOAP84 is lower than

that estimated by TRANSYT-7F. However, this will not
always be the case. At node # 16 for example, [see
Figure IV.3.], because of a high level of saturation,

SOAP84 produces a high value of the estimation of' fuel
consumption. TRANSYT-7F also poses a problem in the es-
timation of fuel consumption. The calculation of the
average speed which excludes the contribution of ex-
ternal links will give different results for the deter-
mination of total travel for intersections with various
ratios of external to internal link volumes but the
same total volume. The effect of the ratio of external

to internal link volumes on fuel consumption estimation

54

are shown in Table IV.2.

 

LINK VOLUHT FUEL CONS. [GZL/HF]

NW :.EIIERNZL : INZERNZI :.RATIO : TWINSYT-7F : SOZPBV : R1710 :

 

99 43 1,921 .02 26.71 10.16 .39
- 90 206 1,999 .10 19.10 14.57 .76
92 274 1,736 .16 19.64 14.11 .72
91 411 1,962 .21 30.12 19.45 .61
67 1,221 1,564 .79 36.42 27.50 .76
97 1,410 1,545 .91 . 45.06 29.66 .66
16 2,394 693 3.49 26.45 33.23 1.26

 

Table IV.2. The effect of the ratio of external

to internal link volumes.

(IIZZLI’Jnlflfi? .FZI'PGEV .: 1?}?2LAIJCAEIUNQ9' ifllll?
.Iwuuuus¢7urms (917' AFLII?JVD!JE (21’1PJEAIJCZZAIJPJFCLAI

The' optimization of traffic signal settings for
a particular network are determined by a given set
of roadway geometrics [supply variables], and the
traffic patterns [demand conditions]. If either the
supply or demand changes significantly, the existing
signal timings may not be optimal, and retiming signals
might be desired. The most important issues addressed

in the maintenance of signal timing are

- level of congestion under existing traffic
conditions; and
- the magnitude of traffic growth in the

future.

In a heavily trafficked network, small increases in
traffic volume might offset the benefits of signal
optimization. 0n the other hand, a network consisting
of light traffic might be able to accomodate the in—
creasing traffic volume without significant effect. This

chapter addresses the magnitude of the traffic impacts

likely to be caused by the increasing traffic, and to
evaluate alternative policies for managing it whenever
needed.

55

56

7.1. DESCRIPTION' or rat STUDY’ $118

A network in a suburban area of the city of
Cirebon, Indonesia, was selected as the case study for
the following reasons

— the availability of traffic signal timing

data;

- the possibility of facing serious traffic
signal problems caused by the increasing
traffic volume in the future under the
existing signal timings; and

- learning the beneficial impacts of signal

timing optimization, by applying TRANSYT-7F
directly to an Indonesian Network.

This network is located near Cirebon harbor which
gives a specific meaning to its traffic. The study
area includes four signalized intersections, all of
which are pretimed and operated in two phases. The
street system operates two way traffic, which consists
of one or two 10 ft width lanes in each direction. No
parking is permitted on the street. The business
activities in the downtown area, and the potential of
new developments in the city is expected to increase
the traffic volumes, which will affect the traffic pat-
tern throughout the network, and could create a serious

57

level of congestion.

  
   

”abidjn

Dr.

2. 000 ft
+——+

street width
not to scale

Figure V.l. Network system of the case study

For this particular network, two issues will
addressed
- how sensitive is the existing signal timing

to the increasing traffic volumes throughout
the network; and

- what is the maximum level of traffic that
can be accepted with signal timing opti-

mization, before major design changes, and

 
  
 

58

other TSM measures would be considered.

A simple' way to examine the network sensitivity to in-
creasing traffic is to assume incremental networkwide
traffic volume, then measure the performances before and

after optimization, by using the TRANSYT model.

7.2. STUDY APPROACH

TRANSYT-7F runs in this study were performed for two

kinds of submodels

- a submodel that simulates, at macro level

the performance with existing signal -
timings; and
- an optimization submodel that seeks the -

’best’ signal settings.

The ’best’ signal setting, as previously described,
was chosen based on a performance index - a weighted
sum of stops and delays. TRANSYT input data characterize
network geometry [road sections, intersections, and the
saturation flows], signal timing parameters [cycle lengths,
phasings, and minimum pedestrian timings if any], and the
traffic volumes.

For the purpose ' of this study, traffic volumes

were varied sequentialy as a proportion of the sa-

59

turation flow, 5, to the values of : .105, .205, .305,
and .405, for both simulation and optimization runs.
The turning traffic was assumed to be 20 percent of
the total volumes, for either left or right turn
flows. The direct outputs of TRANSYT include delay

and stops along with. the optimized signal settings. The

values of the saturation flows were determined by

considering the street geometries, percentage of trucks
and the turning volumes. [221 To measure the impacts
.of these changes, TRANSYT system performance was con-

verted into highway user costs and direct energy con-
sumption. While the assumption that volumes increase
uniformly throughout the network _might not be realistic
for design purposes, it nevertherless provides the first
cut estimation of. the impacts at a sketch planning
level. An alternative way to determine. the frequency of
retiming could be by monitoring traffic growth through
systematic traffic counts, observe the operation of the
intersections, identify the problems, and then apply the
TRANSYT model to evaluate the need for installation of

new timings.
V. 3. RESULTS AND ANAL 751 S
To code the data for TRANSYT—7F runs, an illus-

tration of the link-node diagram is presented in ’ Fig.

v.2. TRANSYT-7F simulation runs were first performed

60

for the existing signal timings. Traffic flows were
varied in the order of : .105, .205, .305, and .405

[4031‘ [3031‘

,I I. {407/ \ [307/

{405/ ‘1 I’ [305]
[[4011V[/301]
[203]
151?Z?1?JV19 .r

(::> 2 node number ::'[207/
[205]‘

[...]; link number

I
[103/ «lg/L

:\[107

it [101/

Figure V.2. Link-node diagram for the case study

61

Figure V.3. Network-wide traffic performance

 

 

 

 

*-- : sinulation run
150. A-—A : optinization run
T”
E
\\
g
$
a
m
is
\.
. 100*
x
a
N
Q o
h
E
c
5*
a
3 O
E 50‘
'H
e
s
A
0 10 20 .30 40 50

9/5

[a] total unifbrn delay vs q/5

[veh-br/br]

To ta] random delay,

62

 

1000‘:

500 1

 

 

 

.__.. : sinulatjon run
A-—A : optinization r 'n
o .10 .20 .30 .40 .50
q/5
[b] Total randal delay vs q/S

fveb-br/br]

Total delay,

63

 

1000“

500*

.___. : sinulation run

~___‘ : optinization run

 

 

 

[c] Total delay

VS

9/ S

.50

[sec/veh]

_Avorage delay,

64

 

400*

3001

200 +

100+

 

.___. : silulation run

a___‘ : optjnization run

 

 

[d] Average delay

VS

9/5

.50

10/Veb/hr]

Total unifor. stops,

65

 

 

 

 

~———o : silulatjoa run
m___‘ : optilizatjon run
1500+
A
1000«
500<
0 10 20 .30 40 .50
9/5
[e] Total unifbrn stops vs q/S

[gal/hr]

Total fuel consumption,

66

 

1000‘

500‘

 

~———- : sinulation run

a___¢ : optimization run

 

 

[f]

Total fuel consunption

VS

.50

9/5

[Ii/hr]

Average speed,

67

 

-———~ : sinulation run
5.... : optinization run

30« \

\

 

 

 

A
20f
101
a )0 20 30 4o

9/5

[g] Average speed vs q/S

68

 

 

 

 

1000‘: .—. : sinulation run
5—... .‘ optilization run

ac

m

.b

q

‘H

m

u

a

2

3 5004

'h

L.

1)

Q. o

0 10 20 30 40 .50

[11] Perfor-ance index vs

9/5

69

where S is the street saturation flow. The optimization
runs then were conducted to seek the optimal signal
settings for the same variation of traffic flows.
The conplete outputs generated by both subnodels are
presented in APPENDIX-4. Figure v.3. a, b, c, d, e,
f, g, and h, illustrate the systemwide performances
predicted by both submodels. The optimization run
for volume variations of .105 and .205, does not
significantly affect the traffic performance. However,
as volumes increase to .305, the network experiences
congestion problems. Some links begin to be over-
saturated. For the traffic volumes of .405, the number
of oversaturated links are dramatically increased and
the network becomes sensitive to any additional traffic
volumes. For example, an additional traffic volume
from .105 to .205, would result in an increased average
delay of [(16.83 - 13.42)/(13.42) t 100 x] = 25.41 x, but
as the volume increases to .305, the average delay in-
creases to [(103.28 - 16.83)/(16.83) * 100 X] = 513.67 X,
a significant increase in terms of average delay !.

The intersection performance for the existing signal

timing at traffic volumes greater than or equal to
.405 deteriorates rapidly, as the number of critical
intersections increases rapidly. For traffic volumes of

.405 all of the intersections become oversaturated.

Signal timing optinization could considerably improve the

70

intersection performance as illustrated in Figure v.3.
However, the benefit of optimization diminishes when the
overall traffic volume increases to more than .405.

Though improvements exist compared to the existing con-

dition performance under similar traffic volumes, the

level of service at the intersection drastically de-
creases. Total stops also increase, and the optimal
cycle length is relatively long. The degree of satura-
tion remains above 85 X, which means the intersections
would still be critical !. [31 Thus, unless such traffic
growth could be avoided throughout the system, or other

changes in travel behavior occured, another TSM strategy

would be needed.

7.4. ENZRUY' AND COST .EKALUATTQN

As was illustrated in Figure V.3., a signal ti-
ming optimization would improve the network performance
for increasing traffic volumes under certain values of
traffic flow. If we consider the case where traffic
volumes increase to .305, the delay would be reduced
by [(358.03 - 54.75)/(358.03) * 100 X] = 84.71 X, Total

stops would be increased by [(9104.40 - 9439.80)/(9104.40)
* 100 X] = 3.68 X, while total travel time could be re-
duced by [(498.51 - 195.24)/(498.51) * 100 X] = 60.84 X.

Fuel consumption would be conserved by [(512.22 - 292.01)

/(512.22) t 100 X] = 42.99 X, and the average speed would

71

be increased by [(11.47 - 29.3l)/(11.47) * 100 X] = 155.54 X.
Furthermore if we assume that this condition occurs on-
ly in ‘the afternoon peak period, a simple estimation
of benefits could be illustrated in Table v.1. [11(31
By assuming that this condition would occur for
two hours per day, and 300 work-days per year, then

the total 'annual benefit would be U.S. $ 535,380.

 

 

 

CONSERVATION : [5] UWTT'COST : [3] COST :
- delay saved [hrs] : 303.28 2.00 606.56
- stops saved [vpb] : ~335.40 .0016 ~ .54
- fuel saved [gins] : 220.21 1.30 286.27
- [$1 TDTML 005T : 892.30/pk-br

 

Table v.1. Benefit estimated for volumes of .305

The contribution from fuel consumption alone would
account for U.S. $ 171,800. Furthermore, if we assume
that the saving during the morning peak period are 75
percent of the afternoon peak, and the savings in the

midday are 50 percent of those in the afternoon peak,

72

then the total annual benefit from fuel saving only

could be U.S. $ 386,500.; an attactive alternative to
be considered!. Similarly, for the traffic flows of
.40S, the annual benefit from savings of fuel consump-

tion alone would be U.S. $ 644,500.

CZLZZLI’JHlEfl? AVJFJYE' (7(21VZ7151723JFCZAK57

VI. 1 . SUMMARY

Total delay, stops and fuel consumption forecasted
by TRANSYT-7F were compared with the results generated
by SOAP84 in this study. The results for delays and
stops were similar and consistent with what was expect-
ed. The linear regression equations presented in table
IV.1. indicate that the results were strongly correllat-
ed. In the case of fuel consumption, TRANSYT-7F
produced some-what higher values than those forecasted
by SOAP84. This can be explained by the difference in

basic computational procedure for fuel consumption in both

models. TRANSYT-7F is used mainly for analyzing the
signalization along an arterial street or a network.
Therefore it includes the traffic flow between the
nodes. SOAP84 only considers the fuel consumption at
isolated intersections. One exception to these results
is shown at node 16, where the total fuel consumption

predicted by SOAP84 is higher than that predicted by

TRANSYT-7F. This can be explained by the formulation
of delay for both models, since fuel consumption is
a linear function of delay. SOAP84 utilizes the
Webster’s model, which overestimates delay for high

values of the degree of saturation. TRANSYT-7F uses

a modified Webster’s equation, and does not increase as

73

74

rapidly as the level of saturation increases. After
we recognize the limitation of Webster’s model, the
results from node 16 are easily understood.

As the case study of the CIRBBON Network illus~
trated, TRANSYT-7F can be used for assessing the impacts

caused by increasing traffic flows. Such evaluations are

useful and can provide an indication of when traffic
signal retiming would be warranted. Signal optimization
is a low cost alternative for expediting traffic flow,
reducing highway user costs and energy consumption.

TRANSYT-7F offers the analyst the advantage of assessing
impacts networkwide, instead of intersection by in-
tersection. Several other positive features of the

TRANSYT-7F program include

- The traffic flow model traces flow patterns
from link to link and incorporates a pla-
toon model to allow one to study the
effects of 'vehicular dispersion. This is
particularly important where there is mixed
vehicle traffic.

- The versatility of the optimization process
in which both offsets and splits can be ma-
nipulated sequentially, and

- The consideration of both uniform and random
delay to traffic in a signal network, thus

considering both system coordination and the

75

capacity effects.

VI. 2. rm” M an opus”!

Based on the experiences gained in this study,
some particular problems will be addressed in using com-
puter models for traffic operation analysis in future

model enhancements and developments. Those are:

STMNTARIZATTON’ or IE? INPUT .0414

Both models use similar input data, however
each model uses different coding schemes
which must be mastered by the user. This

may confuse the unfamiliar users. Unnecessary
effort and confusion could be reduced subs-
tantially by the development of a common

input data coding scheme which can be shared

by several traffic signal models.

PTWSONFL IRAINING

More training is obviously required in the
preparation of inputs and the mechanics of
execution of various programs. Understanding

how to interpret the output is also re-

quired to ensure the potential benefits of

the

models.

.NZINIENANCI

It

the

resources

VI. 3. TRANSFERAIILITY 01' U. S.

The
development

lysis has

recent

been

is natural

capability

of computer

neficial alternatives

any other

strongly influence

conclusion.

third world

However,

developments, current

sidered.

great difference

resulting from some

may limit

the direct

In Indonesia,

the beginning of the

areas .

wasting of

greatly.

world market price

proven

76

to

of

permit.

progress

expect

any

achieved

models

to

be

for

the

models

be one of

considered.

country,

policy,

in

different

this
order

patterns

and

exists

where

by

improvement

as time

the U.S.

the most

For Indonesia,

money constraints

could be an

to

transferability

motorization

has

adopt

trends

in traffic

of results.

such

must

of

and

EXPERIENCE TD INDONESIA

in

traffic operation

cost

attractive

advanced

be

patterns,

environmental factors,

grown rapidly

especially in

the

OPEC country,

government

recent years,

1970’s,
Even-though Indonesia is an
energy will increase the
Particularly in these
oil has

dropped drastically, the.

subsidy

where

77

conservation of domestic consumption is important.

The operation of mixed-traffic in the roadways,
which is- uncommon in the U.S., needs specific conside-
ration as well. Vehicles operate in various speeds

which effects the capacity of the roadway, the smooth-
ness of flow, and the pattern of traffic flows.

Driver behavior, which is different from that in
the U.S., could result in different traffic charac-
teristic which need to be carefully studied. ‘ The fac-
tors effected might be ; the average speed, the value
of headway, the conversion factors into passenger car
units, etc.

Pedestrian behavior, government regulations, techno-
logy of public transportation, communication systems, and

some other factors could significantly effect the traffic

patterns which need to be carefully studied. By consi-
dering these kind of factors, and adjusting them wisely,
the models may still be useful, and the benefit of

using them can be achieved.

A PPEND I CE S

78

APPENDIX—.1

TRANSYT-7F OPTIMIZATION RUN FOR STUDY CASE-I,

IN MICHIGAN A VENUE, LANSING, MICHIGAN

79

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APPENDIX—2

SOAP84 SIMULATION RUN 0F TRANSYT- 7F OPTIMAL TININGS

FOR STUDY CASE-I, IN MICHIGAN AVENUE, LANSING, MICHIGAN

99

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108

 

 

 

 

 

 

 

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REGRESSION ANALYSIS - PROGRAM IN BASIC

111

1312

1 REM [SS/RECR-AN.BAS/CN99/APPENDIx-3]

2 REM BUI 03-86

3 REM ‘

4 REM VARIABLES

5 REM B(I) ESTIMATED COEFFICIENTS

6 REM B1 ESTIMATED CONSTANT

7 REM C(I,J) MULTIPLE CORRELATION COEFFICIENTS
8 REM E SUM SQUARE OF ERRORS

9 REM F FISHER TEST

10 REM M TOTAL NUMBER OF VARIABLES

11 REM N NUMBER OF PERIODS OF OBSERVATION
12 REM R(I) »RESIDUAL VALUES

13 REM R2 CORRELATION COEFFICIENT

14 REM S(I,J) VARIANCE-COVARIANCE MATRIX

15 REM V(I) VECTOR OF STANDARD ESTIMATED ERRORS
16 REM X(I,J) MATRIX OF INPUT VALUES

17 REM 2(1) ESTIMATED Y-VALUES

18 REM

19 REM

20 PRINT : PRINT : PRINT

30 PRINT "MULTIPLE LINEAR REGRESSION"

40 pRINT Itiiiit*fititttfittttttttittt”

50 PRINT : PRINT : PRINT

60 INPUT "NUMBER OF VARIABLES? "1H: PRINT

7o INPUT ”NUMBER OF OBSERVATIONS? ":N: PRINT
Bo DIN AS(H),X(N,N),X1(M),S(N,H),82(N,H),s3(fl,n)
90 DIM B(M),Y(N),R(N),V(N),C(N,N)

100 FOR I-I TO N: PRINT "NAME OF VARIABLE i":I:" ":
110 INPUT A$(I): NEXT I: PRINT

120 FOR I-1 TO M

130 PRINT "DATA GATHERED FOR VARIABLE ”:A$(I):":"
140 FOR J-1 To N

150 PRINT"- OBSERVATION 6'1J: TAB( 14):

160 INPUT X(I,J)

170 NEXT J

180 PRINT

190 NEXT I

200 REM MEAN, STANDARD DEVIATION.

210 FOR I-1 To n:T-0:FOR J-I TO N

220 T-T+X(I,J)

230 NEXT J

240 X1(I)=T/N

250 NEXT I

260 FOR I-I TO H:FOR K-l TO M

270 81-0

280 FOR J-l TO N

290 81-81 + (X(I,J) - X1(I)) * (X(K,J) - X1(K))
300 NEXT J

310 S(I,K)-81/(N-1)

320 S(K,I)-S(I,K)

330 NEXT X,I

340 Nl-H-l

350 FOR J-l T0 N1: FOR K-l TO M1:SZ(J,K)=S(J+1,K+1): NEXT K,J
360 FOR I-I TO H1: FOR J-l T0 N1

370 IF I< >J GOTO 400

380 83(I,J)-1

39o GOTO 410

400 S3(I,J)-O

410 NEXT J,I

420 60808 1330

1313

430 REM CALCULATE THE COEFFICIENTS 3(1)
440 FOR I-I TO M1
450 B(I)-o

460 FOR J-1 TO El

470 B(I)-B(I)+S(1,J+1)*82(J,I)

480 NEXT J,I

490 81-0

500 FOR I-1 TO X1:Bl-81+X1(I+1)*B(I):NEXT I

510 Bl-X1(1)-Bl

520 REX R2, ESTIMATIONS, SEE, F-TEST, CORRELATION
530 S3-0

540 FOR I-l TO N: Y(I)-o

550 FOR J-2 TO M: Y(I)-X(I)+B(J-1)*X(J,I): NEXT J
560 Y(I)-Y(I)+BI

570 R(I)-X(1,I)-Y(I)

580 S3-S3+R(I)*2

590 NEXT I

600 8(1,1)-(N-1)*S(1,1)

610 R2-(S(1,1)-S3)/S(1,1)

620 IF R2-1 GOTO 640

630 F-(RZ/H1)/((1-R2)/(N-H))

640 E-SQR(s3/(N-X))

650 FOR J-1 TO X1

660 V(J)-E*SQR(82(J,J)/(N-1))

670 NEXT J

680 S(1,1)-S(1,1)/(N-1)

690 C(1,1)-1

700 FOR J-z TO K

710 C(J,J)-1

720 Jl-J-l

730 FOR I-1 TO J1

740 C(I,J)-S(I,J)/SQR(S(I,I)*S(J,J))

750 C(J,I)-C(I,J)

760 NEXT I,J

770 FOR I-l TO M

780 S(I,I)-SQR (S(I,I))

790 NEXT I

800 REM OUTPUT

810 PRINT : PRINT : PRINT

820 PRINT "CORRELATION MATRIX"

330 p31”? "fitttfittiitttttiiii"

840 FOR I-1 To M: FOR J-1 TO M

850 IF I<J THEN 870

860 PRINT INT(100*C(I,J))/100: TAB(10*J)

870 NEXT J: PRINT

880 NEXT I

890 PRINT : PRINT : PRINT

900 PRINT "VARIABLE MEAN STD DEVIATION"
910 pRINT Ntitttttitititittitittttttt*ittfitttiittfl
920 FOR I-1 TO N

923 PRINT A$(I)x TAB( 14):X1(I): TAB( 27):S(I,I)
925 NEXT I

930 PRINT : PRINT

940 INPUT "CONTINUE? ”:CS

950 PRINT : PRINT

960 PRINT "REGRESSION EQUATION"

970 pRINT ”fittiittfifltttiiitiitiitfittititittititififl

990 PRINT "DEPENDENT VARIABLE: ”:A$(1)
1000 PRINT fltflifiitifitflttttttiifitttitifiitttit*ifitit”

1020 PRINT ”INDEPNDNT EST BETA ERRORS T-TEST"

lfll4

PRINT ”VARIABLE COEF :"

pRINT "fiiiittttitttitttttiii*tttttitaittttiifiN

PRINT

FOR I-1 TO M1

PRINT A$(I+1): TAB( 11): INT(100*B(I)+.5)/100: TAB( 18);
PRINT INT(10000*(B(I)*(X1(I+1)/X1(1))))/100:

PRINT TAB( 25): INT(100*V(I)+.5)/100:

PRINT TAB( 35): INT(100*(B(I)/V(I))+.5)/100

NEXT I

PRINT ”CONSTANT”: TAB( 11):B1

pRINT "tiiitttttitifltit*tiiiitfitttttitttiittit*ttttt”
DEF FN A(Z)-INT(100*Z+.5)/100
REM STATISTICS
PRINT "DETERHINATION COEFFICIENT
PRINT "CORRELATION COEFFICIENT
PRINT "F-TEST

PRINT ”DEGREES OF FREEDOM .
PRINT "SUM SQUARE OF ERRORS - ": FN A(E)
PRINT fltittiti*ttttiitiiittittiiitiotttitifittttfitittfl
REM RESIDUALS

PRINT : PRINT

INPUT ”CONTINUE? -;cs

PRINT : PRINT

PRINT ”TABLE OF RESIDUAL VALUES”

pRINT ”*ittfiititttitiiitittttitittiiititiitt”

PRINT " # OBSERVATION ESTIMATION RESIDUAL "

pRINT I*iitt*ttfiitfitttittttittifi*ttiiittitttfl

FOR I-1 TO N

PRINT " ”:I: TAB( a); INT(100*(X(1,I))+.5)/100:

PRINT TAB( 1a); INT(100*Y(I)+.5)/100:

PRINT TAB( 30); INT(100*R(I)+.S)/100

NEXT I

pRINT ”titttfitittattitttittiitfitttttttatiittfl

END

REM MATRIX INVERSION

FOR K-l TO M1: FOR I-1 TO M1

IF I>X THEN 1420

PP-Sz(X,X)

FOR J-1 TO M1

S2(X,J)-52(X,J)/PP

83(K,J)-83(X,J)/PP

NEXT J

IF I-X GOTO 1470

PP-SZ(I,K)

FOR J-l TO M1

82(I,J)-82(I,J)-52(K,J)*PP
83(I,J)-S3(I,J)-83(K,J)*PP

NEXT J

NEXT I

NEXT X

FOR I-I TO M1: FOR J-l To M1: 52(I,J)=S3(I,J): NEXT J,I
RETURN

": FN A(R2)
FN A(SQR(R2))

APPENDIX-4

TRANSYT- 7F SIMULATION RUNS FOR THE S TUB Y CASE-I I ,

IN CIRKBON, INDONESIA

115

116

Natl :

- Simulation runs were established for traffic

volune variation of .105; .205; .305; and .405.

- A set of output is presented for traffic -

volune of .305.

- Only the system-wide performances are presented

for traffic volunes of .105; .208; and .405.

117

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APPEND IX—5

TRANSYT- 71' OPTIMIZA TION RUNS F0]? THE S 1'00? CASE-I I ,

IN CIRFBON, INDONESIA

126

127

NDZE :

- Optimization runs were established for traffic

volume variation of .103; .205; .305; and .405.

- A set of output is presented for traffic -

volume of .305.

- Only the system-wide performances are presented

for traffic volumes of .105; .205; and .405.

128

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140

1?}?JFZ?JEI?JVZ?JTEV

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