AN EVALUATION OF DRIVER DECISIONS AND REACHONS
AT AN iNTERSECTiON CONTROLLED BY A STOP SiGN

Thesis for the Degree of M.S.C.E.
MICHIGAN STATE UNWERSITY

Frederick Allan Wagner, Jr.

1963

THESIS

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AN EVAIHATION 01" mm IECISIONS AND REACTION
AT AN MEMO]! CONTROLIED B! A STOP BEN

by'Frederick.Allan Ragnar, Jr.

The problem of determining the most effective modes of controlling
intersections of highways at grade is being studied with analytical and
edge of the characteristics of driver decisions and reactions.

The objectives of this research were:

1. 'To perfbrm.a microscopic examination of an intersection"“
controlled.by a stop sign.to determine and.verify the parameters of the
lag and gap acceptance distributions of the waiting vehicles.

2. To evaluate the influence of the following traffic factors
on the lag and.gap acceptance distributions: vehicle type; pressure of
traffic demand; direction of movement through the intersection; sequence
-of’gap fbrmation; and conditions on the opposite stop signed approach.

3. To determine the parameters of the distributions of starting
delay times of vehicles accepting lags and.gaps, and to evaluate the
influence of certain traffic factors on these distributions.

h. Tb investigate the delays ancountered.by'vehicles waiting

on the stop signed.approaches.

Frederick.Allan wagner, Jr.

The data were collected at an intersection of a four-lane, bi-
directional, intermediate speed, undivided, major state highway with a
two-lane, bi-directional, low speed city street. A.tota1.of #72 minutes
of sample data were gathered.during daylight hours on weekdays, in fair,
dry weather, during the months of August, October, and November, 1961.
The decisions and reactions of 1,203 side street vehicles were observed
and recorded on a multiple pen event recorder. .A.total of 5,179 separate
acceptance-rejection decisions were included in the sample.

The form and parameters of the lag and.gap acceptance distributions
were determined using a graphical curve fitting technique, and a special
application of standard statistical difference tests permitted evaluation
of the influence of traffic factors on the distributions.

The major findings of this research were:

1. The results strongly supported.earlier findings which indi-
cated that the relationship between the logarithmic transfbrm of lag or
gap size and the probability of acceptance follows a cumulative normal
distribution curve. lag acceptance differed significantly from.gap
acceptance. -

2. 0f the traffic factors studied, those which significantly
influenced the parameters of the lag and.gap acceptance distribution
were: pressure of traffic demand; direction of traffic movement during
periods of heavy traffic demand; and main street vehicle sequence during
periods or heavy demand. ‘

3. No evidence was found to indicate that either side street
vehicle type or conditions on the opposing side Street approach signifi-

cantly affected the gap acceptance distribution.

Frederick Allan Wagner, Jr.

h. The results of the studyof starting delay times in
accepting lags and gaps indicated that factors which had. important
influence on the driver decisions, namely pressure of traffic demand
and main street vehicle sequence, also had similar and significant
effects on starting delay time.

5. The components of delay to side street drivers were deter-
mined and are presented to enable those interested to validate the

results of their analytical and simlation model work.

Alt mummy or mrvss usersiom mm mm ‘
AT AN masons]: someones s! A STOP sins

By

Frederick Allan Wagner, Jr.

A .THEBIIB

Submitted to
Michigan State University
in partial fulfillment of the requirements
for the degree of

MASTER OF SCIENCE
Department of Civil Engineering
1963

ACIGWOWIEIBMENT

The writer wishes to acknowledge contributions which made the
completion of this work possible. Dr. Siegfried M. Breuning, the
writer's academic advisor, gave valuable counsel and encouragement
during all stages of the work. The role of Dr. Adolf D. May, Jr. as
teacher and adviser is also acknowledged. Appreciation is extended
to Mr. Asriel Taragin of the Bureau of Public Roads for his perceptive
review of the initial study proposal.

During the preparation of the manuscript, stimulating discussions
of the work were held with Dr. Daniel L. Gerlough, Mr. James B. Rudden,
Mr. Ioren D. Enochson, and Dr. Ralph T. Dames.

Special notes of thanks are due Mr. Richard Buchan and Mr. Claude

Meyers for their assistance in data collection, and Mr. Frank DeRose

of the Michigan State Highway Department for supplying engineering plans.

A debt of gratitude is owed to Mrs. Mildred Wedten for her
excellent typing and: attention to grammatical quality of this work.

Finally, warmest thanks go to my wife, Nancy, for her patience,
understanding ,and direct assistance during all phases of the work.

Without her help, this thesis would never have been completed.

ii

TABIEOPOOMEM'S

2.h.h Graphical Determination of Acceptance
Distributions A 27

2.1+.5 Precision of the Estimates and Tests of
mpotheses 30

111

. Page
Acmomsnom'r ' ii
mm or come . iii
LIST or TASIIS vi
LIST or FIGURES - vii
1. mowcuon 1
1.1 BACKGROUND . .. 1
1.1.1 The Selection of the Mode of Control at an i
. Intersection at Grade 1
1.1.2 Analytical Models of Stop Signed Intersections h
1.1.3 Simulation Models of Stop Signed Intersections 5
1.1.h Current Knowledge of Driver Decisions and
Reactions at Stop Signed Intersections 7
1.2 RESEARCH OSIECIIVES . 11
1.3 RESEARCH LIMITATIONS _ , 12
2. STUDY PROCEDURES , _ 13
2.1 SEIECTION ARI) DESCRIPTION or THE STUD! SITE )3
2.2 DATA COIIECIION INSTRUMENTATION Ann mom . 16
2. 3 DATA REwcrIon mocszE , , 21
2.1; STATISTICAL ANAIXSEB 23
2.h.1 Stratification of the Data . . 23 .....
2.h.2 Grouping Into Class Intervals ’26 -
2.h.3 Confidence Interval Estimation , 26

3.

RESUIIPS

3.1 DECISIONS OF MINOR STREH IRIVERS .

3.2

3.1.1 The Composite lag and Gap Acceptance

30102

3.1.3

3.1.1;

Distribution
Comparison of Legs and Gaps

Evaluation of the Influence of Traffic
Factors on River Decisions

3010301 VGhiCIC Type
3.1.3.2 Pressure of Traffic Demand

3.1.3.3 Direction of Side Street Vehicle
Movement

3.1.3.1; Main Street Vehicle Sequence

3.1.3.5 Conditions on the Opposing Side
Street Approach

Summary of Driver Decision Results

REACTIONS OF MINOR STREET IRIVERS

3.2.1

3.2.2

3.2.3

3.2.h

Starting Delay Time Distributions for
leg Acceptances

Starting Delay Time Distributions for
Gap Acceptances ‘

Influence of Traffic Factors on Starting
Delay Time

3.2.3.1 Pressure of Traffic Demand
3.2.3.2 Main Street Vehicle Sequence

Summary of Driver Reaction Results

3.3 DEIAI MOSED 0N MINORSTRM ms

3.3.1
3.3.2
3.3.3
3.3.1;

Total Delay
Delay in Queue
Delay meue leader

Smry of Delay Inta

iv

Page

32

,32

31+

37
37
37

to

1+7
In
55

55
57

57
57.
62

65
65
67
57
67

h. DISCUSSION
h.1 mTERPREI'ATION or mass .
L2 COMPARISON wITR REIATED RmRARCE
. 1+.3 FUTURE RESEARCH
h.h CONCIUSION
BIBIIOGRAPB! '

APPENDH

73
73

'79

81
83

IISTOPTABIE

2262

Table 1. Average Rates of Traffic Flow During

The Periods of Study 3 17
Table 2. Approximate Turning Percentages of Side

Street (Abbott Road) Traffic During the

Periods of Study 18
Table 3. Summary of the Components of Side Street

Vehicle Delay - ‘ 70

..o—.--o—'—

V1.

. Figure
Figure

Figure
Figure

Figure
Figure

Figure
Figure
Figure
Figure
Figure
Figure
' Figure

Figure

Figure

_ Figure

Figure

2.

3.
h.

50
60

1h.

15.

16.

17 0

LIST OF FIGURES

Intersection Reference Lines
Condition Diagram of the Intersection
Sketch of Top Panel of Survey Device
Sample Section of the Data Chart
Sequence of Main Street Gaps

Stratification of Isg and Gap
Acceptance Ihta

Example of the Graphical Analysis

. Technique

Composite lag and Gap Acceptance

‘ Distribution

Comparison of Composite lag and
Composite Gap Acceptance DistributiOns

Comparison of lag and Gap Acceptance
for Cars

Effect of Vehicle Type on the lag and
Gap Acceptance Distribution

Effect of Pressure of Traffic Demand on
Gap Acceptance Distribution for Cars

Effect of Pressure of Traffic Demand on
lag Acceptance Distribution for Cars

Effect of Direction of Side Street
Movement on Gap Acceptance Distribution
for Cars During Peak Periods

Effect of Direction of Side Street Vehicle
Movement on Gap Acceptance Distribution
for Cars During Offpeak Periods

Effect of Sequence of Main Street Gaps on
Gap Acceptance Distribution for Cars
During Peak Period

Effect of Sequence of Main Street Gaps on

Gap Acceptance Distribution for Cars
During Offpeak Period

Vii

10
15

2h

25

33

35

36

39

1&1

A2

AB

3‘5

Figure

Figure

Figure
Figure
Figure

Figure
Figure
Figure
. Figure

Figure
Figure

Figure
Figure
Figure

Figure

Figure

18.

19.

23.

29.
30.
31.

32.

33.

Effect of Conditions on the Opposite Side Street
Approach on Gap Acceptance for Cars hiring Pesk
Period

Effect of Conditions on the Opposite Side Street
Approach on Gap Acceptance Distribution for are
During Offpeak Pariod -

Summary of Effective Sample Sires

Summary of the Means of the Distributions

Summary of the Standard Deviations of the
Distributions

Summary of the Statistical Tests
Starting Delay Time in Accepting lags
Starting Delay Time in Accepting Gaps

Effect of Pressure of Traffic Demand on Starting
Delay Time in Accepting lags (Succeeding Vehicles)

Effect of Pressure of 'h'affic Demand on Starting
Delay Time in Accepting Gaps

Effect of Sequence of Accepted Main Street Cap
on Starting Delay Time in Accepting Gaps

Total Delay on the Side Street ApprOaches

Delay in Queue on the Side Street Approaches
Queue Leader Delay on the Side Street Approaches
Approximation of the Trends of Side Street Delay
Components as Related to Main Street and Side
Street Traffic Flow

Comparison of Results with Related Findings

viii

2’32
1.3

1‘9
so
51

52

72

V 1. INTROIUCTION

Since the advent of automobile transportation, the problem of
dealing with the conflict of vehicles traveling on roadways intersecting
at grade has been a concern of those responsibIe for safe and efficient
movement of persons and.goods. InterseCtions at grade remain as critical
elements of the highway system in that they are principal sources of
accidents and delays; furthermore, their capacities restrain the entire
system's ability to process traffic. This is particularly evident in
and around.urban areas where population and.traffic demand are concen-
trated.

The control of traffic Operation at intersections has been the
subject of extensive study by traffic engineers in the past. The fact
that interest in this topic remains on a high plane, and that the volume-
.of related research work currently'underway equals that at any point in
history is evidence that much knowledge is yet to be created, and.many
problems have yet to be Solved.

1.1 BACKGROUND
1.1.1 The Selection of the Control.Mode at an Intersection at Grade

The modes of control which have been developed to facilitate traffic?
movement at intersections include:

1. [Traffic_control'signa1.or time sharing mode, in which the
right to proceed.a1ternates in time between the conflict-
ing streams.

2. Stop sign or priority mode, in which one stream is

assigned.the right of way and vehicles on the conflicting

-'1 -

stream are required to stop and yield right of way to
vehicles in the priority stream which are near enough to
‘constitute an immediate hazard. .

3. Yield sign, a special case of the "priority" mode, which
requires a stop only when necessary to yield right of way
to the priority stream.

h. Four-way stop (or more correctly, all-way stop), which
might be considered.a hybrid.of the time sharing and
priority modes. Vehicles in both streams are required.to
stop and priority is generally taken by the vehicle which
was first to arrive.

The specific wording and legal interpretation of traffic ordinances
relating to the four items above vary between Jurisdictions; model
ordinances which reflect the nation wide consensus may be fbund.in
Reference (1).

At intersections along major arterial roadways, either the traffic
control.signa1 mode or the st0p sign mode are usually applied. Conse-
quently, it becomes the task of the traffic engineer to make an objective
selection between the two principal alternatives. In the history of an
intersection, stop sign control is usually applied first. A.most common
decision, therefore, is whether to retain the stop sign control or to
install a traffic control signal.' ‘ .

Davis and Michael (2) have pointed out that general warrants for
intersection control methods have evolved.which are based in part on
empirical data, but which to some degree are merely rules of thumb. The

most recent national standard warrants are contained in a manual (3)

which was prepared.through.a cOOperative effort of municipal, county,

- 2 -

state, federal governments and professional associations. These
warrants are based.on measurements of vehicular traffic volume and
speed, pedestrian volume, accident experience and.other special con-
siderations. .

Gazis and.Potts (h) have recently detected new impetus in the study
_of intersection operations due to developments in the application of
mathematical theory and digital computer simulation. While their
comments pertained.specifically to optimization.of traffic signal
“operation, it will be seen, from.references cited.1ater in this paper,
that the comment pertains with equal.validity to stop signed inter-
section operation, and to the problem of selecting one of the alterna-
tives. Whether an analytical model or a simulation model is utilized,
the approach is to apply the model over full.ranges of’geometric design,-
traffic variables, and, in the case of signalized intersections, timing
of the traffic signal, solving for a measure of effectiveness or per-
formance criterion. Then, fOr any specific intersection condition, the
control mode which provides for the ’best' performance of traffic is
implemented. Such techniques can provide answers which are only as good
as the weaker of the two models, whether the stop sign model or the
traffic signal model is weaker. Performance criteria which have been
commonly proposed include: 1) measurements on the distribution of
individual vehicular delay, such as mean delay or maximum individual
delay; and 2) measurements of intersection throughput (vehicles served‘
per unit of time). -

Relatively speaking, research on Operation under traffic signal
control has been more intensive and.has borne more fruit than research

on the step signed.intersection. This is perhaps the case because at a

,-3_

signalized intersection performance criteria are highly dependent on
signal timing, which can be precisely observed or stated in a model. At
.an intersection controlled by a stop sign, however, where delays are for
the most part encountered by vehicles on the yielding street, performance
is highly dependent on the decisions and reactions of the waiting driver.
The content of the remainder or this paper is limited to the stop sign
mode, and in particular, reports on research performed by the writer
pertaining to driver decisions and reactions.
1.1.2 Ana_1ytical Models of StOp Signed Intersections

One of the earliest applications of theoretical techniques in the
study of stop signed intersections was reported by Greenshields, et al.
(5) , in l9h7. They presented a sample application of probability theory
to determine the percentage of side street cars unnecessarily delayed by
a stop sign in attempting to cross Poisson distributed uni-directional
main street traffic. It was assumed that side street cars were unnec-
essarily delayed if', at their time of arrival at.the intersection, no
main street vehicle was nearer than six seconds. from the intersection.
Raff (6) carried forward the work of Greenshields by generalizing the
theory and applying it to the development of warrants for stOp signs.
His general premise was that a stop sign is warranted if more than 50
percent of the side street traffic is delayed by main street traffic.

More recently, several theoreticians have applied their knowledge
of queueing theory and stochastic‘processes to the highway crossing
problem (7-15). I '

Evans, Herman, and Weiss (16) havecommented on several of these
papers, indicating the general approach and citing the limitations of

such techniques. Generally speaking, assumptions are first made

-14...

relating to: 1) the form of the distribution of arrivals on the main
street and side street; and 2) the gap acceptance criterion. Then,
expressions Of performance values, such as waiting time distributions,
queue length distributions, probability of zero delay, and highway
transparency* are derived. Several interesting comments contained in
Reference (16), pages 2-h, illustrate the rather severe limitations
imposed on the theoretical approach. They are quoted below:

"... The problem of crossing a highway involving two lanes in

Opposite directions, fOr example, becomes extremely difficult to

handle. ... In fact, these theoretical papers concern rather

restricted models which are set up in order that the mathematics

be tractable. It was quite clear from the start that the com-

plexity Of the merging or highway crossing problem is such that

one cannot hope to take into account all Of the detailed real

effects that occur on the streets and highways in such theoretical

studies. ... It is quite clear to us that a deep understanding

of this problem will result from the interplay between theoretical .

work, machine simulation, and.good.observations and.experiments in

the field. ..."
1.1.3 Simulation Models of Stop Signed Intersections

General purpose digital computers have been in existence for little
more than a decade. A.relatively short period of time after their intro-
duction, attempts were made to use them for the simulation of vehicular
traffic. The Dictionary defines to Simulate as "to assume the appearance
of, without the reality; to feign.” The use of a digital computer as a
simulator has become commonplace in a broad.variety of fields Of endeavor.
The foremost examples are, perhaps, in the area Of telephone traffic and
switching problems.

Pioneering efforts in vehicular traffic simulation were reported by

Gerlough (18) in 1955, and Goode, Pollmar, and wright (19) in 1956; the

 

* _
Highway transparency is defined as the percentage of tile during which
a waiting driver would say that it is safe to cross the highway.

- 5 -

former involving a model Of freeway-type traffic and the latter, a
Signalized intersection. Goode, et a1. exposed certain advantages Of
simulation in a very succinct manner: .

"... There is one aspect of the attack on a problem in which simu-

lation is better than both analysis and trial. ... In analysis we

may use only those criteria which are mathematically tractable

(e e.g., least squares, but not maximum absolute deviation), and in

trial, we choose only one criterion because even one is costly to

measure. In simulation, we may select any criterion and "as many

as we like, measuring them continually if necessary. ..."

later simulation models are especially pertinent, in that considera-
tion of stOp signed intersections was included. Stark (20) developed a
program for the Ina-70h to simulate nine blocks of a city street; three
Of the crossing streets were controlled by stop signs. His gap accept-
ance rules were based on a constant acceptable gap in main street traffic
or four seconds. Lawis and Michael (2) and Kell (21) have each developed
models Of a single intersection on which either stop Sign control or
traffic signal control can be imposed. The Lewis-Michael program was
written in IBM 709/7090 FORTRAN language. One -Of the stated Objectives
of their work was to establish a realistic set Of traffic volume
warrants to indicate when to go from stop sign control to semi-actuated
traffic signal control. They made simulation runs using constant values
for time gap in main street traffic acceptable to the waiting driver,
14.8 seconds and 5.8 seconds. Kell's undertaking has similar final
Objectives. He is develOping two separate models, programmed for the
IBM-701, first a stop sign model, and then a traffic control signal
model, with the ability to Operate the signal in three different

manners -- fixed-time, semi-actuated, and full-actuated.* F'or gap

 

*Definitions of these three types of traffic signal Operation may be
found in Reference (3)

-6-

L/

acceptance criteria, Kell utilized a function in which the probability

of accepting a given size time gap follows a log normal distribution.

1.1.h Current Knowledge of River Decisions and Reactions at Sta)
Signed Intersections

Several papers were found in the literature which pertained directly t
or were analagous to driver decisions and reaction at stop signed inter-
sections. Before proceeding with a review of this- work, one should
understand certain terminology which has come into common usage as
related to this tOpic. A gap is considered as the time interval
between arrival of successive main street vehicles at a point in the
intersection. A E is that portion of. current gap remaining when an
approaching side street vehicle stOps or reaches its lowest speed. In
other words, a lag is the time interval between arrival Of a side street.
vehicle and arrival of the next main street vehicle. A lag or gap is
either accepted or not accepted (rejected)by the side street vehicle.

A lag isaccepted if the side street vehicle crosses or enters the main
street before the arrival of the main street vehicle. A gap is accepted
if the side street vehicle crosses or enters the main street between the

' two main street vehicles comprising the gap.

Greenshields, et a1. (5) were the first to study the acceptance and
rejection of lags. They studied an intersection in New Haven, Connecticut
to determine an 'acceptable average-minimum' lag (i.e., the one accepted
by more than 50 percent of the drivers) Of 6.1 seconds.

Raff (6) studied behavior at four intersections in New Haven to
determine the ‘critical lag, ' which was defined as having the property
that the number of accepted lags shorter than this value equals the
number of rejected lags longer than this'value. Critical legs 'at the

.7- f,~

fOur intersections ranged from h.6 seconds to 6.0 seconds. Raff
attempted to evaluate factors which affect the critical lag, and con-
cluded that, of those factors investigated, sight distance was most
significant. Contrary to what might be expected, intersections with
poorer sight distances had lower critical.lag values.

Robinson (22) in the study of an analagous situation of the
decisions Of pedestrians crossing a road, introduced to the traffic
engineering profession the use Of a probability distribution to describe
data of this type. By transforming percentage acceptance to a probit
scale and.gap size to a logarithmic scale, Robinson was able to fit a
straight line to his data.

Mere recently, Bissell (23) reported.an analysis of driver decisions
at two stop signed intersections in Oakland, California and in suburban '
Contra Costa County, California. He treated data in a manner similar to
that used by Robinson. USing a graphical method, he fOund.that by trans-
forming gap size tO a logarithmic scale, the probability Of accepting a
leg or gap followed a normal distribution. .In addition, Bissell investi-
gated the effects Of some traffic factOrs on the acceptance functions,
concluding that drivers proceeding left, straight and.right from the side
street behaved differently. He fOund.no significant differences between

the lag and.gap functions, nor any difference between crossing in front

of a main street vehicle approaching from the left (i.e., near side) and
crossing in front Of one from the right (i. e., far side).

A.comparison of these strictly empirical investigations, including
the present study, with the controlled.experiments conducted by Herman
and weiss (12) at the General Motors Research laboratories should prove

interesting. Here, experimental subjects (drivers) waited.at a stop sign

-a'-

while a single car approached on a crossing path at 30 mph. At an
unspecified time, an Observer, equipped with a stOp watch, called

'mark' and the waiting driver then either accepted or rejected the-lag? ‘

No information was found in the literature pertaining to the ’ '
measurement of fstarting delay time' for drivers accepting lags and
gaps. Starting delay times in accepting gaps and legs are defined by
this writer‘as follows:

1. Starting delay time in accepting gaps is the elapsed time
between arrival of the first main street car comprising a
gap and the complete entry into the intersection of the
side street car.

2. Starting delay time in accepting legs is the elapsed time
between arrival Of a side street car (i.e., either when it.
stOps or reaches its lowest speed) and its complete entry
into the intersection.

Arrivals of main street cars are measured at a line which is the
extension of the side street center line. A side street car is assumed
to have completed its entry into the intersection when its rear bumper
has crossed the line which is an extension of the near side edges of the
main street. These reference lines are illustrated in Figure 1.

Starting delay time is an important parameter in both the empirical
study and the simulation of stop signed intersections .at any time more
than one vehicle is waiting in line at the stOp sign. The problem here
is to determine from what point in time the lag. presented to the second
vehicle should be measured. ‘ Using the above definitions, the arrival of
the second car can be considered as coinciding with the entry of the first

waiting car, and the second car's lag can be measured from this reference.

-9-

Figure 1. Intersection Reference Lines

 

 

 

 

 

Main Street Arrival Line

MAIN

 

Intersection
Entry Lines

 

 

 

 

 

 

smsmm

 

r -—'~——. 1- u... - a.-. _-.~ ... -.—— - ..-. ‘_M’~--‘ “CG——

-10..

Thus, both the central tendency and dispersion of starting delay time
are of interest, and it is rather surprising that such measurements have
not been reported in the past. . .
1.2 RESEARCH OBJECTIVE

With an awareness Of the importance and direct applicability of
results of empirical studies Of driver decisions and reactions at inter-
sections controlled by a stOp sign, and in consideration statements in
the literature calling for verification and refinement of current knowl-
edge in this area, the present study was undertaken. The objectives of
this research were: .

1. To perform a microscOpic examination of an intersection
controlled by a stop Sign to determine and verify the
parameters of the lag and gap acceptance distribution of
the waiting vehicles.

2. To evaluate the influence of the following traffic factors
on the lag and gap acceptance distributions:

a.) Vehicle type: car vs. truck. '

b. Pressure of traffic demand: peak vs. offpeak. '

c. Direction of Side street vehicle movement: left vs.
straight vs. right.

d. Main street (vehicle sequence: near vs. far for lags;
and near-near vs. near-far vs. far-near vs. far-far for
gaps.

e. Conditions on the opposite-side ,strcetzapproachxa car .
present ‘vs.tano.car present. .

3. To determine the parameters of the distributions of starting
delay times of vehicles accepting legs and gaps, and to

' evaluate the influence of" certain traffic factors on these
distributions.

h. To investigate the delays encountered by vehicles waiting
on the side street.
1.3 RESEARCH IJMITATIONS

The primary limitation. of this work is that characteristics of
behavior, at only one intersection were studied. Thus, any direct
applications of the results should be limited to intersections having
generally similar geometric and traffic characteristics.

Since the resources with which to finance the study were rather
limited, the installation Of automatic traffic sensing and recording
equipment which could expedite analysis was not possible. All data A
were sensed manually and recorded on an Esterline-Angus 2O pen event
recorder. Thus, a practical limitation was placed on the size of the
sample by the amount of time required in the tedious data reduction
process. Only as much data as one could reasonably expect to subject to
analysis was collected. As a result, certain Of the stated objectives
could not be fully met because of the lack of adequate sample data.

All sample data were collected during daylight hours in fair, dry
weather during the months of August, October, and November. Any” inter-
pretation Of this work should thereby be made in the light Of these

limitations .

2. STUnr PROCEDURES

2.1. SEIECTION'AND DESCRIPTION OF'THE STUD! SITE

Several factors influenced the selection Of an intersection fOr
study. A.primary consideration was that the gaps in main street traffic-
should.cover the full range Of values which some drivers accept and some
drivers reject. It had been determined from the review of earlier-worke--
that values between one and ten seconds should.be contained in this '
range. The volume of traffic on the street controlled.by the stOp sign
had to be substantial enough to make the question of alternative modes
of control.realistic.* Furthermore, if traffic were very sparse on the '
side street, an excessive amount of time would.be required collecting an
. adequate sample. Other traffic factors of importance were that the side‘
street carry both trucks and cars, and that these vehicles cross, make
right turns and left turns into the main street in order that the effects
of these variables could be evaluated.

Generally speaking, the intersection had to be fairly typical of
those found throughout the country about which the question of alternatives
Of control is raised. Special characteristics, such as substantial hori-
zontal or vertical curvature very near the intersection, an Oblique cross-
ing, severe sight distance restrictions, and.one-way Operation on either

street were to be avoided.

-:

* The selection of the 'best' mode Of control far the intersectiOn studied
was not one of the Objectives of this research. so such decision was
made.

 

-‘1'3-

The intersection selected for stucb', 14-78 (Saginaw Road) and
Abbott Road in East Iansing, Michigan, satisfied the important require-
ments reasonably well. ‘ 14-78 is a major four-lane, bi-directional,
undivided state highway, the arterial route connecting the cities of
Flint and lensing, Michigan. Abbott Road is an important two-lane,

I bi-directional city street which serves traffic to and from the business
district of East Iansing and the campus of Michigan State University.
which are situated approximately one mile south of the intersection.
Figure 2 is a condition diagram of (the intersection representing the
characteristics existing at the time Of the field study.

Pertinent features Of 'the intersection are outlined below.

1. Control devices: roadside and overhead illuminated stop

 

signs facing Abbott. Flashing amber beacons warning 11-78..
2. Speed limits: 25 mph on Abbott, ho mph on 14-78.
3. Lane widths: 10.5 feet on Abbott, 11 feet on 11-78.

h. Sight restrictions: no major Obstructions to vision

 

across all four quadrants.

5. Grade and curvature: essentially flat and tangent within

 

#00 feet of the intersection in all directions.

6. Special right turn lanes: pavement on 14-78 widened eight

 

feet on all but the northwest quadrant to accommodate
decelerating vehicles turning right fiom M-78 and
accelerating vehicles turning right from the northbound
approach of Abbott. It was observed that very little use

was made of these lanes except for eastbound $7.8 vehicles
turning right (south) onto Abbott. The other widened portions

were evidently interpreted by most (rivers as sections of

paved shoulder.
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Traffic volumezl the average rates of traffic flow
measured during the period of field study are presented
in Table 1. .

Turning movements: the approximate percentages 'of Abbott
Road traffic proceeding left, straight and right are shown
in Table 2. It will be noted that the directional move-
ments are rather well balanced, particularly on the
northbound approach. In comparison the turning movements
on M-78 were minor, approximately seven percent left turns
and nine percent right turns in the eastbound direction,
and eight percent left turns and three percent right turns
in the westbound direction.

Traffic composition: of the total sample of side street

 

vehicles, 6.1!» percent were trucks (not including one-half
ton pickup trucks and panel delivery trucks which were
considered as having performance characteristics similar
to passenger cars). Approximately 1‘} percent of the 14-78

traffic were trucks.

Another special consideration noted was that for several years,
especially after the occurrence of a fatal accident on August 15, 1958, .
the residents of the surrounding community had been urging the installa-
tion of a traffic signal at this intersection.

2.2 DATA count-non INSTRUMENTATION AND mocnums

A special purpose survey device was devised especially for this
project. The device was completely self-contained within a package
measuring approximtely one and one-half. feet by one and one-half feet

by three-quarters feet. In the top panel of the package were mounted

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ten normally-closed, push-button microswitches. Each of the switches

was electrically connected to a separate pen of an Esterline-Angus 20

' pen event recorder contained within the package. A sketch of the top
panel is shown in Figure 3. Included on the sketch are the pen numbers

to which the push-buttons were connected. In the following text the push-
buttons will be identified by these numbers. A portion of the front panel
of the package was left open to permit easy access to the 20-pen recorder.
Two 22.5 volt dry-cell batteries connected in series powered the system.

In the Esterline-Angus recorder a paper chart roll is transported,
by a spring wound clock device, past a bank of 20 solenoid actuated pens.
When one of the push-buttons was depressed, the circuit was closed and
a solenoid activated, causing the corresponding pen to be displaced from
its normal position. The pen remained in its displaced position until
the push-button was released.

The survey device was operated by two observers seated in the front
seat of a private automobile parked approximately 15 feet off Abbott Road
in the northeast quadrant of the intersection (see Figure 2). The first
observer: (1) depressed buttons 8, 6, and 1+ upon the arrival of main
street vehicles proceeding left, straight and right, respectively; (2)
depressed button 1 upon the arrival of a northbound side street vehicle;
and (3) depressed button 2 upon the complete entry of a side street
vehicle into the intersection. .In a similar manner the second observer
operated buttons 12, 1h, and 16 upon arrival of main street westbound
vehicles, and buttons 20 and 19 upon arrival and entry of side street
southbound vehicles. For car arrivals on both the main street and side
street arrivals, the buttons were depressed and released inediately:

whereas for trucks, the buttons were depressed for a larger period of

-19-

Figure 3. Sketch ofTop Panel of Survey Device

 

 

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Note: numbers in parentheses next to pushbuttons indicate
,thepennumbers ofthemntreeordertowhichthe
buttons were connected.

 

time. For straight through, right turn, and left turn entries from the
side street, the entry buttons were depressed once, twice in rapid
succession, and three times in rapid succession, respectively. After a
reasonably short period devoted to practice runs, the observers were
able to perform their. assigned tasks with a high degree of proficiency.

A sample section of a survey chart is shown in Figure h, for the
purpose of illustrating the manner in which pertinent data can be
measured. For this survey, a chart. speed of six inches per minute was
used. The chart speed was checked with a stop watch periodically to
insure the maintenance of an accurate time scale.

A total of #72 minutes of sample data were gathered on weekdays
during the months of August, October, and November, 1961. The decisions
and reactions of 1,203 side street vehicles were observed. A'total of
5,179 acceptance-rejection decisions were made, 1,203 relating to lags
and 3,976 relating to gaps. .

2.3 DATA REWCTION PROCEWRE

Extracting pertinent data from the graphical charts was the most
time consuming phase of the project. The chart rolls were "viewed on a
special light table, which had been constructed for viewing rolls of
aerial photographic film. Time measurements were made with the aid of
a plastic template on which the appropriate time scale had been scribed.
All time measurements were estimated to the nearest one-tenth second.

The charts were scanned for vehicle arrivals on the side street.
Each arriving vehicle was numbered and its 'type and direction of move-
ment through the intersection were determined. A check was made to ,
determine if a. vehicle was waiting at the same time on the opposite side
street approach. A sequence of time measurements was then made in the

manner previously illustrated in Figure 3: -
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- 253 -

1. Delay in queue, which applies only if more than one side
street vehicle is waiting.

2. A near-side or a far-side lag. Near-side implies the
direction of main street traffic nearest to the waiting
driver, or in other words, traffic approaching from the
driver's left. For side street right turning vehicles,
onhr near-side lags are relevant.

3. A series of gaps which may have the following sequences:
near-near, near-far, far-near, far-far (see Figure 5)..
gaps are relevant.

h. Delay as queue leader (i.e., first in line). ...- ..._.

5. Total delay, which equals the sum of delay in queue and '
delay as queue leader. ‘

All of the above measurements were recorded in units of seconds on
a single data form, a sample of which is found in Appendix. . - Legs and
gaps which were accepted by side street drivers were circled. Starting
. delay times in accepting lags and gaps were measured and recorded
separately during a second pass through the chart rolls.
2A STATISTICAL ANAHSE

The bulk of the statistical analyses performed related to the lag
and gap acceptance data.
2.h.1 Stratification of the mta '

To permit an effective evaluation of the effects of certain traffic
factors, these data were first stratified in the manner illustrated by
Figure 6. Such stratification is often undertaken to help safeguard

against overlooking or misinterpreting the significance of a given

-23.-

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factor caused by submerging the effects in a larger distribution affected
by other important variables.“ Consideration was given to the possible
use of analysis of variance techniques; however, with an interest in

such a large number of levels of comparison, analysis of variance would
soon have become unwieldy and difficult to interpret.

For each class of data shown in Figure 6, the parameters of the
acceptance distribution were determined. Pertinent comparisons between
classifications, as indicated by the dashed lines in the Figure, were
then made. .

2.h.2 Grouping Into Class Intervals

lag and.gap times ranging between zero and.l§ seconds were grouped
in one second intervals befbre proceeding with the analysis. Fer the
sake of simplicity, the integer values (e.g., 1.0, 2.0, ...) were
treated as the class boundaries, and any data falling exactly on a
boundary was placed in the higher class interval. no leg or gaprgreater
than 15 seco7Ls was rejected, hence all values greater than 15 seconds
were grouped together. I '

2.h.3 Confidence Interval Estimation

For each class interval the frequency of acceptances, A1, and

were known.

rejections, R 3 and the interval sample size, n1 -.A1 +-R

1 1!
The true probability (or proportion) of acceptance far each interval,

P was estimated‘by the statistic

1)

p.

.....1.
pi n1

AecOrding to Dixon and.Massey (2%) the frequenCy, A1,'fo110ws a
binomial distribution. 'Ibr relatively large samples, values of n1?1

andn1 (l - P1) greater than five, the sampling distribution of‘p1

-és-

should have mean P1 and variance P1 (1 - P1)/n1, and the statistic

 

 

 

an approximately unit normal distribution.

For large samples, an interval estimate of P with confidence

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The probability that. the interval estimate computed from a given

. sample contains the population parameter, P , is (l - cc ). For each

1

class interval, an interval estimate of P for (l - a )' - .90 was

1
determined by referring to Table A-9b of Dixon and Massey (2h).

2AA Graphical Determination of 'Accegtance Distributions

 

Working with similar data, Bissell (23) plotted gap size, x1,
against sample proportions, p1, on logarithmic-probability graph paper
and fitted a straight line through the points. This indicated that the
relationship between log X1 and p1 hada form approximating a normal
distribution. He was thus able to estimate the mean and standard

deviation .of the transformed variate, log :1, rather easily.

-27..

Dixon and Massey (2h) discussed the use of this type of graphical
analysis for, data from sensitivity experiments, such as submitting
animals to different dosage levels to determine the lethality of a drug,
or drapping explosive specimens from various heights to determine, sensi-
tivity. The analogy between such data and the lag and gap acceptance
data at hand is evident.

This writer used a slightly modified version of this technique to
determine the form of the acceptance distribution. Rather than plotting

sample prdbabilities, interval estimates-of P were used, and a straight

1
line was fitted to the data by eye which passed through most of the
intervals. An example of this technique is presented in Figure 7. Also
shown is a rectilinear graph which illustrates the relationship between
gap size and probability of acceptance in their natural, untransformed .
state. ' . ‘

The mean and standard deviation of the distribution is estimated by
noting where the line crosses. the 50 percent point,'X.50, and the 15.87

percent line, {1587. Then

mean,log}{=-logxso

standard deviation, 8108 X = log X350 - log 1.1587.

The trans forms should always be used when working with the distributions ,
and the antilogs, or absolute values, only stated in general descriptions
of the results. i ' '

An equation can be written for solving for the probability of

accepting a certain gap size, Xi, in the form

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However, the references indicate that this can only be solved.by
approximate methods. It is much more practical, therefbre, to use the
graph directly or to tabulate selected.values read from the graph.

2.h.5 Precision of the EBtithgngnd_Tbgt3 of Hypotheses

The precision of the parameter estimates of the acceptance distri-
butions, and.testing of statistical hypotheses relating thereto, are
complicated by difficulty in interpreting the effective sample size.
Because the transforms of'gap sizes are not random.normal.variates in
the normal sense of the word, it is believed invalid.to utilise the sum '
of the sample sizes within class intervals, z:n1, 88 the effective
sample size used in estimating the parameters of the parent distribution.

Finney's text (25) is principally devoted to the analysis of the
same general form of data fbund in biological assay. However, the
application of many of the techniques discussed depended on special
sampling techniques common to the biological research field. General
methods suggested were usually'very complex and difficult. One method,

however, which he attributed to Spearman and Karber could be reasonably

....-u.---v

applied to the data at hand.to estimate the variance of the mean of thet
distribution. After working two lengthy samples, it was found that the‘
technique yielded a variance of the mean which could be associated with
a sample size slightly larger than theaverage sample within the one
second class intervals. In order to get on with a reasonably practical

analysis, therefore, it was decided that the average n in each

i

-30..

distribution would be utilized as a conservative estimate of the
effective sample size.
For each of the comparisons of acceptance distributions, two null

hypotheses were tested.
1. null hypothesis: log ll - log E
alternate hypothesis: log 11 P log X2

2 2
2. null hypothesis: 8108 x1 =- 8108 12

2 2
alternate hypothesis: Blog 11 n- 8108 x2
Each hypothesis was tested at the level of significance, at - .05,
and rejection of either caused the conclusion that the two distributions
being compared were indeed different. The reader is referred to stand- , -
ard introductory texts in statistical analysis, such as Dixon and

Massey (21.) or Walker and lev (26) for detailed descriptions of student's

't' test on means and the F ratio test on variances.

-31-

3. assume
3.1 DECISIONS 0F MINOR STREET DRIVERS
. Results of the statistical analysis of'lag and gap acceptance
distributions are presented in graphical form, and the influence of the
traffic factors studied are discussed in the light of difference tests
performed on the parameters of the distributions. For the sake of
clarity, only the linear estimates are shown; however, each of these
estimates resulted from the graphical analysis technique described and
illustrated in Section 2.1+.h. In performing each graphical analysis,
it was fOund that a straight line could be drawn which passed through
a great majority of the series of confidence bands plotted on the
logarithmic-probability paper. This held up well for all levels of .
data stratification. Thus, the results gave rather strong verification
of Bissell's (23) conclusion that the probability of accepting a lag or
gap in main street traffic has a lognormal form.
3.1.1 The Composite Lag and Gap Acceptance Distribution
Illustrated in Figure 8 is an estimate of the acceptance distribution
resulting from combining all driver decision data into one large sample.
Also shown are estimates of the parameters of the distribution, i.e.,
the mean and standard deviation of the log transformed gap size distri-

bution, log X and 8 , along with the effective sample size, '51 ,

log X
' associated with the estimates. The two points. on the line which were
used in computing the estimates are lurked for reference. One can use

the graph to estimate the probability of accepting a given lag or gap.

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It is interesting to note that the absolute value of the mean is
7.h seconds, and that lags and gaps smaller than h.3 seconds are
accepted by fewer than ten percent of the side street vehicles, and
gaps larger than 12.5 seconds are accepted by more than 90 percent. A
total of 335 lags and gaps greater than 15 seconds were presented to
side street drivers, all of which were accepted. I
3.1.2 _C_o_mparison of lags and Gaps

The results of separating the composite data into lags and gaps
are shown in Figure 9. Two null hypotheses on the parameters of the two
distributions were tested. First, the hypothesis that the mean arts.
lag distribution equals the mean of the gap distribution was tested,
using a one-tailed student's 't' test at level of significance 0.6. 3. .05... _
Secondly, the hypothesis that the variances of the two distributions
were equal was tested, using a one-tailed F ratio test at level of ‘
significance or: = .05.. Both hypotheses were rejected, and it was con-
cluded that the two samples are not members of a common distribution.
In other words, the acceptance of lags and the acceptance of gaps should
be treated separately. The rejection of either of the hypotheses would i
have caused the same conclusion to be drawn. The 'mean' of the lag accept-
ance distribution, absolute value 8.00 seconds, and the mean of the gap
acceptance distribution, absolute value 7.20, differed significantly.
Also, the lag acceptance distribution is significantly more disperse
than the gap acceptance distribution. '

The sample was further segregated into cars and trucks, and a
comparison of lag acceptance and gap acceptance for cars was made 3
results are shown in Figure 10. Once again, the hypothesis of equality

for both means and variances was rejected, and it was concluded that

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lag acceptance and gap acceptance for cars are indeed different and

should be treated separately. The absolute values of the means were

8.00 seconds and 7.10 secondsfor legs and gaps, respectively.

3.1.3 Evaluation of the Influence of Traffic Factors on River
Decisions

3.1.3.1 Vehicle Type

The leg and gap acceptance distributions for the two classifications
of side street vehicles, trucks and cars, are presented in Figure 11.
From a logical basis, considering the poorer acceleration capabilities
of trucks, there was reason to expect that differences would be found.
However, neither the hypothesis on the means nor the hypothesis on the
variances was rejected. It was therefore concluded that there was no
evidence to indicate that truck behavior and car behavior are signifi-
cantly different. Until contrary evidence is found, trucks and cars
need not be handled separately. .

If the truck-car comparison had been made separately for legs and
gaps, or for offpeak and peak periods, it is possible that significant
differences would be found. However, the small size of the truck sample
did not permit such further stratification._ There was no way'of knowing
in advance the results of the truck-car comparison. In the original
stratification plan, evaluation of the remaining traffic factors'
influence on the acceptance distribution was to be based on car sample
alone. This plan was not revised. ' >
3.1.3.2 _Pressure of Traffic Demand

A comparison of the“ offpeak period and peak period gap acceptance
distribution for cars is presented in Figure 12. There was no evidence

to indicate that the variances of the distribution were different.

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However, the null hypothesis on the means was rejected, and it was con-
cluded that the two samples were not from a comon distribution. Behavior
during peak and offpeak periods was indeed different; data from the two
periods should be treated separately.

The influence of pressure of traffic demand was more strikingly
illustrated in the case of lag acceptance distribution (see Figure 13)..
The mean of the offpeak distribution differed significantly from the
mean of the peak distributions. Once again, however, there was no
evidence to indicate difference in the variances of the distributions.
3.1.3.3 Direction of Bide Street Vehicle Movement

The gap acceptance-distributions for side street cars waiting to
proceed straight, turn left, or turn right into the intersection were
compared. '

Figure 1% illustrates this comparison for the peak period sample.
Statistical tests were performed on the most widely separated means, and
no evidence of significant difference was found. However, in testing
the extreme values of variance estimates differences were found. The
gap acceptance distribution for right turners was significantly more
disperse than the distribution for left turners. This difference can be
attributed to the right turning driver '3 willingness to accept a greater
percentage of gaps in the low range of the distribution. No significant
differences, either ‘in the means or the variances, were evident in the
comparison of left turns and straight through movements. It was con- ,
cluded that in considering behavior during peak periods, the actions of
right turners must be distinguished from left and straight movements.

An evaluation of the effects of the direction of side street move-

ment was also made for the offpeak period, as illustrated by Figure 15.

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The hypotheses of equality tested for the extreme parameter estimates
could not be rejected. For the offpeak’ period, in other words, there
was no evidence to indicate that the left, straight, and “right samples
did not come from a common distribution. ’

The lack of an adequate sample of lags prevented the conduct of
valid tests regarding the effect of direction of movement on the lag
acceptance distributions.
3.1.3.h Main Street Vehicle Sequence

Another factor investigated was the sequence of main street
vehicles comprising the gaps presented to waiting drivers. Only the
left and straight cars were included in'this analysis, since for right
turns only those gaps in the near side main street traffic are relevant.

During the peak period, the sequence of main street gaps had a
significant influence on the gap acceptance distribution, as shown by
Figure 16. Hypotheses were first tested on the parameter estimates of
the most widely separated distributions (i.e., near-far and far-near).
The mean of the near—far distribution was found to be significantly
larger than the mean of the far-near distribution. There was no evidence
indicating significant differences in the variance estimates. Next, the
far-far and near-near distributions were compared, and no significant
difference was found. Thus, in the consideration of peak period traffic,
near-far and far-near gaps should be treated separately, but far-far and
near-near gaps may be grouped.

A similar evaluation of the effect of main street vehicle sequence
was made for offpeak period traffic. It can be seen in Figure 17_ that
the distributions are in much closer proximity to one another. The

hypotheses of equality applied to the extreme values of mean and variance

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could not be rejected. Therefbre,it was concluded that during offpeak
periods, data need not be segregated.on the basis of the sequence of the
main street gaps. I .

It had.originally'been planned to study acceptance of near legs as
compared with far lags, but this was impossible due to an inadequate
sample of lags.
3.1.3.5 Conditions on the Opposing Side Street Approach

The final traffic factor considered.was the presence or absence of
a vehicle waiting on the opposite side street approach. It was assumed
that this factor is irrelevant to right turning vehicles, hence only
left and straight vehicles were included in the analysis. In both the
peak and.offpeak samples, there was no evidence to indicate that the
decision of the waiting driver was significantly affected.by conditions '
on the opposing approach. Results are presented in Figures'lB and 19.

Once again, data were insufficient to evaluate the effect of this
factor on the lag acceptance distribution.

3.1.h Summary of Driver Decision Results

The results of the study of lag and.gap acceptance distribution of
side street drivers are summarized in.Figures 20, 21, 22, and 23.

Figure 20 is a stratification diagram on which the effective sample
sizes,'Ei, are entered for each item.of classification. -In a similar
manner, in.Figure 21, the absolute values of the estimates of the‘means
of the acceptance distributions are summarized. In Figure 22, the
standard.deviations of the log transformed.distributions are presented.

Finally, the results of the tests of null hypotheses on the parameter

I

estimates are summarized in Figure 23.

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The analysis of the lag and gap acceptance distributions resulted

in the following conc lus ionszl

l. The results of this study strongly supported Bissell's (23)
findings which indicated that the relationship between the logarithmic
transform of lag or gap size and probability of acceptance follovs a
normal distribution curve. i

2. The 1:35 acceptance distribution had a significantly higher
mean and was significantly more disperse than the gap acceptance distri-
bution.

3. There was no evidence to indicate that the lag and gap
acceptance distribution for M differed significantly from that for

cars.

 

. ' .
’4. Both the gap and lag acceptance distributions for cars had

significantly higher means during offmak periods than during ESE
periods.

5. During the offpeak period, there was no evidence t6 indi-
cate that gap acceptance distributions for straight, left and right
movements differed significantly. However, during the peak period. the - -

right turn gap acceptance distribution was significantly more disperse

 

than the left turn distribution.

6. During the peak period, the distribution for cars accepting
near-far gaps had a significantly higher mean than the distribution for
cars accepting far-near gaps. No significant effect of the sequence of
main street vehicles on the gap acceptance distribution for cars was
evident during the offpeak period.

7. In neither peak nor offpeak periods was there evidence to
indicate that the presence of a vehicle on the Opposing side street

approach significantly affected the gap acceptance distribution for cars.

3.2 REACTIONS OF MINOR STREET IRIV'ERS
3.2.1 Starting Delay Time Distributions for lag Acceptances
It is recalled that} in Section 1.1.h starting delay time in accepting
lags was defined as the elapsed time between the arrival of a side street
car and its complete entry into the intersection. In the special case
of more than one vehicle waiting on a side street approach, the arrival
of the second, or succeeding, vehicle was defined as coinciding with the
complete entry into the intersectiOn of the first vehicle in the queue.
Frequency distributions of starting delay time for the first
vehicle and for the succeeding vehicle are presented in Figure 2%. One
imediately notices that the two distributions appear to be different.
Pertinent measurements on the sample distribution are tabulated below.

First Vehicle in Queue Succeeding Vehicle

Sample Size 172 _ 123

Mean . h.37 2.99
Median (50 Percentile) I h.h 2.7
15 Percentile ‘ ' 2.5 ' ‘ 1.7
85 Percentile 6.2 , h.8
Mode 5.25 1.75

Because the distribution for succeeding vehicles was rather highly
skewed and the other approximately normal, the standard tests for statis-
tical difference were not performed. Rawever , it is evident that the
starting delay time for succeeding vehicles has a lower central tendency
and is less disperse than starting delay time for the first vehicle in

the queue .

-5-

Figure 21+. Starting Delay Time in Accepting lags

 

.25
mSTVEHICIE In W '
020 d’

.15 4

 

 

 

.10 ...“

o 1""— ' _ 11:1—

0 l 2 .3 h 5 6 7 8 9'
StartingDelayTims-Seconds '

 

- Proportion
I

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

.25
- 'r-—' suc-nwc VEHICLE ‘
020 “L

015 -‘

 

010 q’

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0 | ’ I
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Starting Delay Time - Seconds

Preportion
I

 

 

 

 

 

 

 

 

 

 

 

 

 

 

.55-

3.2.2 Starting Delay Time Distributions for Gap.Acceptances
Starting delay time in accepting a gap was defined in Section 1.1.h

as the elapsed time between arrival of the first main street car com-
prising the gap and the complete entry into the intersection of the side
street car. ‘The frequency distribution of this variable is shown in
Figure 25. Pertinent measurements on this approximately'normal sample
distribution are tabulated.below; .

Sample Size ' 703

Mean . 3.02

Median (50 Percentile) _ 2.8

15 Percentile 1.8
85 Percentile h.h
Mbde A 2-75

It is interesting to note that, except for the one second difference in
Ithe mode, this sample distribution is very similar to the distribution
of starting delay time in accepting legs for succeeding vehicles.
3.2.3 Influence of Traffic Factors on Starting Delay Time
3.2.3.1 Pressure of Traffic Demand

The sample of starting delay times of succeeding vehicles in accept-
ing lags was segregated-on the basis of period.of the day to reflect
different intensities of pressure of traffic demand. The frequency
distributions fer peak and.offpeak.periods are presented.in Figure 26,

and statistics are tabulated.below.

-57-

.20

Figure 25.

Starting Delay Time in Accepting Gaps

 

015-

.10"

Proportion

.05 d

 

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‘1—

 

1

 

 

 

 

2 3 h 5 6
Starting Delay Time - Seconds

 

7

 

10

Figure 26. Effect of Pressure of Traffic Demand on

Proportion

Proportion

Starting Delay Time in Accepting lags
(Succeeding Vehicles)

 

.30‘

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015.1

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OFFPEAK

 

 

 

 

 

 

 

 

 

 

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Offpeak

Sample Size 66
Mean ‘ 3 . 30
Median (50 Percentile) ' 3.0
15 Percentile ' 1.9
85 Percentile ‘ 5.1
Mode 2-75

Peak
57

2.62
2.2
1.6
h.5

1-75

It is apparent that the central tendency of starting delay time fer

succeeding vehicles in accepting lags is lower during peak periods than

during offpeak periods. 0n the other hand, little difference is seen

in the dispersion of the two distributions.

The sample of first in queue vehicles accepting lags was too small

to be segregated into peak and offpeak period samples.

The effect of pressure of traffic demand on starting delay time in

accepting gaps was also considered. .Offpeak.and.peak period frequency

distributions are shown in.Figure 27, and pertinent statistics are

summarized below.

Ofgpgak
Sample Size hh2
Mean . 3.11
Median (50 Percentile) 3.0
15 Percentile , 1.9
85 Percentile - h-5
Mede . 2.75

Standard.Deviation 1.35

Peak
261

 

2.86 K
2.7
1.7
11.2
2.25
1.1.3

One was not able to determine by visual inspection whether the

distributions differed significantly.
- 60 -

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Proportion

Proportion

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

Figure 27. Effect of Pressure of Traffic Demand on
Starting Delay Time in Accepting Gaps
.25 v
OFFPEAK
020"
015‘
010'1 .—
005‘1 1
o ..r-i - I M.
-l o l ,2 3. l. 5 6 7 8 9 m
Starting Delay Time - Seconds
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PEAK
.20-
.15- '__-l ‘___
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o 7 7 , n l 1
l I T T
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Starting Delay Time - Seconds

-61-

appeared approximately normal, standard deviations were computed and
student's"t' was used to make a one-tailed.test of the null hypothesis
on the means. The hypothesis was rejected.at level of significance
C: I .05. It was therefore concluded.that the mean starting delay time
in accepting gaps was significantly smaller during peak traffic periods.
3.2.3.2 Main Street Vehicle Sequence

From a logical viewpoint, it was expected that starting delay time
in accepting gaps might be affected.to some degree by the sequence of
main street vehicles comprising the accepted gap. In particular, if
first car of the gap was on the £25 side, the side street car might
commence motion earlier and.oomplete entry into the intersection more
quickly than if the first car of the gap was on the near side. The fre-
quency distributions presented in Figure 28 illustrate the effects of I
this factor.

Tabulated.below'are pertinent statistics of the offpeak period
sample distributions.

uFirst Car of Gap 'Near', First Car of Gap 'Far'

Sample Size 2&8 19%

Mean 3.27 . 2.91
Median (5o Percentile) 3.2 2.7

15 Percentile ‘ 2.1 . .121 -.__,
85 Percentile h.5 h.3,
Mode 2.75 2.25
Standard Deviation 1.311 1.31.

The distributions were approximately normal, so the null hypotheses
on the means were tested with student's 't' at leve1.of significance

Ct - .05. It was concluded that starting delay time in accepting gaps,

-5'2‘-

Proportion

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

Figure 28. Effect of Sequence of Accepted Main Street Gap on
Starting Delay Time in Accepting Gaps
.30 ‘m .30 ”um:
First Car in Gap 'Near' First Car in Gap Wash”
025‘ '25—“
020'- 020‘ '-
1 ‘ _ “j
.15- 1 015
,4.
01°— -‘ 0104
.05— ' .05-
I . '
0 HH- 'Ln. ...... o r[ +_ m. n
" ‘ I I I I I .
-l 0 2 h 6 8 -l 0 2 h 6 8 10
Starting Delay Time - Seconds
.30 mm .30 mm“:
1 First Car in First Car in Gap 'Far'
0 t
.25_ Gap Far .25_
.2o—- .20- TI
:1
~01 ' H
i 015‘ .15-
E 1
.10“ .10‘ - .
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402156810 -102h681o

Starting Delay Time - Seconds

-63-

when the first car of the gap was on the far side, was significantly-
smaller than when the first car of the gap was on the near side.

An identical.analysis was made on the peak.period.data.l EVen by
visual inspection of the frequency distributions, one can conclude that
the effect of main street vehicle sequence on starting delay time is
l more marked during peak periods. The statistics for the peak period
sample are tabulated.belowz I

First our of Gap 'Near' First Car of Gap_'Far'

Sample Size L 170 ' 91
Mean _ 3.15 ‘ 2.33
Median ( so Percentile) 3.0 2.2
15 Percentile’ 2.0 - 1.1
85 Percentile “-5 3.3
Mode - 2.75 2.25
Standard Deviation 1.39 1.3%

Once again, the null hypothesis on the means was reJected.atcc = .05.
Thus for peak periods, as well as offpeak, starting delay times in accepting
gaps were significantly smaller when the first car of the gap was on the
‘far side than when the first car was on the near side.
3.2.h Summary of Driver Reaction Results
1. The central tendency Of starting delay time in accepting

lags was greater fer the first vehicle in the queue than for the succeeding

 

vehicle.

2. The distribution of starting delay time in accepting lags
for succeeding vehicles was very similar to the distribution of starting
delay time in accepting gaps. Both of these distributions had lower

central.values during peak.periods than during ofgpgak periods.

-61...

3. Bring both peak and offpeak periods, the starting delay
time distribution for gaps had a smaller mean when the first main street
.car comprising the accepted gap was on the £§r_side than‘when the first
main street car was on the Egg; side. I
3.3 DELAY DIPOSED ON MINOR STREET DRIVERS

The delay encountered.by each minor street vehicle was measured from

the 20-pen recorder charts. Delay in queue was defined as the elapsed

 

time between the arrival of a vehicle at the back of the queue of waiting
vehicles and its arrival as first in the queue. A vehicles arrival as
first in queue was assumed to coincide with the completion of entry into
the intersection of its leader. Queue leader delay was defined as the
elapsed time between the arrival of a vehicle as first in queue and its

V completion of entry into the intersection. It may be recalled that when
the side street approach was clear of other vehicles , a vehicle was
assumed to have arrived (as first in queue) either when it stopped or

reached its lowest speed. Total delay is the sum of in queue delay and

 

queue leader delay.

The analysis of delays was much less exhaustive than was the case
for driver decisions and reactions. The primary objective was to present
sufficient information on delays so that a person who has developed an
analytical or a simulation model may validate his results.

3.3.1 Total Delay

 

Frequency distributions of total side street delay are shown in
Figure 29. Separate distributions are presented for the peak and offpeak
periods and for the northbound and southbound side street approaches .

It can be noted that during the offpeak period, the northbound and south-

bound distributions have a high degree of similarity. During the peak

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period, however, individual delays range up to 3h0 seconds on the north-
bound approach, nearly twice the maximum encountered on the southbound
approach. This difference was attributed to heavier traffic demand and ‘

formation of longer queues on the northbound approach.

3.3.2 Delay in Queue

 

Frequency distributions of delay in queue are presented in a similar
manner in Figure 30 .‘ Hare again, the northbound and southbound offpeak
period distributions are nearly identical; but during the peak period
delay in queue on the northbound approach ranges up to 300 seconds as
compared with a maximum of only 75 seconds on the southbound approach.
3.3.3 Queue leader Delay

F'i‘equency distributions of queue leader delays are presented in
Figure 31. The distributions for the two side street approaches were
very similar during offpeak periods. However, during peak periods,
queue leader delay ranged up to 130 seconds on the. southbound approach
as compared with a maximum of only 60 seconds on the northbound approach.
Furthermore, queue leader delays in the lowest class interval, zero to
five seconds, were less than half as frequent on the, southbound approach
as on the northbound. Apparently, with lower traffic demand and shorter
queues on the southbound approach, the driver is under much less pressure
to cross or enter the main street as quickly as possible.

3.3.11 Summary of Delay Data

Table 3 summarizes the descriptive statistics of the in queue, queue
leader and total delay distributions for side Street vehicles. The mean,
' median, 15 percentile, 85 percentile, and maximum observation of the

distributions are tabulated. .Also shown are the average rates of flow

on the main street and side street associated with the peak and offpeak

period samples.
.. 67 ..

..50-

Proportion

e70 -
060 .1

050-4

Proportion

Figure 30. Delay in Queue on the Side Street Approaches

 

s70-

.60-

 

Southbound

 
 
 
 
 

 

 

 

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Delay in Qleue - Seconds

 

 

 

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Southbound

Northbound

  

 

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0‘ 25 50 75 100 125
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150

' PEAK PERIOD

Delay in mane - Seconds

 

 

I
.175 200 225 250 275 300

Fraportionl

Figure 31.

Pr0port ion

.10“

Queue Isader Delay on the Side Street Approaches

 

. 15"

.05“

OFFPEAK PERIOD

Northbound

Southbound

 

 

 

 

 

 

  
   

 

 

 

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Figure 31. Queue udder Delay on the Side Street Approaches

 

OFFPEAK PERIOD

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Merely to assist the reader in visualizing the statistics presented
in the table, results are presented graphically in Figure 32. Here the
' statistics of the queue leader delay distributions are plotted against
main street flow rates, and the in queue delay statistics are plotted
against side street approach flow rates. The trends of the side street
delay components as related to the flow rates, indicated by the dashed
lines, should be considered only as very rough approximations. It is

hoped that this figure will be viewed in its proper context.

-71-

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' 1+. DISCUSSION

h.1 INTERPRETATION OF REBUIII'S

Generally speaking, the results of this research tendedtoyerify _ t
that which a professional traffic engineer might deduce on the basis-
of logical consideration of the factors involved. 8

For example, the fact that log and gap acceptance differed signi-
ficantly was not surprising. One might expect that a driver who has
Just arrived at a stop sign needs some time to orient his senses to the
decision making process. Furthermore, when such a driver is nearing
the stop Sign, he is often not in as advantageous a position for the
critical observation of main street traffic as if he had been waiting
near the intersection entry line for some period of time. These factors
may help explain why the mean of the lag acceptance distribution was
significantly larger than the mean of the gap acceptance distribution.

With regard to another comparison, it was rather surprising to not
find evidence indicating significant difference intruck and car
decisions. One would normally expect that ,_ on the average, trucks need
to wait for longer gaps. However, the size of the truck sample pro-
hibited stratified comparisons, and if true differences do exist they
may be submerged among the effects of other important factors .

The factor which had the most striking effect on the lag and gap
acceptance distributions was the pressure of traffic demand. The means
of the acceptance distributions were significantly smaller during peak

periods than during offpeak periods. Several factors might be of

-73-

importance in explaining these differences. During the peak period,
many drivers are traveling between work and.home. Befbre they reach
the position of queue leader, they most likely have spent a substantial
period of time in the queue. Furthermore, when they do become the queue
leader, it is likely that one or more vehicles are waiting behind. All
of these factors might be expected.to contribute some degree of impa-
tience.. Of possibly equal importanCe is the higher traffic volume, or
in other words smaller average gaps, on the main street during the peak
period. The driver who rejects a marginal lag or gap may have to wait
a substantial time fer another opportunity to cross or enter.

Reasonable explanations are also possible in the case of the
effects of direction of side street vehicle movement. 'During the peak
period, right turners had.a greater probability of accepting gaps of a '
given size in the lower half of the distribution. This difference may
be the reflection of three factors: (1) the right turners decision is
less complicated.since he needs to consider gaps in only one direction
of the main street; (2) since there are two lanes in each direction on
the main street studied, the main street vehicles may avoid conflict
'with an entering right turner by changing lanes; and (3) the few right
turning drivers who did use the widened.portiOn as an acceleration lane
could.accept smaller gaps. It was interesting that differences due to
direction of movement did.not appear in the offpeak.period sample. Thus,
an example of the appropriateness of a'data stratification procedure was
illustrated.

It is theorized that during offpeak periods drivers feel no special
compulsion to attempt to attain the maximum.performance capabilities of

themselves or their vehicles. 'Then during peak periods, when some degree

-71I-

of compulsion is working, reasonable lower boundaries on gap size
corresponding to maximized perfbrmance-are lower for right turns than
for the other movements. More succinctly, there is more room to
maximize right turn perfbrmance. ‘

There is also a logical basis fer explaining the results relating
to the sequence of main street vehicles.‘ At least three factors are
I believed to be important; (1) if the first car of the gap is on the
near side, it blocks the waiting driver's vision of far side main street
vehicles; (2) if the first car in the gap is on the near side, the
waiting driver cannot normally begin his entry into the intersection
until the near side car has passed; (3) if the-second car of the gap is
_ on the far side, the crossing driver must travel a longer distance to '
clear the area of conflict. In considering a far-near gap, the favorable
condition of all three of these factors are met, whereas in the case of
a near-far gap, all of the unfavorable conditions are working. Near-near
and far-far gaps have a mixture of favorable and unfavorable conditions.

It is also interesting to note that differences in gap acceptance
due to main street vehicle sequence were evident only during the peak
period. The previously discussed hypothesis concerning differences in
motivation and differences in ability to maximize performance could again
be applied.

The results gave no evidence that the presence or absence of a
vehicle on the opposite side street approach significantly affected.gap
acceptance. However, due to inadequacies in the sample size, the compari-
sons were made on distributions which included.both straight and left
turning vehicles. It would.be desirable to test the effects of conditions

on the opposite approach separately for left turns and straight movements.

- 75 -

The study of starting delay times of side street vehicles in
accepting lags and gaps yielded.results which can be closely correlated
with the driver decision data. It was readily apparent that the traffic
factors which had important effects on the acceptance-rejection decision
also influenced the distributions of starting delay times -- and in the
.same direction. For example, the average starting delay time in accept-
ing gaps was lower during periods of heavy traffic demand. It is
impossible to state with assurance that lower starting delays enable
shorter gaps to be accepted, or alternatively, that the decisions to
accept shorter gaps gauge the lower starting delays. Rather, it is
probably more accurate to say that both behavior characteristics are
affected similarly by common factors, such as impatience, degree of
motivation, and the reduced size of main street gaps presented to waiting
drivers.

Regarding another important factor, main street vehicle sequence,
which similarly affects starting delay and.gap acceptance, there is some'
reason to note a causal relationship. It is believed that a partial
reason fer far-near gaps being more readily acceptable is that the
position of the first car in the gap enables the'side street car to start
into the intersection sooner.

Another interesting parallel was that during offpeak.periods the
starting delay in accepting lags fer succeeding vehicles averaged over
one second lower than the starting delay for first in queue lag accept-
ances. To clarify the point, a first in queue lag acceptance was when
a vehicle arrived on a clear side street approach, stopped, and then
entered the intersection before the arrival of the first main street car.

A.succeeding vehicle lag acceptance was when the second car in a waiting

.75.

queue followed the queue leader into the intersection, in effect,
accepting the remaining portion of the gap which the leader accepted.
In most cases, the succeeding vehicle has been waiting second in line
long enough to become oriented to the decision process, and in effect
is observing the gaps in a manner similar to the queue leader. The
reader can verify this point if he has ever had.the common experience
of waiting second in line and commenting to himself or to a passenger,
"he should have taken that gap."

h.2 COMPARISON WIPE REIATED RESEARCH

The results of this study are compared with those Bissell (23),
Greenshields, et a1. (5), and.Raff (6) in.F&gure 33, on a logarithmic-
probability graph. Both Greenshields and Raff estimated central values
for lag acceptance; their results are plotted on the 50 percent line.
Bissell's straight line estimate of the lag and.gap acceptance is shown.

It is evident that the acceptance distributions determined in this
study had significantly higher central tendency than those found in any
of the other studies. The variance of Bissell's lag and gap acceptance
distribution, however, did not differ significantly from the present
findings.

It is believed that an explanation of the differences is related to
differences in the nature of the intersections studied. In particular,
the main street of this study was wider and carried higher speed traffic
than the main streets studied by the others. If one were to extend
Raff's conclusion that better sight distance is associated with higher
critical lags to the comparison at hand, the differences might be
attributed to the better sight distance at the intersection studied by

the writer. it is difficult, however, to expect that Raff's conclusion

-77;

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would hold for intersections with substantially different geometries and
traffic characteristics, such as the one studied.

Of special interest is a comparison of the studies of actual traffic
intersections and the controlled experimentation done by Herman and
weiss (12); their experimental data is also shown in Figure 33. It can
be seen that these data differ markedly from the rest. no lag smaller
than 3.2 seconds was accepted and none larger than h.2 seconds was
rejected. The point where their line crosses 50 percent corresponds to
only three to ten percent acceptance in the distributions of Bissell and
this study. Herman and.Weiss state ..."these experiments were rather
artificial in that the drivers were highly motivated and quickly adapt
to the situation...". However, their results are especially interesting
and useful in that they represent 'maximized' performance characteristics.
h.3 FUTURE RESEARCH.

The conclusions drawn from this research were based on observations
at only one intersection. It would seem interesting and important, there-
fore, to make similar studies of driver decisions and reactions, and the
effects of variable traffic factors thereon, at other intersections. If
such studies were to give strong verification of the conclusions pertain-
ing to the influences of traffic factors, an interesting topic of study
could be presented to the applied psychologist. One might approach the
problem of determining why one intersection has different gap acceptance
characteristics than another from a study of the underlying human factors,
rather than attempting to attribute differences to engineering features.

Certain specific items which could not be adequately handled in this
study might be of interest. Fbr example, the effects of direction of

movement, gap sequence, and conditions on the Opposite approach on lag

- 79 -

acceptance could not be studied here due to inadequate sampling.
‘ Studies might be undertaken to correlate the effects of variables on lag
and.gap acceptance. Another inadequacy was the inability to make a
really detailed study of the effects of conditions on the opposing
approach, particularly as related to the direction of movement of the
car in question and the car opposite. Further study of this factor
might prove fruitful. Although the effects of different types of
vehicles on the side street were studied, no consideration was given
to vehicle type on the main street. Studies to determine whether
acceptance of a gap in which the second.vehicle is a heavy truck differs
from the case in which the conflicting vehicle is a car might be of
value.
tun CONCIIJSION

The major findings of this research were:

1. The results strongly supported earlier findings which indi-
cated that the relationship between the logarithmic transform of lag or
gap size and the probability of acceptance follows a cumulative normal
distribution curve. Iag acceptance differed significantly from gap
acceptance.

2. Of the traffic factors studied, those which significantly
influenced the parameters of the lag and.gap acceptance distribution
were: pressure of traffic demand; direction of traffic movement during
periods of heavy traffic demand; and main street vehicle sequence during
periods of heavy demand.

3. No evidence was found to indicate that either side street
vehicle type or conditions on the opposing side street approach signifi-

cantly affected the gap acceptance distribution.

- 80 -

h. The results of the study of starting delay times in
accepting lags and.gaps indicated that factors which had important
influence on the driver decisions, namely pressure of traffic demand
and main street vehicle sequence, also had similar and significant
effects on starting delay time.

5. The components of delay to side street drivers were deter-
mined and are presented to enable those interested to validate the
results of their analytical and simulation model work.

In the final analysis, these effbrts are wasted unless the findings
can be applied. It is recalledthat theoretical treatment and simulation
both require the application of driver decision and reaction parameters.
In using either of these approaches to arrive at improved warrants-f0r.--
intersection control methods, broad ranges of traffic variables such-as
turning percentages, truck percentages, directional splits, and traffic
volumes must be studied. Realistic models would take into account signie
ficant changes in driver decisions and.reactions associated with these
variables. ‘

, In conclusion, therefore, it is h0ped.that this work will come to
the attention of others, be subjected.to verification, and finally, if

verified, applied to the solution of the problem at hand.

-‘81 -

l.

10.

ll.

13.

BIBLIOGRAPHY

National Committee on Uniform Traffic Laws and Ordinances,
Model Traffic Ordinance, 1956.

 

Iewis, R. M, and Michael, H. L., "The Simulation of Traffic Flow to
Obtain VOlume Warrants for Intersection Control, " a paper presented
to the h2nd.Annual.Meeting of the Highway Research Board, washington,
D. 0., January, 1963.

Nationa1.Joint Committee on Uniform Traffic Control Devices, Manual
on Uniform Traffic Control Devices for Streets and Highways, U. S.

 

Department of Commerce, Bureau of Public Roads Publication,
washington, D.C., June, 1961.

Gazis, D. C. and Potts, R. B., "The Oversaturated Intersection," a
paper presented at the Second International Symposium on the Theory
of Road Traffic Flow, London, England, June, 1963.

Greenshields, B. D., Schapiro, D. and.Ericksen, E. In, Traffic
Performance at Urban Street Intersections, Technical Report No. l,
Yale Bureau of Highway Traffic, l9h7.

 

Raff, M. B., "Space-Time Relationships at Stop Intersections,"
Proceedings of the Institute of Traffic Engineers, l9h9, pp h2-h9.

 

Tanner, J. C., "The Delay to Pedestrians Crossing a Road," Biometrika,
Volume 38, 1951, pp 383-392.

 

Mayne, At J., "Some Further Results in the Theory of Pedestrians and
Road.Traffic," Biometrika, VOlume hl, l95h, pp 375-389.

 

Cohen, J., Dearnaley, E. J., and Hansel, C. E. M., "The Risk Taken
in Crossing a Road," Operational Research Quarterly, Number 6, 1955,
pp 120.

Beckmann, M3, McGuire, C. B. and Winsten, C. B., Studies in the
Economics of Transportation, Yale University Press, New Haven, 1956,

PP 33-h2.

 

 

Little, J. C. D., "Approximate Expected Delays for Several Maneuvers
by a Driver in Poisson Traffic," Journal of Operations Research,
Volume 9, 1961, pp 39-52.

Herman, R. and weiss, G., "Comments on the Highway Crossing Problem,"
Journal of Operations Research, Volume 9, 1961, pp 828-8h0.

 

Oliver, R. M. and.Bisbee, E. F., "Queuing for Gaps in High Flow
Traffic Streams," Journal of Operations Research, volume 10, 1962,
pp lOS-llh.

 

582-

lh.

15.

16.

17..

18.

19.

20.

21.

22.

23.

2h.

25.

26.

weiss, G. H. and.Maradudin, A, At, "Some Problems in Traffic Delay,"
Journal of Operations Research, volume 10, 1962, pp 7h-10h.

 

Tanner, J. C., "A Theoretical Analysis of Delays at an Uncontrolled
Intersection," Biometrika, Volume #9, 1962, pp 163.

 

Evans, D. H., Herman, R. and weiss, G. H., "Queuing at a Stop Sign,"
a paper presented at the Second International Symposium on the Theory
of Road.Traffic Flow, Iondon, England, June, 1963.

webster's New Collegiate Dictionary, 1959 Edition, G. & C. Merriam

 

Company, Publishers.

Gerlough, D. L., "Simulation of Freeway Traffic on a General Purpose
Discrete variable Computer," Ph. D. Dissertation, U.C.LaA., June,

1955-

Goode, H. H., Pollmar, C. H. and wright, J. B., "The Use of a
Digital Computer to Model a Signalized Intersection," Proceedings
of the thhvay Research Board, Volume 35, 1956, pp 5h8-557.

 

 

Stark, M, C., Computer Simulation of Street Traffic, National Bureau
of Standards Technical Note 119, November, 1961.

 

Kell, J. H., “Analyzing Vehicular Delay at Intersections Through
Simulation," a paper presented at the hlst Annual Meeting of the
Highway Research Board, washington, D.C., January, 1962.

Robinson, C. C., "Pedestrian Interval Acceptance," Proceedings of
the Institute of Traffic Engineers, 1951, pp 1hh-150.

Bissell, H. H;, "Traffic Gap Acceptance From a Stop Sign," Master's
Thesis, University of California, Berkeley, May, 1960.

Dixon, W} J. and.Massey, F. J., Introduction to Statistical Analysis,
Second Edition, McGraw-Hill Book Company, Inc., 1957.

Finney, D. J., Statistical Methods on Biological Assay, Charles
Griffen and Company, limited, Iondon, 1952, pp 512-553.

walker, H. M. and Lev, J., Statistical Inference, Henry Holt and
Company, 1953. - ‘

'-83-

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