The Islamic University Gaza

Higher Education Deanship

Faculty of Engineering

Department Civil Engineering

Infrastructure Engineering

غزة – اإلسالمية الجامعة

العليا الدراسات عمادة

الهندسة كلية

قسم الهندسة المدنية

هندسة البنية التحتية

طعات على تقا للحركة الفرعية المتجهة لألمامو سلوك السائقين نمذجة قبول الفجوة الزمنية

في غزة الرباعية األولوية

Modeling Gap Acceptance and Driver Behavior for Minor Straight

Movement at Priority Four-Leg Intersections in Gaza

Submitted by:

Eng. Mustafa Abu Mudalalla

Supervised by:

. Dr. Essam Almasri

A Thesis Submitted in Partial Fulfillment of the Requirements for the Degree of Master

in Infrastructure Engineering

م 4103-هـ 5341

i

DEDICATION

I would like to dedicate this work to the soul of my father who was the light of my life,

my mother, my wife, my lovely kids Yazan, Karam and Nada, and my brothers for

their endless and generous support.

ii

ACKNOWLEDGEMENT

First and foremost, all praise is due to Allah, the Almighty, who gave me the strength,

opportunity and patience to carry out this work. I would like to express my sincere

gratitude and heartfelt thanks to Dr. Essam Almasri; the supervisor of my thesis, for his

strong support and guidance throughout the duration of this research. Deep thanks and

gratitude are also due to my father Mr. Waleed Abu Mudallala and my mother for their

infinite support and encouragement.

I would like to express my thanks to civil engineering students Ruba, Sahar and Rawan

for their help in data collection. I also offer great thanks to my brothers and my sisters

for their love and encouragements. I deeply thank my colleagues in the Civil

Engineering Department at the Islamic University of Gaza for their assistance during

this research.

Finally great thanks to my uncle Adham Abu Mudallala, because without his support

and love I couldn't finish this thesis.

iii

ملخص الدراسة

كر استدداما م يي ننوا التقاطعات المدتلةة يي المد الحر ية وهي األولوية هي األ تقاطعات

التقاطعات التي تتكو م تالقي شار رئيسي وشار ي عي حيث يوضع إشارة قف نو تمهل على الشار

معظم Capacityالة عي. إ عملية اتداذ الق ار يي نوعية التقاطع تعتمد على معايي مدتلةة منها سعة التقاطع

Gap Acceptanceتعتمد على نموذج قبول الةجوة الزمنية اذج ال ياضية لحساب سعة التقاطعالمعادالت والنم

Model يوجد العديد م النماذج المدتلةة والتي ارتكزت يي ينائها على ييانات لوحظت على سائقي يي الدول

هذه النماذج مةئمالالتدطيط والتصميم قبل التأكد م الغ يية وليس م الصواب استددام هذه النماذج يي عملية

يدتلف عنه م المتوقع ن للمد النامية كمدينة غزة على سبيل المرال وذلك ال سلوك السائقي يي المد النامية

يي المد المتطورة.

مدينة يي األولوية تقاطعات على السائقي لدى المقبولة الزمنية الةجوة ومالحظة م اقبة هو الدراسة هذه م الهدف

يناسب المقبولة يما الزمنية للةجوة نموذج ويناء معاي ة ثم وم الةجوة هذه على تؤث التي العوامل ودراسة غزة

تقاطع يي شار الجالء مقايل محطة الب ي ي للوقود حيث جمعت تم اختيار الهدف هذا لتحقيق البيئة المحلية.

حتى مناسب ارتةا على تكو يحيث الم كبات ح كة لتصوي مناسب موضع يي كامي ا ضع و خالل م البيانات

التقاطع وقد اقتص ت هذه الدراسة يقط على ح كة الم كبات المتجهة إلى األمام م الشار منطقة كل تغطى

ة ش طة الم ور.الط يق يواسط جانب الذي تم توقيةهم على السائقي مع استبيانات تعبئة نيرا الة عي وقد تم

و الةجوة الزمنية ثانية 1.3الح جة للناحية الق يبة كانت تق يبا التحليل اإلحصائي للبيانات يي ن الةجوة الزمنية

Highway Capacity Manualحسب ية ثان 7.06 ثانية وهي نقل م القيمة 1.2الح جة للناحية البعيدة كانت

(HCM)يحث الدراسةتق يبا و قد تم يي هذه %43 متوسط االختالف يزيد م سعة الح كة المدروسة ينسبة ا هذ

تأثي ما ال يقل ع عش ي عامال على الةجوة الزمنية والتي تصف خصائص السائقي و الم كبات و ال حالت و

قيمة الةجوة الزمنيةالةجوة هي قبول ق ار التي تؤث على العواملالح كة الم ورية . ويينت الدراسة ن م نهم

الذي يؤث على ق ار سائق يانتظار الةجوة و العاملو تأخي ال والمدة الزمنية لل حلةللسائق السي مدالةاتوعدد

. ياإلضاية إلى ذلك تم يناء نموذج )س عة السيارة القادمة( الذي يحدده السائق لقبول الةجوة الزمنية قبول الةجوة

لتقدي احتمالية قبول الةجوة الزمنية. رياضي

يي تةيد ن يمك الدراسة هذه نتائج ذلك إلى ياإلضاية غزة قطا يي نوعها م األولى ما يميز هذه الدراسة ننها

.غزة قطا يي المحلي للوضع مالئمة ونماذج نسس على المبني والتصميم التدطيط عملية

iv

ABSTRACT

Priority Intersections are the most commonly used among the different types of

intersections in urban cities. The decision-making process about the type of the

intersection depends on different criteria such as intersection capacity. Most of the

equations and mathematical models to calculate the capacity of the intersection depend

on Gap Acceptance Model. Existing models of gap acceptance are mostly based on data

observed for drivers in developed countries. It is not right to use these models in the

process of planning and designing before checking the suitability of these models for

developing cities like Gaza. This is because the behavior of drivers in developing cities

is expected to be different from the behavior in developed cities. Therefore, the aim of

this research is to study the factors that affect accepting gap acceptance in Gaza. It aims

also to build Gap Acceptance model to be suitable to be used in the local environment.

To achieve this goal, an intersection in El-Jalaa Street is selected as a case study. It is

located opposite to the AL-Barbary fuel station. The data was collected by using a

camera to observe the movement of vehicles, so it was located at a suitable height in

order to cover all area of the intersection. This research is limited to the through

movement from minor street to major street. Questionnaires have been filled by drivers

who have been stopped by policeman on the side of the road.

Statistical analysis of the data showed that the near side critical gap was almost 3.8

seconds, and the far side critical gap was 2.9 seconds, which is less than a value of 0.06

seconds calculated according to HCM. This difference increases the capacity of the

studied movement by an average of about 48%. This research studied the impact of

more than twenty factors on gap acceptance including driver, vehicles, trips and traffic

characteristics. The results showed that the most important factors that affects gap

acceptance were the gap value, the number of traffic accidents by driver, the trip

duration, the delay and the driver's gap acceptance criteria (speed). In addition to that, a

mathematical model was constructed to estimate the probability of accepting the gap.

This study is considered as the first of its kind in Gaza Strip. The results of this study

are useful in the planning and designing process which is based on appropriate

principles and models to the local situation in the Gaza Strip.

v

LIST OF CONTENTS

1 CHAPTER 1: INTRODUCTION .......................................................................... 1

1.1 Introduction ........................................................................................................ 1

1.2 Problem Statement ............................................................................................. 1

1.3 Research Aim and Objectives ............................................................................ 1

1.4 Research Importance .......................................................................................... 2

1.5 Research Scope and Limitations ........................................................................ 2

1.6 Brief Research Methodology ............................................................................. 3

1.7 Research Structure ............................................................................................. 3

2 CHAPTER 2: LITERATURE REVIEW ............................................................. 4

2.1 Gaza Background ............................................................................................... 4

2.1.1 History ........................................................................................................ 4

2.1.2 Geography ................................................................................................... 5

2.1.3 Population ................................................................................................... 5

2.1.4 Transportation System ................................................................................ 5

2.2 Definitions .......................................................................................................... 6

2.2.1 Priority Intersections ................................................................................... 6

1.1.1 Gap .............................................................................................................. 7

2.2.3 Lag .............................................................................................................. 8

2.2.4 Headway ..................................................................................................... 8

1.1.5 Follow-up Time .......................................................................................... 8

vi

1.1.2 Zero Gap ..................................................................................................... 9

1.1.0 Critical Gap ................................................................................................. 9

2.3 Gap Acceptance ............................................................................................... 11

2.4 Factors Affecting Driver's Gap Acceptance Decision ..................................... 13

2.4.1 Driver Characteristics ............................................................................... 14

1.4.1 Traffic Characteristics ............................................................................... 15

2.4.3 Gap Characteristics ................................................................................... 17

2.4.4 Vehicle Characteristics ............................................................................. 17

2.4.5 Intersection Characteristics ....................................................................... 18

2.4.6 Driver Inter-influence Factors .................................................................. 19

2.5 Measurement of Critical Gap ........................................................................... 19

1.5.3 Data Collection ......................................................................................... 19

2.5.2 Measurement of Critical Gap .................................................................... 20

2.5.3 Difficulties in Estimating Critical Gap ..................................................... 20

2.6 Models of Gap Acceptance .............................................................................. 21

2.6.1 Introduction ............................................................................................... 21

1.2.1 Lag & Gap Acceptance Modeling Techniques ......................................... 22

2.6.3 Gap Acceptance Models Used in Past Studies ......................................... 30

1.0 Previous Studies ............................................................................................... 33

1.0.3 Y. A. Abdul Kareem (2001) ..................................................................... 33

1.0.1 Rossi et al. (2012) ..................................................................................... 34

2.7.3 Rui-jun Guo & Bo-liang Lin (2011) ........................................................ 35

vii

2.7.4 Rene Lord-Attivor & Manoj K. Jha (2012) .............................................. 37

2.7.5 Sahar Nabaee, Derek Moore, & David Hurwitz (2011) ........................... 38

2.7.6 Gopal R. Patil, Prasad Patare & Jayant P. Sangole (2011) ....................... 39

1.0.0 Sun Yon Hwang & Chang Ho Park (2005) .............................................. 40

2.7.8 J. L GATTIS and SONNY T. LOW (1998) ............................................. 41

1.3 Summary .......................................................................................................... 43

3 CHAPTER 3: RESEARCH METHODOLOGY ............................................... 46

3.1 Main research phases ....................................................................................... 46

3.2 Preliminary Phase ............................................................................................. 47

3.2.1 Literature Review ..................................................................................... 47

3.2.2 Problem Formulation ................................................................................ 47

3.2.3 Proposed Model ........................................................................................ 48

3.3 Data Collection Phase ...................................................................................... 48

3.3.1 Study Site .................................................................................................. 48

3.3.2 Data Collection ......................................................................................... 52

3.3.3 Data Coding & Processing ........................................................................ 56

3.3.4 Data Organizations ................................................................................... 58

3.3.5 Sample Size ............................................................................................... 59

3.4 Model Specifications ........................................................................................ 59

3.4.1 Model Description .................................................................................... 59

3.4.2 Method of Model Work ............................................................................ 60

3.4.3 Model Variables ........................................................................................ 62

viii

4 . CHAPTER 4: RESULTS AND DISCUSSION ................................................ 68

4.1 Data Description ............................................................................................... 68

4.2 Traffic Count .................................................................................................... 69

4.2.1 Traffic count data ...................................................................................... 69

4.2.2 Traffic count Results ................................................................................. 70

4.3 General Statistics for the Collected Data ......................................................... 74

4.4 Analysis of The Critical Gap/Lag .................................................................... 79

4.4.1 Morning Period Critical Gap Values ........................................................ 79

4.4.2 Morning Period Critical Lag Values ......................................................... 81

4.4.3 Afternoon Period Critical Gap Values ...................................................... 83

4.4.4 Afternoon Period Critical Lag Values ...................................................... 85

4.4.5 Intersection Critical gap/lag Values .......................................................... 87

4.4.6 Factors Affecting Critical Gap Values ...................................................... 92

4.5 Comparing Critical Gap Value......................................................................... 94

4.5.1 Morning Critical Gap values ..................................................................... 95

4.5.2 Afternoon Critical Gap values .................................................................. 95

4.6 Comparing Potential Capacity Value ............................................................... 96

4.7 Gap Acceptance and Driver Behavior Models ................................................. 97

4.7.1 Gap Model Calibration and Validation ..................................................... 98

4.7.2 Other Gap/lag Models ............................................................................. 104

4.7.3 Driver Response to Near side/Far side Gaps/Lags ................................. 105

ix

5 CHAPTER 5: CONCLUSIONS AND RECOMMENDATIONS ................... 108

5.1 Introduction .................................................................................................... 108

5.2 Conclusion...................................................................................................... 108

5.3 Recommendations .......................................................................................... 109

REFERENCES ............................................................................................................ 110

ANNEX 1: Questionnaire ........................................................................................... 113

ANNEX 2: Critical Gap Graphs for Factors ............................................................ 114

ANNEX 3: Conflicting Flow ..................................................................................... 134

ANNEX 4: Details of Gap Model ............................................................................... 135

ANNEX 5: Details of Far Side Gap Model ............................................................... 138

ANNEX 6: Details of Near Side Gap Model ............................................................. 142

ANNEX 7: Details of Lag Model ............................................................................... 146

ANNEX 8: Details of Near Side Lag Model ............................................................. 150

ANNEX 9: Details of Far Side Lag Model ................................................................ 154

x

LIST OF ABBREVIATIONS

CA Cellular Automata

GAPS Gap Acceptance Processing System

HCM Highway Capacity Manual

NOCC3 Night Owl Cyclops Compact Monocular

PC Passenger Car

PCBS Palestinian Central Bureau of Statistics

PCI Priority Controlled Intersections

PHF Peak Hour Factor

SD Standard Deviation

Sec Second

SPSS Statistical Package for the Social Sciences

STSoftware Driving Simulators for Driver training and Assessment

TOD Time of the Day

TWSC Two-Way Stop-Controlled

xi

LIST OF TABLES

Table 3.1: Information of the Observer Record .............................................................. 58

Table 3.2: Information from Roadside Interviews .......................................................... 58

Table 3.3: Information from Video Record .................................................................... 58

Table 3.4: Gap Acceptance Variables ............................................................................. 66

Table 4.1: Summary of the collected data ...................................................................... 68

Table 4.2: Traffic count for near side-morning .............................................................. 69

Table 4.3: Traffic count for far side-morning ................................................................. 69

Table 4.4: Traffic count for near side-afternoon ............................................................. 70

Table 4.5: Traffic count for far side-afternoon ............................................................... 70

Table 4.6: Traffic count results for near side-morning ................................................... 71

Table 4.7: Traffic count results for far side-morning ..................................................... 71

Table 4.8: Traffic count results for near side-afternoon ................................................. 71

Table 4.9: Traffic count results for far side-afternoon .................................................... 71

Table 4.10: Basic Descriptive statistics for uncategorized variables .............................. 74

Table 4.11: General statistics for interviewed drivers .................................................... 76

Table 4.12: Accepted/rejected gaps and lags for interviewed drivers ............................ 78

Table 4.13: Gap/lag values summary ............................................................................. 91

Table 4.14: Average gap/lag values ................................................................................ 92

Table 4.15: Critical gap at different levels of the studied variables ............................... 93

Table 4.16: Base critical gaps and follow-up times for TWSC intersections. ............... 95

xii

Table 4.17: Potential capacity compare. ......................................................................... 97

Table 4.18: Gap Model Details. ..................................................................................... 99

Table 4.19: Significant Variables of Gap Models in Past Studies. ............................... 103

Table 4.20: Result of Independent Samples T- Test between Lag and Gap. ............... 105

Table 4.21: Proportions between "Lag" and "Gap" for Rejected/Accepted Gap.......... 106

Table 4.22: Result of Independent Samples T- Test between Far Side Gap and Near

Side Gap. ....................................................................................................................... 107

Table 4.23: Result of Independent Samples T- Test between Far Side Lag and Near Side

Lag. ............................................................................................................................... 107

xiii

LIST OF FIGURES

Figure 3.1: Research Methodology Diagram .................................................................. 46

Figure 3.2: Illustration of Straight Movement ............................................................... 49

Figure 3.3: Intersection Google Maps Picture ................................................................ 51

Figure 3.4: Intersection Photo from Filming Location ................................................... 51

Figure3.5: Illustration of Near/Far Side Gap Types Diagram ........................................ 53

Figure 4.1: Vehicle type percentages-Near side morning ............................................... 72

Figure 4.2: Vehicle type percentages-Far side morning ................................................. 72

Figure 4.3: Vehicle type percentages-Near side afternoon ............................................. 73

Figure 4.4: Vehicle type percentages-Far side afternoon ............................................... 73

Figure 4.5: Near side critical gap-Morning .................................................................... 80

Figure 4.6: Far side critical gap-Morning ....................................................................... 80

Figure 4.7: Critical gap-Morning .................................................................................... 81

Figure 4.8: Near side critical lag-Morning ..................................................................... 82

Figure 4.9: Far side critical lag-Morning ........................................................................ 82

Figure 4.10: Critical lag-Morning ................................................................................... 83

Figure 4.11: Near side critical gap-afternoon ................................................................. 84

Figure 4.12: Far side critical gap-afternoon .................................................................... 84

Figure 4.13: Critical gap- Afternoon .............................................................................. 85

Figure 4.14: Near side critical lag-afternoon .................................................................. 86

Figure 4.15: Far side critical lag-afternoon .................................................................... 86

xiv

Figure 4.16: Critical lag-afternoon ................................................................................. 87

Figure 4.17: Intersection near side critical gap ............................................................... 88

Figure 4.18: Intersection far side critical gap ................................................................. 88

Figure 4.19: Intersection near side critical lag ................................................................ 89

Figure 4.20: Intersection far side critical lag .................................................................. 89

Figure 4.21: Intersection critical gap ............................................................................. 90

Figure 4.22: Intersection critical lag .............................................................................. 90

1

1 CHAPTER 1: INTRODUCTION

1.1 Introduction

Priority Intersections are the most commonly used among the different types of

intersections in urban cities. Priority intersection is an intersection which is controlled

by stop/yield signs, without a traffic signal or police existence. The decision-making

process about the type of the intersection depends on different criteria such as

intersection capacity. Most of the equations and mathematical models to calculate the

capacity of the intersection depend on Gap Acceptance Model. This model is based on

driver behavior.

Driver behavior at priority intersection depends on decision making process. Therefore,

the interest of the researcher is to understand how driver takes his decision in accepting

or rejecting the gap, and to study the factors affecting decision process.

1.2 Problem Statement

Existing models of gap acceptance are mostly based on data observed for drivers in

developed countries. It is not right to use these models in the process of planning and

designing before checking the suitability of these models for developing cities like

Gaza. This is because the behavior of drivers in developing cities is expected to be

different from the behavior in developed cities. Intersection analysis throughout various

countries is performed using various traffic models. These models are formulated using

ideal value and based on data observed on drivers in developed countries. Various

parameters such as gap values are developed to suit ideal field conditions based on

research data collected from the respective country.

1.3 Research Aim and Objectives

Giving this context, the aim of this research is to observe the gap accepted by drivers on

priority junctions in Gaza City, and to study the factors that affect gap acceptance.

The objectives of this research are:

1. To define and understand the concept of critical gap at four legs priority

intersection (not separated).

2

2. To monitor and observe the accepted critical gap at priority intersection in Gaza.

3. To study the factors affecting gap acceptance.

4. To compare observed data of critical gap with those obtained from the Highway

Capacity Manual (HCM) and other models.

5. To build and calibrate a gap acceptance model (formula) suitable for Gaza.

1.4 Research Importance

This study is considered as the first in Gaza Strip, and one of few studies in developing

countries. The results of this study will be useful in traffic planning and designing

process in Gaza. The study results will help in taking right decision for intersection

types and intersections designing.

The output model of this study for estimating probability of accepting critical gap is

suitable for local environment and commensurate with Gaza driver behavior.

1.5 Research Scope and Limitations

The scope of this study will be limited for intersections in Gaza city only. The reason

for this limitation is the time and financial constraints. Additional research limitations

are as follow:

1. The research is limited to the relationship between driver behavior and gap

acceptance at Four-leg-intersections for straight movements from the minor road to the

major road.

2. Some of the factors that are not considered in the research are as follows: factors

related to the detail geometrical design of the intersection; factors related to drivers'

psychological and socio-economic status; factors related to weather, pavement and light

conditions; and the in-vehicle environment of the driver. These factors are not

considered in this research because they either would complicated the research goals or

don't have a significant impact on the driver’s decision to accept or reject a gap.

3. Data for the research are collected during peak hours in the morning and afternoon

when weather conditions are ideal (i.e., dry pavement) with unrestricted sight distance.

3

1.6 Brief Research Methodology

The methodology of this study starts with the literature review on critical gap. The

concentration is on estimating critical gap values in developing countries and it's

relation to driver's behavior in priority intersections. The literature review seeks for case

studies applied in cities of developing countries especially in the cities that have similar

conditions.

After carrying out the literature review and deciding which approach is suitable for

Gaza, data collection is carried out. The data collected is based on simultaneous use of

video camera and field administrated questionnaire. Video camera is used to record

traffic operation at study site. Video tapes are later viewed to extract traffic data. The

questionnaire is designed to collect factors that affect driver's gap acceptance behavior.

Based on data collected from video records & questionnaires, analysis of the data using

SPSS & Excel programs is done. Data collected is used to model building and

validation. Finally the main findings and conclusion are summarized.

1.7 Research Structure

This thesis is organized into five chapters:

Chapter one presents the introduction chapter which includes background, problem

definition, objectives, scope of the study significance of the study and research

methodology.

Chapter two reviews briefly the literature related.

Chapter three describes the methodology , approach for the analysis and evaluation of

the results.

Chapter four includes description of the data and variables, determine the values of

critical gaps and determine the model that has been reached in the study of the behavior

of drivers and a statement of the most important factors affecting the decision-making.

Chapter five includes conclusions and recommendations in addition to some thoughts of

future researches.

4

2 CHAPTER 2: LITERATURE REVIEW

This chapter presents the related definitions and summarizes the basic findings of the

conducted literature review regarding factors that affecting driver's gap acceptance

behavior, data collection procedures, methods of calculating critical gap and gap

acceptance models. As the aim of this research is to study the critical gap in Gaza City,

a brief background on Gaza city is first presented.

2.1 Gaza Background

Gaza city is one of the oldest cities in the world which was established in about 3000

B.C. The modern paved road began in Ottoman period. Jafa-Jerusalem road was the

oldest which was constructed in 1867. Gaza city area is 74 km2. It contains many

ministries, universities and institutions (Shaat in Al-Jazzar,2012).

Gaza city is the main and the largest city in Gaza Strip. It has the highest concentration

of institutions. Gaza city transportation network suffers from traffic congestion in

different spots.

2.1.1 History

Arab Canaanites tribes were the first inhabitants in Palestine and in Gaza city around

3000 BC. They construct cities, roads and urban life, and they developed an alphabet.

From the beginning and because of its location Canaanites land was a battlefield among

the great power and empires. Muslim Arab army’s conquest of Palestine was in 638.

The Muslim control continued on Palestine till the Ottoman period until 1917. After the

First World War, British captured Palestine from Ottoman Turks in 1917. Then

Palestine was fallen under British mandate. During this period, more and more Jews

immigrated to Palestine and started to organize terrorist groups. In 1948, the

establishment of the Jewish state was announced on all the Palestinian land except Gaza

strip and west bank. Gaza strip was fallen under Israeli occupation in the six day war in

1967. In 1987, the Palestinian uprising has begun, until the city was returned in 1993 to

the Palestinian self-rule after Oslo agreement. In 2000, the second Palestinian uprising

was launched. In 2005, Israel removed all its settlements from Gaza Strip and withdrew

its forces. Israel set a blockage on Gaza strip after Hamas victory in the Legislative

5

Council election in 2006, and launched several aggressions on Gaza strip in 2008 and

2012 (Shashaa, in Al-Jazzar,2012).

2.1.2 Geography

The Gaza city is located in Gaza Strip; which is a coastal strip on the Mediterranean

Sea. Gaza Strip is bordered by Sinai desert in the South and the Mediterranean sea in

the West and (Israel) settlements in the East and North. The city is located between two

continents; Africa and Asia. This geographical location gives the city special economic,

military and transportation status. Gaza has warm rainy climate winters and humid, hot

summers, with relatively small amount of rain fall in winter between 200 to 400 mm,

while the main source of drinking water of Gaza city is the ground water (Wikipedia,

2012).

2.1.3 Population

Gaza city has the largest Population Density in the Palestinian territory, according to a

2009 census by the Palestinian Central Bureau of Statistics (PCBS). Gaza city had a

population of 526,793 inhabitants. And a Population Density equals to 7,119

(Person/km2). Most of the Gaza population is Muslim and there is a small Palestinian

Christian minority of about 3500 inhabitants (PCBS, 2010).

2.1.4 Transportation System

Gaza city road network combines between the Radial network system in the old part of

the city and Grid system in the new part of the city. The Ministry of housing and public

work as cited by Palestinian Central Bureau of Statistics explained that the total Gaza

city network length in 2010 was 62 Km. The roads are divided into three main

categories which are Main, Regional and local roads (PCBS, 2010).

Gaza city traffic composition includes private cars, taxis, buses, trucks, motorcycles,

tuktuki, and others. According to Palestinian Central Bureau of Statistics the total

number of licensed Vehicles in Gaza strip in 2012 equals to 60,901veh (PCBS, 2012).

Transportation system in Gaza Strip consists of road transport only. The Gaza strip has

a small and poorly developed road network. The road network consists of 61 km of

main roads, 57.8 km of regional roads and 511 km of local road (PCBS, 2007). There

6

was a single railway line running from north to south along its center. The main road in

Gaza city is Salah al-Din road, which passes through the middle of Gaza City. The Road

runs also along Gaza Strip from Rafah Crossing on Egypt border to Erez Crossing on

Isreal border. Some of other important roads are Omer Almokhtar, Jamal Abed al naser,

Al Jlaa, Al Nasr and Alwehda road.

Most governmental and non-governmental organizations are located in Gaza city and

concentrated in the middle part resulting in serious traffic congestion especially in major

arterial roads (Almasri , 2012).

2.2 Definitions

2.2.1 Priority Intersections

Oflaherty as cited in Almasri (2012) identified the intersection as an area shared by two

or more roadways and its main role is to allow the change of route directions.

Priority intersections can be defined as intersections that are controlled by a stop or

yield sign, or a flashing beacon (Rene & Manoj 2012, Abdul Kareem 2001).

Abdul Kareem (2001) detailed the definition as it is a one which has a major road and a

minor road crossing each other at the same level. At such an intersection the major road

traffic has the right of way over the minor street vehicles whenever conflicts occur. The

traffic flow is prioritized in the following order:

1. Major road through traffic,

2. Major road right turning traffic,

3. Major street left turning traffic,

4. Minor street through traffic, and

5. Minor street left turning traffic.

According to Rene & Manoj (2012), intersections controlled by signs (i.e., stop or yield

signs) have been proven to be the most complex type of intersection to analyze. The

geometry of unsignalized intersections ranges from T-intersection (three–legged) to

cross intersections (four-legged) to multi-legged intersections.

7

Bottom & Ashworth (2007) see that priority intersections are the scene of considerable

traffic delays and numerous accidents.

Garber & Hoel (in Al-Jazzar ,2012) stated that traffic control aims to provide efficient

and safe operating system for all of the traffic movements on highways. Traffic control

may be achieved by using traffic signals, signs, or markings to regulate the traffic

movement. To insure a proper control type for any intersection the control device must

be simple and clear and should placed in the driver cone of vision and in suitable place

to allow adequate response time when driving at normal speed.

The majority of existing intersections in Gaza city are priority controlled; because

priority controlled intersections (PCI) have two main advantages. The first is that the

main road flow is not delayed. The Second is that the (PCI) is the most economical

intersection control method (Al-Jazzar, 2012).

2.2.2 Gap

A gap can be defined as the time interval between the passage of two successive

vehicles on the major road at a priority intersection (Abdul Kareem 2001, Abu Sheikh

1997, Dissanayake, LU , Ping 2001).

Gattis & Sonny (1998) defined the gap as the time interval between passage of one

vehicle and the arrival of the next vehicle. In strict technicality, the gap is measured

from the back bumper of the front vehicle to the front bumper of the next vehicle.

Other studies like Kearney et.al (2006) and Patil, Patare & Sangole (2011) defined the

gap between two vehicles as the interval of time between the moment the rear of the

lead vehicle reaches the crossing line to the moment the front of the tail vehicle reaches

the crossing line .

While Hwang & Park (2005) stated that: “Gap” means the time and space that a subject

vehicle needs to merge adequately safely between two vehicles.

HCM (2000) defined the gap as "the time in seconds for the front bumper of the second

of two successive vehicles to reach the starting point of the front bumper of the first".

8

2.2.3 Lag

Gattis & Sonny (1998) and Abdul Kareem (2001) defined the lag as the time interval

between the arrival of a side street vehicle at an intersection and the arrival of the next

main street vehicle.

Patil , Patare & Sangole (2011) and Abu Sheikh (1997) defined it as the time elapsed

after a right turn intended vehicle reaches the stop line until a major approach

conflicting vehicle reaches the conflict point.

Adebisi (in Abu Sheikh, 1997) also stated that lag is the portion of the last gap in the

major stream remaining when a vehicle at minor road reaches the intersection point

from which it is ready to execute the desired maneuver.

2.2.4 Headway

Guo & Lin (2011) and Patil , Patare & Sangole (2011) defined headway as the time

distance from front bumper to front bumper between two successive vehicles passing an

observation point.

Traffic control system handbook as cited in Gattis & Sonny (1998) defined headway as

the time interval between the arrival of two successive vehicles. Headway differs from

gap because it is measured from the front bumper of the front vehicle to the front

bumper of the next vehicle.

Luttinen (in Guo & Lin ,2011) saw that it is the sum of the time used by a vehicle to

pass the observation point (occupancy time) and the time interval (gap) to the arrival of

the next vehicle .

Troutbeck and Brilon (in Guo & Lin , 2011) stated that headways are considered equal

to gaps if one ignores the differences in major-stream vehicle lengths and speeds.

Gattis & Sonny (1998) defined minimum headway as the minimum gap maintained by a

vehicle in the major traffic stream.

2.2.5 Follow-up Time

The follow-up time is defined in the HCM (1994) as the time span between the

departure of two consecutive opposed vehicles that use the same gap under a approach.

9

HCM (2000) has similar definition as the time between the departure of one vehicle

from the minor street and the departure of the next vehicle using the same gap under a

condition of continuous queuing.

The HCM suggested standard values for the follow-up time ranging from 2.1 sec to 3.4

sec (Velan & Aerde, 1996).

Kyte (in Gattis & Sonny ,1998) defined the follow-up time as the minimum headway

between first vehicle and the second vehicle, and subsequent vehicle pairs, as they enter

the same major stream gap when a continuous queue exists on the minor street

approach.

As quoted by Panchavati (in Gattis & Sonny ,1998) he assumed that there is a fixed

dependency of follow-up time and gap time according to the following equation:

Follow up time = 0.6 Gap time (1)

2.2.6 Zero Gap

Zero gap can be defined as the gap size in major street traffic that was not used by any

minor street vehicles' (Kyte et al. in Gattis & Sonny ,1998).

2.2.7 Critical Gap

The critical gap is the time interval between two successive vehicles considered to be

just adequate for a minor road vehicle' enter or cross the main road (Abdul Kareem

2001, Abu Sheikh 1997).

Critical gap is the threshold by which drivers in the minor stream judge whether to

accept a gap. If the gap is larger than critical gap, drivers accept it and enter the

intersection; otherwise, drivers reject the gap and wait for the next gap. Many previous

researchers assume that critical gap is a fixed value (Guo & Lin, 2011).

Guo & Lin (2011) had another definition for critical gap which can be described as

follows:

10

1. When the ratio of the probability of accepted gaps not larger than a fixed value and

the probability of rejected gaps larger than that value is equal to the ratio of total

rejected coefficient and total accepted coefficient, such a value is the critical gap; or

2. Critical gap is the gap in a major stream whose cumulative probability is equal to the

total rejected coefficient.

Drew (in Nabaee, Moore & Hurwitz, 2011) defined the critical gap as the size of the gap

for which half of all traffic will reject larger gaps while half will accept smaller gaps .

While Roess (in Nabaee, Moore & Hurwitz, 2011) assumed that the most commonly

accepted definition for critical gap is the minimum usable gap accepted by the minor

approach drivers.

The HCM (1985) defined critical gap as the median time headway between two

successive vehicles in the major street traffic stream that is accepted by a driver in a

subject movement that must cross and/or merge with the major street flow.

HCM (1994) defined critical gap as "the minimum time interval between vehicles in a

major traffic stream that permits side-street vehicle at a stopped controlled approach to

inter the intersection under prevailing traffic and roadway conditions in seconds" .

HCM (2000), had similar definition which is "the minimum time in seconds, between

successive major stream vehicles in which a minor street vehicle can make a maneuver.

Raff (in Patil, Patare & Sangole, 2011) defined the critical gap as the gap for which the

number of accepted gaps shorter than it is equal to the number of rejected gaps longer

than it.

2.2.7.1 Rate of Temporal Decay of the Critical Gap

It is common knowledge that, as motorists wait at the stop line for an acceptable gap in

the opposing traffic stream, they may become impatient and be willing to accept a

smaller gap: This temporal decay of the required critical gap arises primarily from an

increase in driver aggressiveness. The smaller critical gap may also be a result of

improved decision times, reduced maneuver times due to quicker acceleration, and a

11

willingness by the motorist to accept reduced comfort and safety in exchange for a

shorter time (Velan & Aerde ,1996).

2.3 Gap Acceptance

Gap acceptance or rejection is fundamental to the description and understanding of

traffic movement at priority or stop sign intersections.

Gap acceptance is the decision of a side-street (minor road) driver to use a gap created

in a major road traffic to merge or maneuver safely with the major road traffic. A gap

may be accepted if it is large enough or rejected if it is too small. Thus it is expected

that the acceptance of an available gap by a driver depends hot only on the size of the

gap but also on the drivers' sensitivity to such a gap (Abdul Kareem , 2001).

Nabaee, Moore & Hurwitz (2011) assumed that drivers on minor approaches have

shown a tendency to accept a gap when "the benefit from entry is greater than the

associated risk". When the waiting time exceeds the drivers' expectation and tolerance

limit, they will accept higher levels of risk associated with smaller gaps.

Darzentas (in Abu Sheikh, 1997) defined gap acceptance behavior as : The decision

making process of whether or not to enter the path of an oncoming vehicle.

Golias (in Abu Sheikh, 1997) defined gap acceptance function as: The function that

defines the probability of accepting a randomly selected gap by certain driver.

Gattis & Sonny (1998) illustrate the difference between accepting gap & lag as follow.

When entering an intersection, all drivers decide whether to accept or reject a lag or

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

the arrival of the first main street vehicle. A gap is accepted if the side street vehicle

crosses or enters between the arrivals of two main street vehicles that form a gap.

Wagner (in Gattis & Sonny, 1998) concluded lag and gap acceptance differed at a 0.05

level of significance, while Adebisi (1982) assumed lag and gap acceptance values

were similar if drivers come to a complete stop.

12

“Reject gap” is the time interval that subject vehicle fails to enter a main lane due to the

main lane’s vehicle obstacle flow. “Maximum reject gap” is the largest reject gap in the

middle of the reject gaps of the individual vehicles (Hwang & Park, 2005).

Robertson (in Abu Sheikh, 1997) explained the accepted/ rejected gap or lag as: Gap or

lag that a minor stream driver uses (accepts) to move into the major stream while

rejected gap or lag is one which the minor stream driver does not use.

Cooper and Wennell (in Abu Sheikh, 1997) defined queue acceptance as : Acceptance

of large gaps in major stream by two or more drivers waiting on minor road in a queue.

Rene & Manoj (2012) described gap acceptance as follows:

This decision of gap acceptance is guided mainly by two motives:

- To minimize the total travel time when entering the main road.

- To proceed as safely as possible onto the main road.

As the opposing flow rate on the main road increases, the two motives conflicts with

each other, which makes the decision to accept or reject a gap difficult to understand.

This process may lead to two different choice model forms;

- The choice among different available gaps.

- The choice to accept or reject the current gap.

In 1985, Ben-Akavia and Lerman described the choice of accepting or rejecting a gap in

their research as a function of the following:

- Defining the choice problem.

- Developing or generating various alternative choices.

- Evaluating the alternative choices.

- Choosing one of the evaluated choices.

- Implementing the chosen choice.

13

Troutbeck (in Abu Sheikh ,1997) described the gap acceptance theory as: The theory

that deals with driver gap acceptance behavior and it bas two elements :

a. Measurement of the usefulness of a gap of (t) seconds long to an entering driver

measured by gap acceptance parameters (critical gap, move-up time);

b. Estimation of the frequency of acceptable gaps of duration, t, in the opposing traffic

stream.

Theory of choice: A collection of procedures which define decision maker, available

alternatives, alternative attributes and characteristics, and the decision rule (mechanism

used by decision maker to process available information and decide at a unique choice)

(Ben-Akiva and Lerman ,1985).

Despite the large number of research studies conducted on the gap acceptance

phenomenon, there still remains a lack of understanding the driver’s decision to accept

or reject a gap.

2.4 Factors Affecting Driver's Gap Acceptance Decision

In the past years, researchers have made an effort to investigate the factors that affect

the driver's gap acceptance/rejection decision. The studies showed no consistency with

their conclusion which proves the complexity in the gap acceptance theory.

The driver’s characteristics, traffic's characteristics, vehicle characteristics, trip's

characteristics, and intersection characteristics play a major role in the driver’s behavior

at the intersection.

Drivers in Gaza Strip do not usually comply with the traffic law and do not usually

respond positively to the needs of other drivers and also they do not usually behave well

at road intersections (Sarraj, 2001).

Researchers have found that the relationship between the driver’s behavior and the gap

acceptance or rejection is difficult to understand and to model as drivers having

different personal characteristics and attributes.

14

2.4.1 Driver Characteristics

Human (driver) behavior on transportation networks always plays a major role in the

flow of traffic.

Driver factors which affect gap acceptance behavior include driver age, sex, level of

education, level of familiarity with area (Tupper, Jr Knodler & Hurwit 2011, Farah et al.

2007, Adebisi 1982, Abu Sheikh 1997, Juo & Lin 2011, Rene & Manoj 2012, Kearney

et al 2006, Bottom & Ashworth 2007, Gattis & Sonny 1998, Dissanayake, LU , Ping

2001).

Old and female drivers need longer gaps (Abu Sheikh, 1997).

The older driver especially older female driver showed a conservative driving attitude as

a compensation for reduced driving ability but also showed to be the most vulnerable

group for relatively complex driving (Patil , Patare & Sangole, 2011).

Dissanayake, LU, Ping (2001) stated that there are statistically significant differences in

gap acceptance capabilities among the three considered driver age groups. older drivers

required significantly longer gaps during nighttime.

Connelly et al. (in Hunt, Harper & Lie, 2011) found an evidence that gap-acceptance

decisions improve with age, with adults making better decisions than older children who

make better decisions than younger children.

Adebisi (1982) , Abu Skheik (1997), Abdesi & Sama (1989) and Bottom & Ashworth

(2007) have mentioned driver experience, "previous year mileage", as a possible factor

which can affect driver gap acceptance behavior.

Some researchers indicated that it is the ability of minor stream driver to guess the

correct speed of the major stream vehicle that affects his behavior (Troutbeck in Abu

Skheik 1997, Rene & Manoj 2012).

Kearney et al. (2006) found that more cautious drivers are more likely to reject small

gaps than less cautious drivers (who are likely to jump at the first reasonable chance to

cross.

15

Velan & Aerde (1996) indicated that the critical gap is the sum of several components:

the decision time required by the motorist to accept a gap, and a buffer time for the

opposed driver to feel comfortable and safe.

2.4.2 Traffic Characteristics

A main factor that affect gap acceptance is the traffic flow rate at main road (Adebisi

1982, Abu Sheikh 1997, Guo & Lin 2011, Rene & Manoj 2012, Abdul Kareem 2001).

Ignoring the influence of traffic volume at main road may lead to more than 100 %

errors in the estimated values of critical gaps (Adebisi, 1982).

However, results about the effect of major stream volume are not in full agreement, as

Wohl and Martin (in Abu Sheikh, 1997) showed that no significant difference in gap

acceptance behavior was observed for two average main stream volumes of 470 and 620

vehicle per hour. In Nigeria, Adebisi (1982) investigated the effect of major traffic flow

on drivers' gap acceptance behavior . The data showed that the estimated critical gap

was larger than the aggregated critical gap for low major traffic flow and conversely,

the critical gap was smaller for high major traffic flow. Tian et al. (2000) showed that

drivers use shorter critical gap at higher flow (and hence delay) conditions. And with

the increase of major stream volume or minor stream vehicle delay, drivers tend to seek

smaller gaps. However, driver’s critical gap cannot be reduced to the minimum

threshold probably determined by the follow-up time value or the maximum rejected

gap value.

Another traffic factor that affects driver gap acceptance behavior is delay or waiting

time at minor road. Driver critical gap will probably decrease as the amount of time

waited increases (Adebisi 1982, Ashworth and Bottom 2007, Abu Sheikh 1997). Abdul

Kareem (2001) indicated that one of the parameters that can be used as indirect

measures of driver’s sensitivities to gap is duration of stopped delay experienced by the

side street driver before the gap becomes available. Bottom & Ashworth (2007) found

that waiting time was found to increase the probability of a given size gap being

accepted. Tian et al. (2000) found that with the increase of delay, the critical gap tends

to decrease. For the two particular sites analyzed, the driver’s critical gap is about 5.5

seconds when the average delay is short (less than 40 sec/veh). Also Kearney et al.

(2006) indicate that drivers who experience long waits will accept smaller gaps.

16

Madanat et al in (Abu Sheikh, 1997) stated that number of previously rejected gaps is

merely another measure of delay. They also stated that the latter represents the situation

better. Furthermore, Madanat, et at. have modeled stop bar and queue delays separately

but they found that it is better to combine both in one variable termed "total delay" .

Another traffic factor that affect driver gap acceptance behavior is the speed of the

oncoming vehicle (Adebisi 1982, Abu Sheikh 1997, Guo & Lin 2011, Rene & Manoj

2012). Again, reported effects of this factor are controversial. Some studies indicated

that critical gap length would increase as speed increases. Other studies revealed a

negative effect of speed on gap acceptance. In general, Ashworth and Bottom (2007)

have found that the minimum acceptable gap "critical gap" decreases as oncoming

vehicle speed increases & drivers are prepared to accept shorter gaps when fast vehicles

are approaching.

Hunt ,Harper & Lie (2011) in their study stated that number of studies have indicated

that drivers may rely solely or heavily on distance when making gap assessments; that

is, they accept or reject gaps based on how far away the oncoming vehicle is and neglect

the speed of that vehicle. Drivers having relatively large critical gaps are making

decisions when approaching vehicles are farther away and therefore errors are likely to

be larger.

Another factor also was discussed by Abu Sheikh (1997) as he found that queue size at

minor road is not a significant factor in gap acceptance decision. Kyte et al. (in Gattis &

Sonny,1998) explained how a long queue-waiting time may reduce the driver's critical

gap. As the longer the time a driver spends in queue, the better he or she will be able to

estimate the size of upcoming gaps and the driver may come to accept a shorter gap.

Also Cooper and Wennell (in Abu Sheikh,1997) stated that the gap acceptance behavior

of a turning vehicle does not depend on the presence of vehicles waiting behind it. Rene

& Manoj (2012) stated that the queue size at minor stream affects driver decision to

accept or reject a gap.

Maneuver type is another factor that affects driver gap acceptance behavior. Higher

critical gaps are to be expected for left turns compared to right turns (Adebisi 1982,

Velan & Aerde 1996).

17

Arrival time of the minor stream vehicles was found to affect gap acceptance behavior

where drivers are reluctant to accept lags (Troutbeck in Abu Sheikh, 1997).

Level of pedestrian activity at priority intersection is another factor that affects gap

acceptance with long gaps accepted at higher pedestrian levels (Gattis & Sonny, 1998).

Wagner (in Gattis & Sonny ,1998) found evidence that drivers accept smaller lags and

gaps during peak periods than during off-peak hours .

2.4.3 Gap Characteristics

Availability and duration (size) of gaps occurring in major stream are the main factors

that affect driver gap acceptance behavior (Abu Sheikh 1997, Gattis & Sonny 1998).

Kearney et al. (2006) found that drivers presumably accept the first gap judged to be

crossable, then the selected gap will be the minimally acceptable gap. Tian et al. (2000)

found that the highest maximum rejected gap values were observed when the ending

gap vehicles were major street left turns. The through movement from the right side

always yielded higher maximum rejected gap values than that from the left side. The

observation confirmed general experience that the vehicles from the right side usually

put more pressure on the minor street driver, where the minor street driver needs to

accelerate to the desired speed if he/she decided to enter the intersection. With a small

turn angle, the movement maneuver is easier comparing to a perpendicular angle or a

large angle, and the critical gap tends to decrease. Rene & Manoj (2012) mentioned

types of gaps, such as lead gap, lag, gap, and front gap, the number of vehicles entering

the gap, and its distance as direct parameters that affect driver's behavior.

Almost all gap acceptance models developed so far express the probability that a

randomly selected driver would accept a given gap as function of the characteristics of

this gap particularly its length.

2.4.4 Vehicle Characteristics

Vehicle characteristics which affect gap acceptance include; vehicle type, vehicle

occupancy and engine capacity .Vehicle type (truck or passenger car) also affects gap

acceptance significantly.

18

Rene & Manoj (2012) mentioned presence of a passenger in the turning vehicle & class

of the turning vehicle as effective factors on driver's behavior. Bottom and Ashworth (in

Abu Sheikh, 1997) indicated that stronger vehicles accept shorter gaps and that accepted

gaps are longer where oncoming vehicle is commercial vehicle even when the effect of

speed is removed. Bottom & Ashworth (2007) stated also that drivers allow longer

critical gaps for commercial vehicles than for private cars. Tian et al. (2000) found that

the critical gaps for heavy vehicles were significantly higher than those for the

passenger cars, and large variations also existed among heavy vehicles. Hunt, Harper &

Lie (2011) and Farah et al. (2007) predicted that increasing the salience of the speed of

vehicles and feedback about accuracy of speed judgments would lead to improved gap

judgments.

2.4.5 Intersection Characteristics

These characteristics include site distance and visibility, pavement condition, road

geometry and type of control.

Polus (in Abu Sheikh, 1997) stated that type of control cannot, by itself, explain the

differences in accepted gaps. Neudorff (in Abu Sheikh, 1997) stated that shorter gaps

are accepted at intersections with restricted sight distance.

HCM (1994) listed two more factors that may also affect driver gap acceptance

characteristic: the adequacy of intersection sight distance and corner radii. Various

traffic studies have listed the minor street driver's waiting time, the major traffic flow,

visibility (day or night), the existence of a queue on the minor street, the stop type

(rolling or complete stop), and the vehicle type as possible elements that affect gap

acceptance behavior.

Tian et al. (2000) found that the major factors affecting critical gap and follow-up time

include intersection geometry (e.g., multi-lane or single lane, 4-leg or 3-leg), and

approach grade. With the increase of the number of lanes on the major street or the

number of legs at the intersection, the critical gap tends to increase due to the increase

of the difficulty of the movement maneuver. And with the increase of the approach

grade, the critical gap tends to increase.

19

2.4.6 Driver Inter-influence Factors

It is expected that driver behavior can be affected by the behavior of other drivers at the

scene. Not much concern was devoted to identifying and studying the effects of driver

inter-influence factors on gap acceptance behavior (Abu Sheikh , 1997).

2.5 Measurement of Critical Gap

2.5.1 Data Collection

Rene & Manoj (2012) and Abu Sheikh (1997) illustrated several methods in collecting

the data required to analyze the number of accepted and rejected gaps. These methods

have been employed in previous gap acceptance research studies. The methods include:

- Time-lapse photography (time motion pictures).

- Controlled field experiments.

- Closed circuit television or video camera.

- Event pen recorder actuated. (This is done by either an observer using a hand operated

switch board or by road tubes/cables.)

- Laboratory driving simulation experiments.

- Laptop computer.

-Automatic vehicle detectors.

- Audio tapes in combination with microcomputers

Over a number of years, interest in the use of time lapse cine films for the measurement

of speed, headway, and delays has given way to the use of video recordings.

Abdul Kareem (2001) used stop watches manually to time individual vehicles as they

pass the intersection from the major road. The gaps accepted or rejected by the major

road vehicles were observed and noted also. The time head- way of the vehicles on the

major road was simultaneously recorded. The observation point was located at about

10m away from the intersection. The time on the stop watch at the observation point

was recorded.

20

Rossi et al. (2012) used direct observation, collection and coding of gap-acceptance data

at a real road intersection; and developed the virtual intersection using the Driving

Simulators for Driver training and Assessment (STSoftware), driving simulator and

execution of driving tests. The experimental observations were collected during peak-

hour periods through video camera recorder. The videos were processed using

application software that allows the user to record. The data were organized in a

database and then processed using a software procedure that extracts the following gap-

acceptance information for each driver decision:

Dissanayake LU, Ping (2001) collected information in the field using a computer

program, which was particularly developed for that purpose. This data collection

software was developed using Microsoft Access 97 and is capable of collecting the

required data related to the gap acceptance behavior. The main functions of the software

were to record the available gaps on the major road , the accepting/rejecting, and the

response of the minor road drivers to those available gaps for left-turn or through

movements. For nighttime observations, a special night vision device (Night Owl

Cyclops Compact Monocular – NOCC3) was used to see the drivers in order to decide

the age group of the driver.

2.5.2 Measurement of Critical Gap

Critical gap can be found using graphical methods or analytical and empirical methods.

(Adebisi 1982, Abu Sheikh 1997). In graphical methods, critical gap is associated to

the point of intersection of the two curves representing number of rejected gaps greater

than time (t) and number of accepted gaps less than (t) where (t) extends over the

possible time length of the observed gaps Despite of the simplicity of the graphical

method, its findings show high correlation with findings based on other analytical

methods (Adebisi, 1982). Due to difficulties embedded in measuring the critical gaps,

many analytical methods were developed to estimate this important parameter.

2.5.3 Difficulties in Estimating Critical Gap

Difficulties in measuring and estimating critical gaps include:

21

a. Critical gap (by its nature) cannot be measured exactly (Abu Sheikh 1997, Rossi et al.

2012). Its value for a given driver is somewhere between the longest gap he rejects and

the gap he eventually accepts.

b. Driver reaction to lags is different than his reaction to gaps, as drivers with multiple

rejections will be over represented in the sample. Each driver who rejects a number of

gaps will be presented by as much times as the number of gaps he rejected. While a

driver who accepts the first gap/lag will be presented in the sample only once (Hewitt in

Abu Sheikh, 1997).

Rossi et al. (2012) showed that difference between mean critical gaps estimated from

simulator dataset and from field dataset is statistically significant. In particular, the

mean critical gap from simulation is higher than the one estimated from filed data.

2.6 Models of Gap Acceptance

2.6.1 Introduction

In studies of vehicular gap-acceptance behavior, the choice to accept or reject a gap of a

certain size is generally considered as the result of a driver decision process which

includes, as inputs, subjective estimates of a set of explanatory variables, given specific

objective factors. These subjective evaluations are usually affected by a high degree of

uncertainty, which can be properly treated both by classical probabilistic and

deterministic models (Rossi et al., 2012).

Calibration and validation of these models are usually based on gap-acceptance data

collected at real intersections, generally using observations based on video survey.

According to HCM (2000), gap acceptance modeling begins with the recognition that

TWSC intersections give the minor street driver no positive indication as to when it is

safe to leave the stop line and enter the major traffic stream. The driver must determine

both when a gap in the major traffic stream is large enough to permit safe entry and

when it is his or her turn to do so, based on the relative priority of the competing traffic

streams. This decision making process has been formalized into what is known as gap

acceptance theory, which relies on three basic elements:

1. the size and distribution (availability) of gaps in the major traffic stream;

22

2. the usefulness of these gaps to the minor stream drivers; and

3. the relative priority of traffic streams at the intersection.

2.6.2 Lag & Gap Acceptance Modeling Techniques

There are two approaches to derive critical gap values: the deterministic and the

probabilistic approach.

Deterministic models are developed based on the assumption that all drivers are

homogeneous and consistent (Patil, Patare & Sangole ,2011). The deterministic critical

values are treated as a single average value. The fundamental assumption is that drivers

will accept all gaps that are larger than the critical gap and reject all smaller gaps. HCM

has adopted the deterministic approach in the TWSC capacity formula (Gattis & Sonny

,1998). The critical is assumed to be the same for all drivers (Patil, Patare & Sangole

,2011).

The probabilistic methods incorporate variations in drivers and traffic attributes. This is

a more realistic approach (Patil, Patare & Sangole ,2011). As an alternative,

probabilistic models solve some of the inconsistency elements in gap acceptance

behavior by using a statistical treatment of minor street drivers' gap acceptance

behavior. This means that drivers' perceptions of a minimum accepTable gap is treated

as a random variable (Gattis & Sonny ,1998).

2.6.2.1 Deterministic Models

The deterministic model has been the conventional approach of gap acceptance studies.

Several critical gap definitions have been used, such as the median, the mean, or a

particular gap size where the percentage of rejection and acceptance are the same.

Common examples include Greenshields, Raff, and acceptance curve methods that

involve data compilation and manipulation techniques.

2.6.2.1.1 Greenshields Method

The classical Greenshields method employs a histogram to represent the total number of

acceptances and rejections for each gap-range. The vertical axis of the histogram

represents the number of gaps accepted (positive value) or rejected (negative value) of a

certain gap-range, and the horizontal axis represents the gap size range. The critical gap

23

is identified as the gap-range that has an equal number of acceptances and rejections. As

a reminder, Mason et al. noted that certain results from Greenshields analysis must be

interpreted with caution because of small sample sizes (Mason, Fitzpatrick, and

Hardwood in Gattis & Sonny ,1998).

2.6.2.1.2 Raff Method

The earliest method for estimating critical gaps seems to be that of Raff and Hart

(Brilon, Koeing & Troutbed ,1999).

Raff defined critical gap to be the size of the gap whose number of accepted gaps

shorter than it is equal to the number of rejected gaps longer than it. This definition

takes the form of the intersection of the two cumulative curves on a number-of-

acceptances versus gap-range graph. The rejection curve is obtained by using the total

number of rejected gaps with gap size larger than the given gap size. The acceptance

curve is formed by a cumulative curve that represents the total number of accepted gaps

with gap size less than the given gap size (Gattis & Sonny ,1998).

The original Raff definition only uses lag acceptance and rejection data. This approach

is considered statistically wasteful by some researchers, since useful gap acceptance and

rejection data are omitted (Miller in Gattis & Sonny ,1998). ''There are two approaches

to remedy this shortcoming. Fitzpatrick decided to combine the gap and lag data based

on the notion that there is no statistical significance between lag and gap data. An

alternative approach is to separate the lag and gap data into "lag only" and "gap only"

curves'' (Gattis & Sonny ,1998).

Let Fr(t) and Fa(t) be the probability distribution functions (PDFs) of rejected and

accepted gaps, respectively. Then Fr(t) and Fa(t) can be obtained empirically by in situ

measurements. Thus, the observed probability that a gap of length t is rejected is Fr(t),

and that it is not rejected is 1-Fr(t).

More than forty years ago, Raff (1950) introduced a macroscopic model for estimating

the critical gap. He defined the critical gap as the value of t where the functions 1-Fr(t)

and Fa(t) intercept. That is, the value t at which is defined as the estimated critical gap

tc (Ning Wu, 2006).

24

𝐹(𝑡) = 1 − 𝐹𝑟(𝑡) (2)

Raff's method was used in many countries in earlier times. Because of its simplicity, it

is still being used today in some research projects.

2.6.2.1.3 Acceptance Curve Method

Both theoretical and empirical considerations suggest that when the dependent variable

is a binary variable, the shape of the response function will frequently be curvilinear.

This also means that the response function for such binary variables is noted to shape as

a tilted "S", with y = 0 and y = 1 as asymptotes. The dependent variables of this

response curve are the cumulative probability of accepting a gap of a specific length.

The x-value corresponding to the 0.5 probability may be used as critical gap size (Gattis

& Sonny, 1998).

2.6.2.2 Probabilistic Modeling

Probabilistic modeling is more complex than deterministic modeling. Seven modeling

techniques are discussed.

2.6.2.2.1 Logit Method

The logit method is basically a weighted linear regression model. As opposed to the

fitted least squares model, the weighted least square provides efficient estimates when

the error variances are unequal. It can only be used, however, when the error variance is

known completely or at least known up to a proportional constant (Gattis & Sonny,

1998).

Dissanayake, LU & Ping ( 2001) explained the logit model as follows: The logit model

was used to fit the distributions of gap acceptance, which is defined by the following

equation:

𝑝 = e ƒ(t)

1 + e ƒ(t)

(3)

where, p = probability of accepting a gap smaller than t,

t = time length of a gap in seconds, and

25

f(t) = linear function related to gap t.

The linear function has the form:

𝑓(𝑡) = 𝑎(𝑡 − 𝑏) (4)

Where, a and b are constants to be estimated. By combining the two equations , the

format of the equation is:

𝑙𝑛 (𝑝

1 − 𝑝) = 𝑎 (𝑡 − 𝑏) (5)

After a and b are estimated by linear regression analysis based on data collected in the

field, the probability of accepting a gap can be fitted by using the logit model. The gap

acceptance curves can then be plotted based on the accepted gaps and corresponding

probabilities.

According to the critical gap definition used in this study, the probability p would be 0.5

when t is equal to the critical gap. By substituting p = 0.5 into the third equation, it can

be inferred that t = b. This result indicates that the value of b is the critical gap.

2.6.2.2.2 Probit Analysis

Probit analysis is a statistical technique used to treat the percentages of a population

making binomial responses to increasingly severe values of a stimulus. In the context of

gap acceptance studies, the value of stimulus is the size of gap (Gerlough and Huber in

Gattis & Sonny, 1998).

Probit techniques for the estimation of critical gaps have been used since the 1960s. The

formulation for this type of models is quite similar to the logit concept. In their original

form, however, these models do not use the utility term. Instead, the size of the critical

gap, tc, is directly randomized by an additive term, Ɛ ". Thus we formulate for a

consistent driver d:

𝑡𝑐. 𝑑 = 𝑡𝑐 + Ɛ d (6)

Where: tc,d = critical gap for driver d (s)

tcˉ= average critical gap for the whole population of drivers (s);

26

Ɛ d = deviation of the critical gap for driver d from tcˉ (s).

The probability that a driver will accept a major street gap of size t is

𝑝𝑎(𝑡) = ɸ (𝑡 − 𝑡𝑐

ơ Ɛ)

(7)

where _(∅z) is the value for the standardized cumulative normal distribution function at

point z.

The terms t*c and _ơ Ɛ " are parameters of the model. They can be evaluated by

regression techniques for the probit if the proportion of accepted lags is used as an

estimate for pa(t) (Brilon, Koeing & Troutbed ,1999).

2.6.2.2.3 Siegloch Method

Gattis & Sonny (1998) described the Siegloch model as follow: To use the Siegloch

method as a queue acceptance model, the minor road should be saturated with queued

traffic. Kyte et al. (in Gattis & Sonny ,1998) illustrated a method developed by Siegloch

which provides a direct link between gap acceptance theory and the definitions of these

parameters. In this method, both the size of the major traffic stream gap and the number

of minor stream vehicles (n) using each major stream gap during periods of continuous

queuing are recorded. The mean gap size used by n vehicles is computed and is plotted

against n. The resulting regression line that best fits these points is used to calculate the

critical gap and the follow-up time. The value of zero gap (to) is obtained as the X-axis

intercept. The slope of the regression line is the reciprocal of the follow-up time (tf).

The critical gap (tg) is then obtained by the summation of zero gap plus one-half of the

follow-up time.

Brilon , Koeing & Troutbed (1999) described the model as: Let g(t) be the number of

minor street vehicles that can enter the conflict area during one minor stream gap of size

t. The expected number of gaps of size t within the major stream is qp h(t) where h(t) is

the statistical density function of all gaps (or headways) in the major stream. Thus, the

amount of capacity that is provided by gaps of size t during an hour is qp h(t)g(t).

𝑐 = qp ∫ ℎ(𝑡). 𝑔(𝑡)𝑑𝑡∞

𝑡=0

(8)

27

This equation for the capacity of unsignalized intersections forms the foundation of the

whole gap-acceptance theory. Siegloch, as a consequence of this theory, proposes a

regression technique for the derivation of g(t) from field observations. For this

estimation technique we need to observe saturated conditions. A linear regression

function is used to represent the observation data where t is the dependent variable and

g is the independent variable:

𝑡 = 𝑎 + 𝑏. 𝑔(𝑠) (9)

where the parameters a and b are the outcome of the regression analysis. If tc(critical

gap time) and tf (follow up time) were constant values, where

𝑡𝑜 = 𝑡𝑐 −𝑡𝑓

2 (s) (10)

With the assumption that h(t) can be described by the exponential distribution leads to

the well-known Siegloch formula for the capacity of an unsignalized intersection of the

simple type :

𝑐 = 3600

𝑡𝑓. 𝑒−𝑝.𝑡𝑜

(11)

The advantage of Siegloch's procedure for the estimation of tc and tf is its close relation

to the subsequent capacity theory. The drawback for practical application is the fact that

this method can only be applied for saturated conditions, which are difficult to find in

many practical cases.

2.6.2.2.4 The Lag Method

The following conditions are assumed: consistent drivers, and independence of the

minor street vehicle arrival time and the traffic situation on the major street. Then the

proportion pa, lag (t) of drivers who accept a lag of size t is identical to the probability

that a driver has a tc value smaller than t. Thus we can state

𝑃𝑎, 𝑙𝑎𝑔 = 𝐹𝑐(𝑡) (12)

All lags should be measured using traffic observations at an unsignalized intersection.

Whether a lag has been accepted or rejected should also be noted. Then the time scale is

divided into W segments of size ∆t, e.g., ∆t =1 s. For each interval i we look at

28

Ni = number of all observed lags within interval i

Ai = number of accepted lags within interval i

𝑎𝑖 = 𝐴𝑖

𝑁𝑖

(13)

If ti is the time at the center of interval i, then

𝐹𝑐(𝑡𝑖) = 𝑎𝑖 (14)

The mean critical gap then is

𝑡𝑐 = ∑ 𝑡𝑖. [𝐹𝑐(𝑡𝑖) − 𝐹𝑐(𝑡𝑖 − 1)]

𝑊

𝑖=1

(15)

where W=number of intervals size ∆t. Similarly, the standard deviation for the

distribution Fc(t) could be estimated. For practical application this method has some

drawbacks. For the method, in each interval, i, a sufficiently large sample should be

available. This demands very long observation periods because with low major street

traffic flow it takes a while to observe enough smaller lags, and with large major street

volumes most minor street vehicles have to queue before they can enter the conflict

zone. Consequently, although a large number of drivers' decisions have been observed,

there will be very few lags that can be used for this estimation procedure. Another

disadvantage of this method is that it only addresses rather relaxed situations where no

queuing occurs. An additional problem could be that the critical value for the lags might

be systematically different from that for the gaps. As a result of all of these problematic

aspects, the lag method is not used in practice. It provides us only some insight from a

theoretical point of view (Brilon , Koeing & Troutbed, 1999).

2.6.2.2.5 Ashworth's Method

Under the assumption of exponentially distributed major stream gaps with statistical

independence between consecutive gaps and normal distributions for ta and tc, the

average critical gap tc can be estimated from µa (the mean of the accepted gaps ta in s)

and ơa (the standard deviation of accepted gaps) by

29

𝑡𝑐 = µa − 𝑝. ơa2 (16)

where p=major stream traffic volume (vps). If ta is not normally distributed, the solution

might become more complicated. However, for a gamma distribution or a log-normal

distribution of ta and tc, this equation is still a close approximation (Brilon , Koeing &

Troutbed, 1999).

2.6.2.2.6 Harders' Method

Harders 1968 has developed a method for tc estimation that has become rather popular

in Germany. The whole practice for unsignalized intersections in Germany is still based

on tc and tf values, which were evaluated using this technique.

The method only makes use of gaps. The method is similar to the lag method. The time

scale is divided into intervals of constant duration, e.g. ∆t=0.5 s. The center of each

interval i is denoted by ti. For each vehicle queuing on the minor street, we have to

observe all major stream gaps that are presented to the driver and, in addition, the

accepted gap. From these observations we have to calculate the following frequencies

and relative values:

Ni = number of all gaps of size i; that are provided to minor vehicles

Ai = number of accepted gaps of size i

𝑎𝑖 = 𝐴𝑖

𝑁𝑖

(17)

Now these ai values can be plotted over the ti. The curve generated by doing this has the

form of a cumulative distribution function. Part of the method is that each gap t<1s is

assumed to be rejected and that each gap t>21s is assumed to be accepted. For practical

application, it is not guaranteed that ai=function (ti) is steadily increasing over the ti,

which should be the case for Fc(t). Therefore, the ai values are corrected by a floating

average procedure, where each ai is also weighted with the Ai values.

Finally, the estimation of tc is given by the expectation of the thus formed Fc(t)

distribution function. From the descriptions, this method appears to be a more pragmatic

30

solution without a strong mathematical background (Brilon , Koeing & Troutbed,

1999).

2.6.2.2.7 Maximum likelihood procedures

Maximum likelihood techniques for the estimation of critical gaps seem to go back to

Miller and Pretty 1968. To understand the basic elements of this method, let us assume

that for one individual minor street driver d we have observed:

rd = largest rejected gap (s);

ad = accepted gap (s).

The maximum likelihood method then calculates the probability of the critical gap tc

being between rd and ad. To estimate this probability, the user must specify the general

form of the distribution Fc(t) of the critical gaps for the population of drivers and then

assume that all drivers are consistent. The likelihood that the driver's critical gap will be

between rd and ad is given by Fa(ad)-Fr(rd).

The likelihood L* within a sample of n observed minor street drivers that the two

vectors of the rd and ad have been obtained. The logarithm L of the likelihood L* is

given by

𝐿 = ∑ ln (𝐹𝑎(𝑎𝑑) − 𝐹𝑟(𝑟𝑑))

𝑛

𝑑=1

(18)

In practice, the log-normal distribution is often used as the distribution of the critical

gaps tc. The mean critical gap within this distribution has been found to be an

accepTable quantity for the representation of average driver behavior (Brilon , Koeing

& Troutbed, 1999).

2.6.3 Gap Acceptance Models Used in Past Studies

Hagring (2000) illustrated some examples for models used in many studies as follow:

Hansson (1975) used probit analysis, together with the bias correction suggested by

Ashworth (1968), to estimate critical gaps in stop and yield intersections. Troutbeck

(1984) employed the maximum likelihood model for estimating critical gaps in

roundabouts. Thedeen (1979) derived the relationship between the distributions of

31

offered gaps, accepted gaps and critical gaps. Yahya (1997) employed this method for

the analysis of critical gaps in T-junctions. Daganzo (1981) introduced the multinomial

probit model to estimate the mean critical gap and its variance, within and across

individuals. Mahmassani and Sheffi (1981) derived a probit-based model by which it

was possible to estimate the dependence between the critical gap and the number of

rejected gaps. Teply et al. (1997) used the logit model for the estimation of critical gaps.

Patil , Patare & Sangole (2011) also illustrated other examples: "Hamed et al.

developed a binary probit model to explain the drivers’ probabilities of accepting or

rejecting the gap for the left turn maneuvers at urban T-intersection. Multiple regression

model is developed for the prediction of intersection mean critical gap. The results show

that distribution of critical gaps is influenced by drivers’ socioeconomic characters,

expected waiting time, time of the day and the trip purpose. Aggressive behavior of

drivers at unsignalized intersection is studied by Kaysi and Abbany . A model was

developed that predicts the probability of driver performing aggressive maneuver. The

study concluded that age, car performance, and average speed on the major road are the

major determinants of aggressive behavior. Ruskin and Wang use cellular automata

(CA) to study traffic flow at an urban unsignalized intersection. The authors observed

that CA able to reproduce many features of urban traffic that were difficult with gap-

acceptance models. Rengaraju and Rao carried out a study to identify suitable

probability distribution models for vehicle arrivals at uncontrolled intersections under

mixed traffic conditions. It was observed that Poisson distribution gives a close fit to

vehicle arrivals, if traffic volume is less than 500 vehicles/hour/lane. For higher traffic

volumes, multivariate distribution is suggested. The authors in another study developed

a model to estimate possible conflicts at urban uncontrolled intersection. In yet another

study on uncontrolled intersection , they used simulation to model the conflicts at

uncontrolled intersections."

Tian et al. (2000) used linear regression to identify the significance of various factors on

gap acceptance . The analysis was a macroscopic level as the analysis was based on the

average critical gap obtained from observing a number of drivers.

Wu (2006) developed new model for estimation critical gaps at unsignalized

intersection. The theoretical background of the new model is the probability equilibrium

32

between the rejected and accepted gaps. The equilibrium is established macroscopically

using the cumulative distribution of the rejected and accepted gaps. The model yields

directly the probability distribution function of the critical gaps.

Rossi et al. (2012) studied the right turn movement from minor. In this work data

collected from laboratory experiments of driving behavior (questionnaire and driving

simulator sessions) have been used to develop a fuzzy model and a logit model of gap-

acceptance behavior at priority intersections.

Dissanayake, LU , & Ping (2001) used a logit model to fit the distributions of gap

acceptance, to study the differences in gap acceptance capabilities of different driver

age groups under daytime and nighttime.

Hagring (2000) used a maximum likelihood method for estimating the different critical

gaps for the case of two major lanes at roundabouts

In (Gattis & Sonny ,1998) lag and gap acceptance values were calculated according to a

number of alternative modeling techniques which are the Siegloch, Greenshields, Raff,

acceptance curve, and logit methods for through & left turning vehicle for nonstandard

stop-controlled intersections.

Guo & Lin (2011) proposed a four new methods for calculating critical gap. The

probability density function of the rejected and the accepted gap can be deduced by

introducing the exponential rejected proportion function. The relation among variables

of these functions can also be obtained. It was concluded that the exponential model of

rejected proportion is more often practical than the linear model.

Patil, Patare & Sangole ( 2011) developed Probit and Logit models for predicting the

probabilities of gap acceptance of right turning two-wheelers at a three legged

intersections. NLOGIT 4.0 is used for the model development.

The probabilistic model is used in this research as it incorporates variations in drivers

and traffic attributes.

33

2.7 Previous Studies

2.7.1 Y. A. Abdul Kareem (2001)

This research was prompted by the need to obtain acceptable gaps for motorists at some

priority intersections in Ilorin, Nigeria, the researcher studied four stop-sign

intersections,

2.7.1.1 Objectives

1. To determine the average gap accepted to the minor street driver.

2. To determine the volume at which the critical gap occurs and predict drivers attitude

when at the minor street of apriority intersection.

2.7.1.2 Data Collection

The following sets of data were collected on four different priority intersections within

Ilorin metropolis: time headway/gaps in the major road traffic, gaps accepted/rejected

by the side street drivers, traffic volume on the major road. The four intersections made

up of two 4 - leg and two 3 – leg intersections. Data were collected on a weekday which

was considered a representative of weekdays. For the weekends also, one of them was

used to represent them.

2.7.1.3 Gap Data Collection

This was done manually by the use of stop watches to time individual vehicles as they

pass the intersection from the major road. The gaps accepted or rejected by the major

road vehicles were observed and noted also. The time head- way of the vehicles on the

major road was simultaneously recorded. The observation point was located at about

10m away from the intersection. The time on the stop watch at the observation point

was recorded. The difference in time between the passages of two successive vehicles is

the time headway or in this case the gap.

2.7.1.4 Factors Considered

Critical gap of a driver depends on his characteristics and his style of driving. It also

depends on the design of the junction, the size and speed of the trailing vehicle creating

the gap as well as the weather.

34

2.7.1.5 Findings

It was observed that the critical gap during the weekday was smaller than the

corresponding value for the weekend. This could be attributed to the rush to work which

makes the motorists to a smaller gaps.

The busier intersections had smaller critical gaps of 3.2 secs. during the weekdays.

Heavy vehicles were observed to accept large gaps while smaller vehicles accepted

smaller. Similarly, it was observed that on the average younger male drivers accepted

dangerously low gaps of between 2.5 and 3.0 seconds.

The average gap acceptance for weekday was 3.6 sec, while for weekend was 4.0 sec.

2.7.1.6 Conclusion

Gap acceptance at the priority intersections studied varied amongst male and female

drivers, young male and older male drivers. It also varied between heavy and light

vehicles. Gap acceptance at such intersections can be improved if the intersections are

well designed with flared entry lanes, channelized left turning bays and ensuring that the

sight distance is large. This improvement will in turn increase the capacity and overall

efficiency of the intersections

2.7.2 Rossi et al. (2012)

The paper proposes a comparative analysis of random utility models and fuzzy logic

models for representing gap-acceptance behavior at priority intersections, based on data

collected from driving simulator tests. Explanatory variables not detecTable from on

site observations were observed in the experiments. The proposed models include

driving styles variables in addition to variables commonly used in gap-acceptance

studies.

2.7.2.1 Data Collection & Methodology

The data used in the analysis are gap-acceptance observations (driver decisions)

collected from driving simulator experiments, in which the virtual environment has

been built with the aim to reproduce a real three-leg priority intersection located in a

sub-urban area near Venice.

35

The dataset obtained from the collected data contained a total of 4,384 decisions

(gap/lag acceptances and rejections), where 1,914 gaps/lags correspond to acceptances

(right turn maneuver completed).

The full dataset has been divided in a calibration dataset (70% of data) and a validation

dataset (30% of data), to identify/calibrate the models and evaluate their performances,

In this work data collected from laboratory experiments of driving behavior

(questionnaire and driving simulator sessions) have been used to develop a fuzzy model

and a logit model of gap-acceptance behavior at priority intersections. Laboratory

experiments allowed to observe and record information about explanatory variables not

detectable from direct observations (on site), and to include them in models with the

aim to better describe, understand and simulate driver’s choices. On the other hand the

use of a fuzzy model allowed to overtake problems concerning non-homogeneous

explanatory variables and uncertain and imprecise information on the system.

2.7.2.2 Conclusion

The results obtained indicate that both logit and fuzzy models show good capability of

representing real driver’s gap acceptance behavior, but neither model definitely

dominates the other;

Extension of the sample size (number and stratification) in order to better represent the

population of drivers and their driving styles;

Dynamic calibration of model parameters, to allow model results to reflect "in real

time" spatial and temporal variations of driver behavior (for example, the tendency of

drivers to accept smaller gaps with increasing waiting times). This aspect, which was

not considered in this study, appears to be particularly important for a realistic

representation of gap-acceptance behavior within traffic micro-simulation models.

2.7.3 Rui-jun Guo & Bo-liang Lin (2011)

This paper designed a survey method of rejected and accepted gaps. In this paper, the

focus was on investigating the critical gap and capacity at the priority-controlled

intersection, in which the major and minor stream are both a one-way traffic flow.

36

2.7.3.1 Assumption of Critical Gap

1. Independence between arrival times of the minor-stream vehicles and the ones of the

major-stream vehicles; and

2. Driver behavior is both homogeneous and consistent.

Based on assumption (1), the distribution form of all headway samples in major stream

should be the same as the distribution form of part of samples when the vehicles in the

minor stream arrive before the intersection. Therefore, the headway distribution in the

major stream can be simulated by using the latter samples. These headway samples can

be divided into accepted headway and rejected headway,

Four new methods for calculating critical gap were proposed. The probability density

function of the rejected and the accepted gap can be deduced by introducing the

exponential rejected proportion function. The relation among variables of these

functions can also be obtained.

2.7.3.2 Definition of Critical Gap

1. When the ratio of the probability of accepted gaps not larger than a fixed value and

the probability of rejected gaps larger than that value is equal to the ratio of total

rejected coefficient and total accepted coefficient, such a value is the critical gap; or

2. Critical gap is the gap in a major stream whose cumulative probability is equal to the

total rejected coefficient

2.7.3.3 Findings

It was concluded that the exponential model of rejected proportion is more often

practical than the linear model, and the typical capacity functions were improved by

using the accepted proportion function.

1. There are many former methods to calculate critical gap including maximum

likelihood method, Hewitt’s method, and Raff’s method. Most methods estimate the

practical value of critical gap based on field samples. In their proposed new method

calculations of critical gap and capacity are theoretically obtained and constitute the

system of gap acceptance theory. Raff’s method is only a special case of their method.

37

2. Based on a typical capacity model of gap acceptance theory, the new method

calculates capacity as the sum of two parts, since every gap has an accepted probability.

So the new formula is deduced by using the accepted proportion function.

3. Compared with the former models, these new methods for calculating capacity are

too complicated for practical calculation, and should be further simplified.

2.7.4 Rene Lord-Attivor & Manoj K. Jha (2012)

This research discusses various gap acceptance strategies at priority intersections and

develops a research framework for gap acceptance in developing countries, such as

Ghana, Africa. This research focused on gap acceptance and driver behavior at T-

intersections (unsignalized intersections) for left and right turning vehicles from minor

streets onto major streets, in five major cities in Ghana.

2.7.4.1 Problem Statement

Developing countries, particularly the Republic of Ghana, tend to use the HCM to

analyze and design intersections without changing certain values in the program (e.g.,

gap). The HCM values used in developing countries may not produce the appropriate

measure of effectiveness (MOE) for a particular developing country since traffic and

driver characteristics may be entirely different in those countries.

2.7.4.2 Factors

The scope of this research related to the factors that affect driver’s decision to accept or

reject a gap is as follows: factors related to driver’s gender and age, factors related to

the acceleration capability of the turning vehicle, factors related to gap size, opposing

traffic flow, presence of a following vehicle, speed and type of opposing vehicles,

factors related to the type and condition of the vehicle, factors related to the distance of

travel and travel time of the trip, and factors related to the type of passengers in the car.

2.7.4.3 Data Collection & Modeling

Data for the research will be collected during off-peak hours in the AM, PM and

midday when weather conditions are ideal (i.e., dry pavement) with unrestricted sight

distance. The method to collect the data is a combination of the closed circuit television

or video camera and the event pen recorder.

38

The probabilistic binary model (PBM) used in the Discrete Choice method is adopted in

this research. The PBM is used where the probability of accepting a gap is predicted

using the utility of that exact gap.

2.7.4.4 Conclusion

The results of these critical gaps compared to the 1985 HCM left turn critical gaps were

high. Recent research has proved that the driver behavior at priority intersections in

developing countries has drastically changed over time and will continue to adapt to the

changing transportation environment. Field observations from transportation research

studies conducted in developing countries shows that driver’s react aggressively when

entering the roadway from a minor road.

2.7.5 Sahar Nabaee, Derek Moore, & David Hurwitz (2011)

A novel procedure was developed and validated for the accurate observation of

naturalistic driver gap acceptance behavior at unsignalized T- intersections.

Specifically, two-way stop-controlled intersections with a two way left turn lane

(TWLTL) on the major road were examined. Three intersections were included as

experimental locations. A sample size was collected of approximately 875 minor street

vehicles which were exposed to over 2400 individual gaps. Characteristics such as

gender, approximate age, vehicle type, presence of a queue behind the lead vehicle, and

presence of passengers in the vehicle were collected as a function of the time of day

(TOD). This work provides updated measures for the accepted gap as TOD varies, as

well as exploring how accepted gaps are related to the wait time of a vehicle at the stop

line. The studied movements were right or left turning from minor to major approach.

2.7.5.1 Data Collection

The data collection protocol required pairs o f researches in the field to complete the

observations with the requisite degree of accuracy. One researcher was responsible for

running the GAPS software on the laptop while the other captured detailed information

about the drivers and vehicles approaching the stop sign on the minor street. This

detailed information included gender, approximate age, presence of passengers, queue

size and vehicle type, which was input into the program database at the completion of

each site visit. Once all data had been collected, macros imbedded in the GAPS

39

software reduced the data into a file easily transferred and analyzed in Microsoft Excel.

A high definition camera was used to record one of the stop controlled intersections

while manual data collection was taking place. The video was reduced in slow motion

to provide accurate information. Each accepted gap greater than 15 sec. was removed

from the analysis.

2.7.5.2 Findings

The GAPS software provides reasonably accurate measurements of minor street

vehicle’s wait time and accepted gaps. The relationship between wait time and accepted

gap generally takes the shape of a negative exponential distribution. As the wait time

increases, shorter gaps are more commonly accepted than longer ones. When

considering age categories, teen drivers usually tend to accept shorter gaps than their

older counterparts. There is little shift in left turn gap acceptance behavior among older

drivers (no statistical difference at 95%), while teen drivers show a relatively larger shift

in their behavior at different times of the day (statistically significant at 95%). It appears

that the development of a queue behind the left turning vehicle decreases the accepted

gaps by 1.17 seconds with statistical significance. Also, presence of passengers

influences the gap acceptance behavior and decreases the accepted gaps by 0.85 seconds

with statistical significance.

2.7.6 Gopal R. Patil, Prasad Patare & Jayant P. Sangole (2011)

The main focus of this paper is to model the gap acceptance behavior of the right

turning (in India the driving is on the left side of a road) two-wheelers at three-legged

uncontrolled intersection using probit and logit models.

2.7.6.1 Problem Statement

Most of priority intersections in India do not have stop or yield sign, and even if they

exist, drivers do not follow indicated priority. Drivers usually do not care much about

the conflicting traffic; they attempt to enter intersection, even if a conflicting vehicle is

about to collide. All these non-standard conditions create very complex travel behavior

at unsignalized intersections. Two-wheeler is the smallest in physical dimensions in all

motorized vehicles. Moreover the traffic related characteristics of two-wheelers are

significantly different from the rest of the vehicles.

40

2.7.6.2 Data Collection

Data are collected during the morning time (10-11 am) on typical weekdays. The major

road at the two intersections is four-lane divided. Video recording technique was

adopted for data collection. Video filming was done from a vantage point to cover all

the three legs of the intersection up to the merge area. Another camera was placed at the

road level to get information on driver’s attributes (gender and approximate age) and

vehicle occupancy. Recording is done for about 40 minutes at each intersection on

working days. Various attributes extracted from the video recording are vehicle arrival

rate, gap/lag accepted or rejected, type of conflicting vehicle, drivers gender and age

group, vehicle occupancy, number of gaps rejected, and intersection clearance time. The

recordings from the camera placed at ground are used for extracting occupancy,

approximate driver’s age, and gender for two-wheelers.

2.7.6.3 Findings

A smaller percentage of young drivers compared to non-young drivers reject the gap.

Additionally, almost no gap of greater than about 4 sec is rejected by young drivers, but

almost 10% of the non-young drivers reject a gap of 4 sec. The critical gap for two-

wheelers is 2.5 seconds. The separate analysis of lag and gap resulted in a critical lag of

2.65 seconds and a critical gap of 2.33 seconds. These values of critical lags/gaps are

much smaller than the critical lags/gaps reported in other studies. Both probit and logit

models are statistically significant and intuitively logical. The validation results in

overall 81% accurate prediction.

2.7.7 Sun Yon Hwang & Chang Ho Park (2005)

The purpose of this study is to describe in detail the gap acceptance observed in a

merging process and to present a gap acceptance model which can explain decision-

making procedure during a lane-changing. In this study, they developed a gap

acceptance model of composed explanatory variables with which the behaviors of a

driver during lane-change can be simulated.

41

2.7.7.1 Factors & Models

The factors that affect gap acceptance are gap size, subject vehicle’s velocity, on target

lane lead vehicle and lag vehicle’s velocity, and subject vehicle’s type, remaining

distance until lane changing finish and, delay.

To reflect the decision-making process of a driver on whether or not to change lanes, a

model structure for lane-change. To change lanes, it is most important to check whether

it is safe to proceed with the lane-change. Most lane-changing models are based on the

gap acceptance model. The model presented herein is theoretically based on the discrete

choice model.

2.7.7.2 Findings

They found that of the space gap is a more important variable than the time gap.

Because drivers run at their own speed, they tend to be more restrained by space than

time. That is, drivers generally consider distance as a more important factor for

determining the safety of a certain lane change. The factors determining gap acceptance

include the lead gap, lag gap, front gap, heavy vehicle and the remaining distance.

Congestion greatly affects gap acceptance. Whether conditions are congested or not

depends on gap acceptance.

2.7.8 J. L GATTIS and SONNY T. LOW (1998)

This report presents gap- and lag acceptance findings from an examination of one non-

standard stop-controlled intersection. Non-standard intersections at which the right-of-

way is assigned in a different manner, such as giving priority to a left turn movement

and requiring the opposing through-street movement to stop.

2.7.8.1 Preliminary Considerations

1. Initial Traffic Operation Observations

First, a signalized intersection approximately 2.5 km (1.5 mi) south of this intersection

created some platooning in northbound traffic. Second, the railroad track parallel to and

on the west of Gregg Avenue is higher than the roadway, restricting the vision of

southbound through drivers trying to monitor eastbound traffic. During high volume

periods (e. g., 4 p.m. to 6 p.m.), this non-standard T-intersection experienced excessive

42

delay on the southbound approach. In many cases total delay per vehicle exceeded 45

seconds, which is the delay defined as level-of-service F .

2. Observational Problems

Four problems were noticed during the preliminary studies of traffic patterns.

The first problem was driver confusion, perhaps among drivers that were either new to

the area or wary of other road users. There were many instances that indicated drivers

were confused by the right-of-way pattern. The second problem was that southbound

through drivers would sometimes underestimate. the size of the upcoming lag or gap.

The third problem was the inefficiency in traffic operations. The fourth problem

involved aggressive eastbound left-turning drivers occasionally entering the intersection

without an adequate-size gap. When this happened, northbound drivers were forced to

slow in order to avoid a rear end collision.

2.7.8.2 Data Collection Procedure

A traffic classifier was placed 46 m south of the intersection to collect northbound

traffic speeds and arrival times. Two flexible road tubes spaced 3 m apart were laid

perpendicular to the northbound traveled way. The classifier was located upstream in

order to record the passage time and speed of northbound traffic in advance of the actual

intersection. To obtain southbound and eastbound arrival and departure times, a video

camera was aimed to cover north and west intersection approaches.

Lag and gap acceptance values were calculated according to a number of alternative

modeling techniques. The Siegloch, Greenshields, Raff, acceptance curve, and logit

methods were used.

2.7.8.3 Findings

1. A southbound driver accepting a very small lag or gap could have assumed that all

approaching northbound vehicles (i.e., those with the right-of-way) were going to

proceed straight and not turn left in front of the southbound vehicle.

2. The majority of the critical gap values were greater that the critical lag values. Two

possible explanations for this phenomenon are apparent. The first explanation is that

drivers were more willing to accept a lag than a gap of the same size. The second

43

explanation was that the proportion of lag acceptance data was relatively larger than the

rest of the data.

3. The lag/gap values from the southbound through versus northbound were smaller

than those found in the HCM.

4. The only valid conclusion was that a non-standard stop-controlled pattern might

increase the intersection capacity only under some traffic flow patterns.

5. The values found according to the Raff method often were lower than others, and the

Logit method produce values that were usually higher than others.

2.8 Summary

The literature review led to the conclusion that:

1. Driver gap acceptance behavior at priority intersections can be modeled using a

logistic regression model.

2. Each gap can be treated as an observation in an independent sequential binary choice

process, as in this approach probability can be expressed in terms of probability of

accepting a gap by a given driver.

3. The gap definition that to be used is: the time interval between the moment the rear of

the lead vehicle reaches the crossing line to the moment the front of the tail vehicle

reaches the crossing line.

4. The lag definition that to be used is: the time interval between the arrival of a side

street vehicle at an intersection and the arrival of front of the next main street vehicle.

5. Critical gap/lag is found according to Raff by using graphical method, which is the

time (t) that number of accepted gaps less than (t) is equal to number of rejected gaps

larger than (t).

6. Previous studies considered many factors that affect driver gap acceptance, some of

them were not considered in this study like nationality, day & night time periods,

geometric characteristics for intersections (site distance and visibility, pavement

44

condition, road geometry and type of control), Level of pedestrian activity at priority

intersection.

7. Previous studies give less attention to factors that affect driver gap acceptance and

did not mention their effect on gap acceptance; in this study more attention is made and

study for these factors is conducted like: speed of oncoming car, familiarity of driver

with area, the type of vehicle( private or taxi), queue size behind minor street vehicle.

8. New factors that affect driver gap acceptance are studied here like: the year

production of vehicle, the number of years owing the vehicle and the factor that driver

take his decision to accept the available gap ( speed of oncoming car or distance of the

oncoming car or both of them).

The most important characteristics of this study are:

1. It is the first in Palestine, and one of the few studies in the Arab countries.

2. Most of case studies were on T- intersection, while this study deals with four-leg

priority intersection.

3. The through movement from minor street to major street is studied, where previous

studies in developing countries dealt with right or left turning movement.

4. Data are collected at different times and the differences are to be studied.

5. Data have to be collected on a normal weekday which is considered a representative

of weekdays.

6. Two kinds of gap/lag are studied separately in the same time, the near side gap/lag,

and the far side gap/lag for the same vehicle.

7. Some studies used manual methods to collect and analyze data, but on this study

computer software was used for previewing video and extracting data, and computer

software was used to analyze these data.

8. Pilot field study should be conducted previous to data collection in order to determine

difficulties in data collection, to determine proper methods and ways to have best data

matching and to train data collection team on survey.

45

9. Separate models are developed for each of near side and far side gap/lag in addition

to a model for the whole intersection gap/lag.

46

3 CHAPTER 3: RESEARCH METHODOLOGY

This chapter covers the main research phases and steps. It covers the technical gap

acceptance modeling issues and considerations which include problem formulation,

model selection, model specification, model dependent and independent variables and

data collection methods.

3.1 Main research phases

Figure 3.1 describes the methodology adopted in this research.

Figure 3.1: Research Methodology Diagram

4. Data Analysis & Review

Model DsecriptionCalculating Traffic

FlowCritical Gap

Results' Analysis

Develop Factors Affecting Gap

Model

Comparison Between Factors

3. Model Specification

Model Specification Model Variables Method of Model Work

2. Data Collection Phase

Site Selection Data CollectionQuestionnaire

Design & CheckingData Coding &

ProcessingData Organization

1. Preliminary Phase

Litertature Review Problem Formulation Proposed ModeL

Research Methodology

47

The methodology of this work includes:

1. Preliminary Phase: This phase was concerned with defining driver gap acceptance

phenomenon at priority intersections; formulating this phenomenon; and selecting a

proper behavioral modeling to investigate it.

2. Data Collection Phase: This phase covers site selection for the research; designing

and checking questionnaire to collect information from drivers; identification of

variables for model; and finally collecting data from video records and questionnaires,

organizing and coding of data.

3. Model Specification: This phase involves description of selected model; identifying

model variables that affect driver's gap acceptance and establishing of basic gap

acceptance relationship.

4. Data Analysis & Review: This phase forms the main body of the research. It includes

model building; reviewing of collected data; connecting data from questionnaire &

video records; analyzing these data; comparison between results; and detecting factors

that affect gap acceptance.

3.2 Preliminary Phase

3.2.1 Literature Review

The first step was reviewing the literature on critical gap. The concentration was on

estimating critical gap values in developing countries and it's relation to driver's

behavior at priority intersections. The literature review seeked for case studies applied

in cities of developing countries especially in the cities that have similar conditions.

3.2.2 Problem Formulation

A driver arriving at an intersection controlled by a stop or yield sign (priority

intersection) observes a lag and probably a number of gaps in the major stream of the

intersection. The driver evaluates lag and the gaps giving his or her utility and makes a

choice on when to accept or reject the desired gap. Through the decision making

process, numerous factors may affect the driver’s decision to accept the gap. Factors

such as the environment, density of vehicles on the main road, number of available

48

gaps, geometric conditions, age, and sex may affect the driver’s decision to accept or

reject a gap. The process of accepting or rejecting a gap is considered to be a choice and

cannot be treated as a uniform decision. This choice cannot be determined for each

driver that arrives at the intersection. Hence, this decision is considered to be random as

each driver may have their individual characteristics that may trigger the decision to

accept or reject a gap. In other words, the characteristics of each driver vary. Due to the

uncertainty of accepting and rejecting a gap, predicting the probability of driver's

accepting and rejecting available gaps is the closet gap acceptance value that can be

used for analysis purposes (Rene &Manoj, 2012).

3.2.3 Proposed Model

The literature review led to the conclusion that driver gap acceptance behavior at

priority intersections can be modeled using a logistic regression model, and the critical

gap is calculated using Raff method.

3.3 Data Collection Phase

3.3.1 Study Site

Data needed to build behavioral models for driver gap acceptance in this study is

collected at four-leg intersection. Each leg permits three movements of traffic, which

are left, straight and right movements. Previous research such as Mhna et al. (2013)

studied the left-turn from major. In this research, the work is extended to the straight

movements from minor road to major road which is shown in Figure 3.2.

49

Straight Movement

Straight Movement

Minor Street

Major street

Major street

Minor Street

Figure 3.2: Illustration of Straight Movement

3.3.1.1 Site Selection Procedure and Criteria

Abu Sheikh (1997) and Dissanayake, LU & Ping ( 2001) illustrated criteria that are

considered while investigating potential study site, which are:

a. Surrounding land use: Higher preferences are given to intersections surrounded by

mixed land use.

b. Traffic characteristics: Preferable traffic characteristics include an accepTable traffic

volume sufficient to obtain needed sample size; an accepTable variation of traffic

volume to enable observing peak and off-peak characteristics; an accepTable vehicle

type mix to enable observing gap acceptance characteristics for different vehicle types;

and the volume on the minor road should not be too small in order to be able to records

many observations as possible during a certain period of time.

c. Geometric characteristics: All investigated sites are four-leg junctions located at dual,

with standard lane width and proper visibility.

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d. Proximity of other intersections: It is preferred that no other junctions exist in the

vicinity of the studied intersection. A proper separation of no less than 250 meters is

considered . (Abdul Kareem ,2001).

e. Availability of space for conducting driver's interviews: Enough space to conduct

road side interviews for drivers should be available.

f. Availability of proper location for camera: Preference is given to intersections where

proper location to mount the video camera to achieve proper coverage of the

intersection is available.

g. Speed : Speed limit for the major and minor roads should not be more than 50km/hr

and 40km/hr respectively (Abdul Kareem ,2001).

3.3.1.2 Selection of Study Site:

Considering the above criteria , around 20 sites are investigated. They are screened into

two groups; the first group includes around seven sites which, in general, meet the

desirable criteria. the second group includes the remaining sites that lack for some of

the desirable criteria. Further screening and field investigations are made for sites in the

first group to select one appropriate site which is Gaza college intersection.

The selected intersection meets all the criteria to an acceptable level as follow:

1- The intersection is surrounded by mixed land use, ( residential, commercial , and

petrol station).

2- The intersection is four-leg junction located at two lanes carriageway, with standard

lane width.

3- The intersection has an acceptable traffic volume sufficient to obtain needed sample

size, an acceptable variation of traffic volume, and an acceptable vehicle type mix.

4- The intersection is far away by more than 250 meters from other intersections.

5- There is enough space to conduct road side interviews for drivers without blocking

traffic.

51

6- Availability of high buildings to mount the video camera to achieve proper coverage

of the intersection .

The selected site is shown in Figure 3.3, Figure 3.4

Figure 3.3: Intersection Google Maps Picture

Figure 3.4: Intersection Photo from Filming Location

52

Data needed to develop behavioral models for driver gap acceptance at priority

intersections are collected from this site. Initial traffic count is conducted prior to the

collection of driver gap acceptance data. The results of analyzing these counts along

with the experience gained from the pilot data collection survey are used to decide the

number of interviews, the proper sampling procedure, and the survey time needed to

collect a sample with appropriate size.

3.3.2 Data Collection

There are two possible ways of defining the observation in gap acceptance studies:

a. Each gap can be treated as an observation in an independent binary choice process.

b. Each driver with his group of gaps is considered as one observation. (Abu Sheikh,

1997)

The first approach is adopted in this research, as in this approach probability is

expressed in terms of probability of accepting a gap by a given driver, while the second

approach assumes that a driver selects one specific gap out of several options (gaps)

through a single comparison of all the available gaps. This might be unrealistic

representation, since gaps offered to driver are not known to him prior.

3.3.2.1 Driver Response-Base Classifications

Based on driver response each observation is classified into:

1.Accepted near side gap/lag: A gap which is accepted by a minor stream driver into the

near side major stream traffic.

2. Accepted far side gap/lag: A gap which is accepted by a minor stream driver into the

far side major stream traffic.

3.Rejected gap/lag: A gap/lag which is rejected(not used) by a minor stream driver

aiming to execute a given maneuver.

4.Untested gap: A gap occurred while no minor stream driver exists at the intersection.

This type of gap cannot be included in the model. Figure 3.5 illustrates the near/far side

gaps

53

Far Side Gap

Near Side Gap

Major Street

Minor Street

North

Figure3.5: Illustration of Near/Far Side Gap Types Diagram

3.3.2.2 Data Collection Methodology

Data for this research are collected based on the simultaneous use of video camera and

field administrated questionnaires.

Video-based technology offers advantages and is gaining popularity as a data collection

method. Video data constitutes a permanent record by replaying the video data.

Researchers can observe special problems or review specific operational situations

several times. Video data can be entered directly into the computer, eliminating errors

that often occur when researchers transcribe field data sheets. Video data collection

methodology may produce higher quality traffic data than manual methods. Researchers

can easily obtain event-times data with accuracy of 0.1 second. Also, by using the

54

frame-by-frame replaying feature, a researcher can exercise careful and unhurried

judgment when unusual, complicated, or rapid events occur. Data from video records

may be reduced by frame-by-frame viewing or by replaying at normal speed while

recording events with computer software (Gattis & Sonny, 1998).

Video recording technique is adopted for data collection. Video filming is done from a

vantage point to cover all the four legs of the intersection up to the merge area. The

camera is placed on the terrace of a nearby building in such a way that a good view of

all the four approaches is obtained for getting attributes of the traffic stream. Recording

is done for about 100 minutes at the intersection on working days on two different

periods.

The recordings are played at slow speed on a screen to extract the data and provide

accurate information about the exact time vehicles arrived at the intersection, initiated a

through movement, and the length of available gaps in main traffic stream. Lags/gaps

are measured in 1/100th of second. All vehicles are divided into 3 categories (car,

bus/truck, taxi).

The following gap-acceptance information for each driver decision are extracted from

video:

1.Type of time interval (lag or gap)

2. Interval time size

3. Minor street vehicle waiting time at stop line

4. Category of minor street vehicle

5. Traffic Volume

6. Driver decision (interval acceptance or rejection)

7. Number of vehicles accepting the same gap.

8. Queue size at minor stream.

A field questionnaire is used to collect other data items which cannot be extracted from

video tape as shown in Annex 1;these items include:

55

1. Driver characteristics (age, sex, education , driving experience, crash experience...).

2. Vehicle characteristics(age, engine capacity, occupancy ...).

3.Trip characteristics( trip purpose and duration).

A road side interviews was made downstream at far enough distance (60 m) from the

intersection in order to:

1. Minimize traffic operation interruption.

2. Minimize possible alteration in driver gap acceptance behavior by not attracting their

attention and awareness.

A total of ten persons are employed for collecting required data. These comprised of:

1. Supervisor: to supervises the performance during the survey period.

2. Two policemen: to assists in stopping drivers to be interviewed.

3. Two cameras operators.

4. Vehicle observer: to notes down the plate number and data of the interviewed

vehicles in exact order .

5. Four roadside interviewers.

Data for the required maneuver are collected at normal weekday during common

periods ( 10:00-11:40 A.M and 1:00-2:30 P.M ).Periods are selected like this for

capturing variation in traffic operations and gap acceptance characteristics in peak and

off-peak times.

It is revealed from the pilot survey that some drivers find difficulty in answering some

of the questions. Therefore, interviewers are trained to explain the questions in a simple

way.

Furthermore, it is revealed that none of drivers have estimated the speed and distance of

the opposing vehicle which he have crossed in front of it. Therefore, two questions

related to estimating the speed and distance of opposing car are modified to be an

estimation of the degree of car speed/distance. They are classified into categories (fast,

56

slow, moderate speed) ,(far, near, moderate distance). The actual speed and distance that

obtained from video are transformed into same categories.

Besides, it is revealed importance of recording the color and the brand of the

interviewed cars in addition of the time of the interview. This helps in data matching

later.

3.3.3 Data Coding & Processing

Data coding and processing include three stages which are questionnaire design, video

data coding and data matching.

3.3.3.1 Questionnaire Data

Each driver involved in the experiment respond to a questionnaire which collects socio

economic information, such as age, gender, education, income and driving experience

(years of driving, kilometers driven per year), in addition to personal information. Data

collected from drivers interviews are extracted from questionnaires and checked.

3.3.3.2 Video Data

Data are extracted from video films in two steps:

A. Direct observation and manual coding to extract the following data:

Type of oncoming vehicle.

Type & color of minor stream vehicle.

Driver response to each gap(accept/reject).

Queue size at the time of gap acceptance.

Type of acceptance (gap/lag).

B. Direct observation and digital coding to extract gap length, speed of oncoming car

and the studied cars as well, traffic volumes at minor & major road and delay imposed

on the studied vehicles. Data items needed to derive these variables are collected using

(Windows Video Maker) program. The resulted data are stored in a spread sheet using

Microsoft Excel program to be analyzed using SPSS program.

57

3.3.3.3 Data Matching

One basic step in data processing is to match data collected from interviews to data

extracted from video tapes. The main controlling key in this process is the vehicle plate

numbers and time of interview.

The matching process is finalized through the following steps:

1.The vehicle plate numbers recorded by the roadside interviewers are matched to the

vehicle plate numbers noted down by the vehicle plate number's observer.

The plate number's observer noted down the plate number of each of the minor stream

vehicles executing the studied maneuver in the exact order by which they executed the

maneuver. Therefore, the result of this step is the arrangement of the data collected in

the roadside interviews in the same sequence by which the interviewed drivers had

executed the studied movements. He also noted down the type and color of the vehicles.

2. Serial numbers of the minor stream vehicles which are recorded by the plate observer

are matched to the data set extracted from the video record. Note that there is one data

set per vehicle and that the number of the observations in each set equals the number of

gaps/lags which are offered to the driver. The first vehicle as per the observer's record is

given the serial number 1 and all the preceding vehicles in the video record are excluded

from any further analysis. The result of step 2 is the matching of data sets collected in

roadside interviews to the data sets extracted from video record.

3. The accuracy of the results of the matching process is confirmed by cross checking

the type and color of vehicles as recorded in roadside interviews against the type and

color as observed in the video record and as recorded by the vehicle plate number's

observer.

4. At the completion of the matching process, data sets are refined and finalized in terms

of removing the cases for which roadside interviews were not conducted and removing

the measures and characteristics like vehicles color and plate number which were

needed to complete the matching process.

5. The data set for the interview represents all of the data items collected during the

interview to model the driver behavior of gap acceptance, while the data set extracted

58

from the video record represents the data for gaps/lags that were offered to calculate the

critical gap/lag and to connect with driver behavior

The following Tables illustrates an example for the above steps.

Table 3.1: Information of the Observer Record

SN. Plate Number Type Color

1 2537 Kia White

2 4597 Hyundai Black

3 0079 Mercedes Blue

4 4632 Volkswagen White

5 7981 BMW Green

Table 3.2: Information from Roadside Interviews

SN. Plate Number Type Color Data Set

1 2537 Kia White 1

2 4597 Hyundai Black 2

3 7981 BMW Green 3

Table 3.3: Information from Video Record

SN. Type Color Video

1 Kia White 1

2 Hyundai Black 1

3 Mercedes Blue 1

4 Volkswagen White 1

5 BMW Green 1

3.3.4 Data Organizations

Model developed in this study is the logistic regression to study driver's behavior at

priority intersections. The driver behavior towards gap acceptance is different, it is

59

possible that some drivers may evaluate and reject several gaps before accepting a gap,

while other drivers will accept the first time interval(lag) offered to them.

The decision process in the gap acceptance phenomenon is different in terms that there

is only available gap(decision subject) at a time and two possible outcomes of the

process ( reject or accept the gap). Therefore, the dependent variable was given two

codes( 1, 0 ), when driver rejects gap, the variable takes value of 0, and when he accepts

gap the variable takes value of 1.

3.3.5 Sample Size

One of the advantages of logistic regression modeling is that it depends on data

distribution using Bernoulli distribution, which allows better use of data through given

dependent variable the probability value of (1,0).Literature review revealed that a small

samples as 50 data points could produce reasonable results (Abu Skeikh, 1997).

3.4 Model Specifications

3.4.1 Model Description

Binomial or binary logistic regression can be used to predict the probability of the

observation takes one of two groups dichotomous outcome variable. The explanatory

variables can be continuous or categorical.

The requirements for simple logistic regression :

1- One dependent binary variable such as sex ( male, female ) ( yes, no )

2- One Independent continuous or categorical variables such as( height, time

of exercise, gender, marital status )

The requirements for multiple logistic regression :

1- One dependent binary variable such as gap acceptance choice ( yes, no ).

2- Two or more Independent continuous or categorical variables such as( height, time

of exercise, gender, marital status )

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3.4.2 Method of Model Work

The logistic regression can be used to predict the probability of the categorical

dependent variable based on one or more categorical and continuous predictors. Logistic

regression helps to calculate the adjusted odds ratio for the effects of other variables in

the model.

Logistic regression is the method for examining associations in epidemiological studies

such as cross sectional study and case-control study where the outcome is binary for

predicting a subject is a case or a control.

The logistic regression equation is written as:

(Y) Log odds of the outcome = (b0) + b1X1 + b2X2 + b3X3 + ......... (19)

(Y) Log odds of the outcome = (b0) + b1X1 + b2X2 + b3X3 + .........

Y : The log odds of the outcome coded ( 0 =q=1-p, 1=p )

A : Constant, Intercept, the coefficient of Y when X = 0

B : It is the rate of change in Y with a unit change in X

X : The independent variable that predict the probability of the outcome

3.4.2.1 Assumption

The logistic regression modeling has four assumption which are:

1. The sample must be representative of the population.

2. The relationship should be strong between the outcome and the explanatory variables.

3. The relationship must be linear between the logit transformation of the dependent

variable and the continuous independent variable

4.No multicollinearity .

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3.4.2.2 Model Formulation

Assuming that the average values of ( y) the actual or the viewing at a particular value

of the variable (x) is E(y), and the variable e represents the wrong e= y-y form it can

be written as follows:

E (y

x) = b0 + b1x + e (20)

It is well known in regression that the right end of these models takes the values of (∞

to-∞ ), but when we have variables ; one binary that is variable (Y ) , then the simple

linear regression is not suitable , because :

E (y

x) = p(y = 1) = p′, so the value of the right side is limited between the two values

(0,1 ). Thus, the model is not viable from the standpoint of regression . Therefore, one

of the ways to solve this problem is to enter conversion athlete appropriately on the

dependent variable ( y),and it is known that the values of probability is between (0≤p≤1

) and then the ratio (p/q) is an amount trapped between (0,-∞ ) , that is 0≤p/q≤0.Taking

the natural logarithm of (p/q), the value of the field becomes trapped between

(-∞≤ logp /q≤∞ ).So, the regression model can be written in the case of one independent

variable in the following form :

log.p

q= bo + and

(21)

And if there are more than one independent variable, the model will be in the form of:

log.p

q= bo + ∑ bjxij

k

i=1

(22)

Where: i=1,2,....n, j= 1,2....k

and it can be written in the form of:

p = 1

1 + exp [bo + ∑ bjxijki=1 ]

(23)

exp= inverse of natural logarithm

62

The logistic regression model is simply converting the logarithm linear regression.

Hence, it would be appropriate to use the properties of Logistics Distribution, which

restricts the estimated possibilities between (0,1). Estimating regression model

parameters is done by using the method of Maximum Likelihood(ML); one of the

famous method in statistical estimation methods. The function of ML measures

possibilities for a number n of independent variables as (p1,p2,...pn), which are located

in the sample and represents the multiplication of these possibilities.

3.4.3 Model Variables

In chapter two, numerous factors and variables were illustrated which they can affect

driver gap acceptance behavior. This research investigates the effects of the main driver,

traffic, vehicle, trip, and gap factors on driver gap acceptance.

3.4.3.1 Dependent Variables

Dependent variables is an indicator variable, either acceptance or rejection of a gap. The

actual choices are observed and takes a value of either one when accepting or zero when

rejecting.

3.4.3.2 Independent Variables

Independent variables that are modeled in this research include the following:

3.4.3.2.1 Driver Characteristics and Attributes

Based on literature survey, the following factors seem to be relevant to the studied

model:

1. Age & sex: It is expected that younger drivers accept shorter gaps, also male drivers

are hypothesized to accept shorter gaps than female.

2. Driving experience: It is expected that experienced driver will accept shorter gaps.

3. Level of education: As level of education increase, accepted gap is expected to

increase.

4. Familiarity with the site: Driver familiar with the site may accept shorter gaps.

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5. Ability to estimate the speed and distance of oncoming vehicle: If the estimated speed

is less than the actual speed, then drivers are expected to accept shorter gaps.

6. Accident and traffic violation records: Drivers with higher accident and traffic

violation rates are expected to accept shorter gaps.

3.4.3.2.2 Traffic Characteristics and Attributes

Based on literature survey, the following factors seem to be relevant to the studied

model:

1. Major stream volume: it is expected that driver will accept shorter gaps at higher

major stream volume.

2.Speed of oncoming vehicle: as discussed earlier there are variations in the effect of

this factor on gap acceptance. Here it is expected that as speed of oncoming vehicle

increases, accepted gap will decrease. This factor is connected with ability of the minor

street driver to estimate speed of oncoming vehicle.

3.Minor street delay: It is hypothesized that accepted gaps will decrease as delay

increase.

4. Queue size: driver is expected to accept shorter gaps when the queue of vehicles

waiting behind him is long.

3.4.3.2.3 Vehicle Characteristics and Attributes

The following factors seem to be relevant to the studied model and will be investigated:

1.Vehicle age: Driving newer vehicles may make drivers more confident about the

ability of their vehicles, and hence they may accept shorter gaps.

2.Engine capacity: drivers riding powerful vehicles are expected to accept shorter gaps.

Information on engine capacity in liters will be collected and will be used as indicator

for vehicle strength.

3.Vehicle type: drivers of trucks are expected to accept longer gaps, while drivers of

taxis are expected to accept shorter gaps compared of private cars.

64

4.Vehicle occupancy: it is expected that as vehicle occupancy increase, the accepted gap

will increase.

5. Type of transmission: drivers in cars with automatic transmission may accept shorter

gaps compared to driver in cars with manual transmission.

6.Vehicle ownership period: driving same car for a long period may make drivers more

confident about the ability of their vehicles, and hence they may accept shorter gaps.

3.4.3.2.4 Gap Characteristics and Attributes

Based on literature survey, the following factors seem to be relevant to the studied

model:

1. Type of gap(gap/lag): drivers respond indifferently to lags and gaps. In this research

it was studied if there is significant difference.

2.Gap/Lag type(near side/far side): drivers respond indifferently to near side and far

side gap /lag. In this research it was studied if there is significant difference.

3. Gap size: it is expected as gap size increase, acceptance probability will increase.

4.Size of gaps preceding the accepted gap: if the next gap is apparently long, driver may

reject the current gap, if the next gap is very short, driver may accept the current gap.

On the other hand, if the preceding gap is long enough, driver may try to compensate

for loosing such a gap, and he may try to accept the current gap even if it is short.

5.Number of rejected gaps: driver is expected to accept shorter gaps as number of

rejected gaps increase, this factor is similar to delay time.

3.4.3.2.5 Trip Characteristics and Attributes

Based on literature survey, the following factors seem to be relevant to the studied

model:

1. Trip purpose: It is expected that driver gap acceptance is sensitive to trip purpose, as

he for example may accept shorter gaps when he make a trip to work compared to

making a family trip.

65

2. Trip length: the travel distance may affect gap acceptance, as drivers traveling short

distances may accept longer gaps compared to drivers who may travel long distances.

3. Trip time: during peak hours, drivers may accept shorter gaps.

All of the independent variables are illustrated in Table 3.4:

66

Table 3.4: Gap Acceptance Variables

Group Variable Unit Source

Driv

er characteristics

Age Years Questionnaire

Sex Male/Female Questionnaire

Driving experience Years Questionnaire

Education Categories Questionnaire

Familiarity with site Number of times driver passes the site

monthly

Questionnaire

Accident & violation

records

Number of accidents in last 2years.

Number of traffic violation in last

year.

Questionnaire

Ability to estimate

oncoming car speed&

distance degree.

Difference between actual and

estimated speed/distance (categories).

Questionnaire

& Video

Traffic

characteristics

Major street volume Volume in 15 min (veh/15 min) Video record

Oncoming vehicle speed Meter / second Video record

Minor street delay Queue head delay in seconds Video record

Queue size Number of vehicles in queue Video record

Veh

icle characteristics

Vehicle age Years Questionnaire

Engine capacity Liters Questionnaire

Vehicle type Categories( PC, Taxi, Truck) Questionnaire

Vehicle occupancy Number of persons inside vehicle Questionnaire

Vehicle ownership Years Questionnaire

Transmission type Automatic/ Manual Questionnaire

Gap

characteristics

Type of gap Gap/lag Video record

Gap size Seconds Video record

Size of preceding gaps Actual size in seconds Video record

Number of rejected gaps Actual number of gaps rejected by the

driver before he accepts a gap

Video record

Tr

ip

char

acteris

tics Trip purpose Categories Questionnaire

67

Group Variable Unit Source

Trip length Time driver need to reach his

destination

Questionnaire

Trip time Categories ( peak-off-peak) Observation

68

4 . CHAPTER 4: RESULTS AND DISCUSSION

This chapter gives a summary of the collected data; provides the general description and

analyses conducted for these data; and discusses the critical gap derived for different

levels of drivers. The chapter also outlines the deriving of gap acceptance models in

addition to calibration and validation for these models.

4.1 Data Description

Data used in this study was collected in April 2014 from four-legs priority intersection

according to the methodology described in Chapter 3. One weekday was chosen as a

pilot survey for morning, and another day for morning and afternoon data. Based on the

traffic count at the intersection, a minimum of hour and half survey was carried out to

collect data.

The survey period was sufficient to get target sample size. Table 4.1 presents a

summary of the collected data.

Table 4.1: Summary of the collected data

Item Morning Afternoon

Total number of cars observed at minor road 125 75

Percentage of the interviewed drivers 73.6 % 53 %

Total number of gaps/lags evaluated by the

interviewed drivers

493 245

Average number of gaps/lags per interviewed driver 5.35 6.125

The total of observed cars are 200 car, and the total of interviewed drivers is 132 driver,

with an average 5.6 number of gaps/lags per interviewed drivers. As shown in previous

69

Table the average number of gaps/lag per interviewed driver for afternoon observations

is higher than morning.

4.2 Traffic Count

The count of major traffic volume was done for the two periods for each of the nearside

and far side of the straight movement from video records as described below.

4.2.1 Traffic count data

The next Tables summarize the conflicting major traffic count for the near side/far side

of the straight movement.

Table 4.2: Traffic count for near side-morning

Time Passenger car Truck Busses Other Total Sum

10:00-10:15 35 3 4 13 59

10:15-10:30 37 4 4 11 61

10:30-10:45 42 3 3 7 59

10:45-11:00 39 3 6 9 64 243

11:00-11:15 46 3 3 6 62 245

11:15-11:30 34 5 4 7 56 240

11:30-11:45 27 4 3 8 46 228

11:45-12:00 29 3 6 6 51 215

Sum 289 28 33 67 457

Table 4.3: Traffic count for far side-morning

Time Passenger car Truck Busses Other Total Sum

10:00-10:15 31 2 3 14 53

10:15-10:30 34 2 2 9 49

10:30-10:45 27 4 2 15 51

10:45-11:00 35 2 2 11 52 204

11:00-11:15 38 2 4 9 57 209

11:15-11:30 40 3 3 8 58 217

11:30-11:45 26 5 2 10 47 213

11:45-12:00 31 2 4 11 52 213

Sum 262 22 22 87 417

70

Table 4.4: Traffic count for near side-afternoon

Time Passenger car Truck Busses Other Total Sum

1:00-1:15 31 2 3 17 55

1:15-1:30 28 3 2 18 53

1:30-1:45 35 4 6 10 62

1:45-2:00 43 2 5 12 67 237

2:00-2:15 40 3 4 9 61 242

2:15-2:30 38 3 3 11 58 248

2:30-2:45 32 2 2 13 51 237

2:45-3:00 26 4 4 7 46 216

Sum 273 23 29 97 453

Table 4.5: Traffic count for far side-afternoon

Time Passenger car truck busses other total sum

1:00-1:15 28 1 2 14 46

1:15-1:30 26 2 4 20 55

1:30-1:45 36 3 3 17 62

1:45-2:00 35 4 4 15 63 225

2:00-2:15 37 2 3 13 58 237

2:15-2:30 36 1 4 14 58 240

2:30-2:45 37 3 3 15 61 239

2:45-3:00 30 2 3 9 47 224

sum 265 18 26 117 449

From previous Tables we can see that the afternoon traffic volume is higher than the

morning volume. Also the near side traffic volume is higher than the far side volume in

both of morning and afternoon periods.

4.2.2 Traffic count Results

The next Tables and Figures summarize the traffic count results for the near side/far

side conflicting major traffic for the straight movement. The traffic volume, is used as

an indicator in studying the variance of critical gap between morning and afternoon, and

between near side and far side. As shown in next graphs and Tables, there is not a

significant difference between traffic volumes, and percent of heavy traffic.

71

Table 4.6: Traffic count results for near side-morning

Near Side-Morning

Peak hour 33:35- 30:35 a.m

Peak hour volume (veh) 145

Max flow rate @ peak 21

PHF 0.250

Table 4.7: Traffic count results for far side-morning

Far Side-Morning

Peak hour 33:10- 30:10 a.m

Peak hour volume (veh) 217

Max flow rate @ peak 58

PHF 0.953

Table 4.8: Traffic count results for near side-afternoon

Near Side-Afternoon

Peak hour 1:10- 3:10 p.m

Peak hour volume (veh) 248

Max flow rate @ peak 67

PHF 0.925

Table 4.9: Traffic count results for far side-afternoon

Far Side-Afternoon

Peak hour 1:10- 3:10 p.m

Peak hour volume (veh) 240

Max flow rate @ peak 63

PHF 0.952

72

Figure 4.1: Vehicle type percentages-Near side morning

Figure 4.2: Vehicle type percentages-Far side morning

69%

7%

8%

16%

% of vehicle type

passenger car

truck

busses

others

67%5%

6%

22%

% of vehicle type

passenger car

truck

busses

others

73

Figure 4.3: Vehicle type percentages-Near side afternoon

Figure 4.4: Vehicle type percentages-Far side afternoon

As shown in pervious Figures the percentage of heavy vehicles in major stream ranges

from 10% to 15 %, while the percentage of passenger cars ranges from 62 to 69 %.

These statistics give an indicator that there is not a significant difference between traffic

composition for both far side and near side traffic.

65%5%

7%

23%

% of vehicle type

passenger car

truck

busses

others

62%

4%

6%

28%

% of vehicle type

passenger car

truck

busses

others

74

4.3 General Statistics for the Collected Data

Table 4.10 details out the general statistics for uncategorized variables of the

interviewed drivers.

Table 4.10: Basic Descriptive statistics for uncategorized variables

Item Level Percent

Number of persons

inside vehicle

Average 2.8

Min 1

Max 20

Vehicle Model

Average 1985

Min 1979

Max 2013

Vehicle ownership

(Year)

Average 4

Min 1

Max 31

Engine power

Average 1600

Min 900

Max 4200

Trip Time (min)

Average 18

Min 2

Max 60

Age (year)

Average 37

Min 20

Max 76

Driving experience

(year)

Average 15

Min 0.5

Max 50

Familiarity with site

(number/week)

Average 15

Min 1

Max 100

No. of accidents

Average 0.2

Min 0

Max 4

No. of traffic violations

Average 0.93

Min 0

Max 16

Queue size (number of

vehicles)

Average 0.3

Min 0

Max 3

Delay (sec)

Average 5

Min 0

Max 36.7

75

The previous variables were categorized by the help of using previous Table data in

addition to using related literature review. For example the average of the variable of

number of persons inside the vehicle is 2.8 person, so this variable can be categorized

into two levels (1 to 2 persons, and => 3 persons).

Table 4.11 details out the general statistics for interviewed drivers in the morning and

afternoon.

The basic observations on Table 4.11 include

1. There was just one case for female driver, which cannot give an indicator for sex

factor impact on gap acceptance.

2. Other factors have an acceptable variance in categorical levels.

3. In both of the variables number of accident and number of traffic violation, high

percentage of interviewed drivers recorded zero accident (83.9%) and traffic violation

(68.7%).

76

Table 4.11: General statistics for interviewed drivers

Item Level Percent % Categories

Vehicle Type

Taxi 23.7

Private 61.8

Bus/Truck 14.5

# persons inside vehicle 1 to 2 66.4 Normal

>=3 33.6 Middle

Vehicle Model >2003 38.2 Old

=<2003 61.8 New

Vehicle ownership <=2 52.7 Moderate

>2 47.3 High

Engine power <1600 45 Normal

>1600 55 Strong

Transmission Type Automatic 26

Manual 74

Trip Purpose

Work 77

Social/entertainment 16.1

Other 6.9

Trip Time

<10 43.5 Short

10 to 30 46.6 Middle

>30 9.9 Long

Sex Male 99.3

Female 0.7

Age <35 48.1 Young

>35 51.9 Old

Driving experience

< 3years 6.9 Normal experience

3 to 8 25.2

Moderate

experience

> 8 67.9 High experience

Education level

Primary 8.4

Preliminary 51.9

University 39.7

Familiarity with site

<10 48.8 Low familiarity

10 to 20 29.7 Middle familiarity

>20 21.5 High familiarity

Gap acceptance Criteria

Distance 38.2

Speed 19.1

Speed+ distance 42.7

speed

<30 Km/hr 32.9 Low

30 to 55 54.1 Moderate

> 55 13 Fast

Distance

< 30 m 9.1 Near

30 to 80 25.2 Moderate

> 80 65.7 Far

No. of accidents 0 83.9

77

Item Level Percent % Categories

1 12.2

>1 3.9

No. of traffic violations

0 68.7

1 15.2

> 1 16.1

Table 4.12 details out the number of accepted/rejected gaps/lags for each of the

variables of interviewed drivers.

78

Table 4.12: Accepted/rejected gaps and lags for interviewed drivers

Item Categories

No. of accepted

gap/lag

No. of rejected

gap/lag

Total No. of observed gaps/lags = 738

Gap/Lag Gap 161 319

Lag 97 161

Vehicle Type

Taxi 60 109

Private 160 301

Bus/Truck 38 70

# persons inside

vehicle

1 to 2 172 307

>3 86 173

Vehicle Model =>2003 110 219

<2003 148 261

Vehicle ownership <=2 134 296

>2 124 184

Engine power <1600 46 87

=>1600 212 393

Transmission Type Automatic 68 134

Manual 190 346

Trip Purpose

Work 200 332

Social/entertainm

ent 40 82

Other 18 66

Trip Time

<10 54 130

10 to 30 180 308

>30 24 42

Sex Male 256 477

Female 2 3

Age =<35 126 246

>35 132 234

Driving experience

< 3years 12 21

3 to 8 74 123

> 8 172 336

Education level

Primary 20 39

Preliminary 138 244

University 100 197

Familiarity with site

<10 130 225

10 to 20 76 149

>20 52 106

Gap acceptance

Criteria

Distance 100 177

Speed 48 88

Speed +distance 110 215

Speed

<30 Km/hr 84 158

30 to 55 140 260

> 55 34 62

79

Item Categories

No. of accepted

gap/lag

No. of rejected

gap/lag

Distance

< 30 m 23 44

30 to 80 65 121

> 80 170 315

No. of accidents

0 218 387

1 32 81

>1 8 12

No. of traffic

violations

0 178 342

1 40 66

> 1 40 72

The basic observations on Table 4.12 include:

1. The Percentage of accepted lag is higher than the percentage of accepted gap, this

indicates that drivers have higher tendency to accept lags.

2. Drivers who base their gap acceptance decision on estimating the distance of

oncoming vehicle have high tendency to accept gaps/lags.

3. The tendency to accept gaps/lags in work trip is high compared to non-work trip.

4. The tendency to accept gaps/lags in long trip time is higher compared to short trip

time.

5. The tendency to accept gaps/lags for drivers who have high record of traffic

violations and accidents is higher compared to low or zero record.

4.4 Analysis of The Critical Gap/Lag

This section presents the analysis results for gap data using Movie Maker & Excel

programs to determine the values of critical gap/lag .

Critical gaps are found using Raff's definition in which the critical gap/lag corresponds

to the intersection points of the cumulative curves drawn for the number of rejected

gaps longer than time t, and the number of accepted gaps accepted shorter than t.

4.4.1 Morning Period Critical Gap Values

The value of near side critical gap in morning is 3.8 sec as shown in Figure 4.5

80

Figure 4.5: Near side critical gap-Morning

The value of far side critical gap in morning is 2.8 sec as shown in Figure 4.6

Figure 4.6: Far side critical gap-Morning

The value of morning critical gap (near side + far side) is 3.6 sec as shown in Figure 4.7

0

50

100

150

200

250

0 2 4 6 8 10 12 14 16

No

. of

gap

s

Time

Near Side Critical Gap- Morning

No. of accepted gaps < t No. of gaps rejected > t

0

10

20

30

40

50

60

70

80

0 2 4 6 8 10 12 14 16

No

. of

gap

s

Time

Far Side Critical Gap-Morning

No. of accepted gaps < t No. of gaps rejected > t

81

Figure 4.7: Critical gap-Morning

From Previous Figures it is clear that:

1. The value of critical gap is affected by the length of gap whether it was accepted or

rejected.

2. Increasing the number of rejected short gaps leads to reduce the value of critical gap.

3.There is a clear difference between far side and near side values, as the value of far

side critical gap is less than near side critical gap, due to the delay that driver usually

experiences at near side, so he accepts shorter gap at far side.

4. The value of the critical gap at morning for the two stages is near to the value of the

near side critical gap.

5. Values of critical gap were small due to the reckless behavior of drivers and lack of

respect to traffic signs.

4.4.2 Morning Period Critical Lag Values

The value of near side critical lag in morning is 4.0 sec as shown in Figure 4.8

0

50

100

150

200

250

300

0 2 4 6 8 10 12 14 16

No

. of

gap

s

Time

Critical Gap-Morning

No. of accepted gaps < t No. of gaps rejected > t

82

Figure 4.8: Near side critical lag-Morning

The value of far side critical lag in morning is 3.0 sec as shown in Figure 4.9

Figure 4.9: Far side critical lag-Morning

The value of morning critical lag is 3.5 sec as shown in Figure 4.10

0

20

40

60

80

100

0 2 4 6 8 10 12 14 16

No

. of

lag

Time

Near Side Critical Lag_ Morning

No. of accepted lag < t No. of rejected lag > t

-10

0

10

20

30

40

50

60

70

0 2 4 6 8 10 12 14 16

No

. of

lags

Time

Far Side Critical Lag- Morning

No. of accepted lag < t No. of rejected lag > t

83

Figure 4.10: Critical lag-Morning

From Previous Figures it is clear that:

1. The value of the morning critical gap is larger than the morning critical lag.

2. The value of near side critical lag is larger than far side critical lag for the same

reasons mentioned previously , and due to that drivers usually when accept the near side

gap/lag, he tried to accept a gap/lag that lead to less traffic conflicting in the far side.

4.4.3 Afternoon Period Critical Gap Values

The value of afternoon near side critical gap is 3.6 sec as shown in Figure 4.11

0

20

40

60

80

100

120

140

160

0 2 4 6 8 10 12 14 16

No

. of

lags

Time

Morning Critical Lag

No. of accepted lag < t No. of rejected lag > t

84

Figure 4.11: Near side critical gap-afternoon

The value of afternoon far side critical gap is 3.1 sec as shown in Figure 4.12

Figure 4.12: Far side critical gap-afternoon

-20

0

20

40

60

80

100

120

0 2 4 6 8 10 12 14 16

No

. of

gap

s

Time

Near Side Critical Gap-Afternoon

No. of accepted gaps < t No. of rejected gaps > t

-5

0

5

10

15

20

25

30

35

40

45

0 2 4 6 8 10 12 14 16

No

. of

gap

s

Time

Far Side Critical Gap-Afternoon

No. of accepted gaps < t No. of rejected gaps > t

85

The value of afternoon critical gap is 3.4 sec as shown in Figure 4.13

Figure 4.13: Critical gap- Afternoon

From Previous Figures it is clear that:

1.There is a clear difference between far side and near side values, as the value of far

side critical gap is less than near side critical gap, for the same reasons mentioned

previously.

2. Values of critical gap were small due to the reckless behavior of drivers and lack of

respect to traffic signs.

4.4.4 Afternoon Period Critical Lag Values

The value of afternoon near side critical lag is 4.5 sec as shown in Figure 4.14

-20

0

20

40

60

80

100

120

140

160

180

0 2 4 6 8 10 12 14 16

No

. of

gap

s

Time

Critical Gap-Afternoon

No. of accepted gaps < t No. of rejected gaps > t

86

Figure 4.14: Near side critical lag-afternoon

The value of afternoon far side critical lag is 2.8 sec as shown in Figure 4.15

Figure 4.15: Far side critical lag-afternoon

The value of afternoon critical lag is 3.4 sec as shown in Figure 4.16

0

10

20

30

40

50

0 2 4 6 8 10 12 14

No

. of

lags

Time

Near Side Critical Lag-Afternoon

No. of accepted lag < t No. of rejected lag > t

-5

0

5

10

15

20

25

30

35

0 1 2 3 4 5 6 7 8 9

No

. of

lags

Time

Far Side Critical Lag-Afternoon

No. of accepted lag < t No. of rejected lag > t

87

Figure 4.16: Critical lag-afternoon

From Previous Figures it is clear that:

1. The value of afternoon critical lag is equal to afternoon critical gap.

2. The value of near side lag is also larger than far side lag.

4.4.5 Intersection Critical gap/lag Values

The value of whole near side critical gap(morning + afternoon) is 3.8 sec as shown in

Figure 4.17

0

10

20

30

40

50

60

70

80

0 2 4 6 8 10 12 14

No

. of

lags

Time

Critical Lag-Afternoon

No. of accepted lag < t No. of rejected lag > t

88

Figure 4.17: Intersection near side critical gap

The value of far side critical gap is 2.9 sec as shown in Figure 4.18

Figure 4.18: Intersection far side critical gap

The value of near side critical lag is 4.0 sec as shown in Figure 4.19

-50

0

50

100

150

200

250

300

350

0 2 4 6 8 10 12 14 16

No

. of

gap

s

Time

Intersection Near Side Critical Gap

No. of accepted gap < t No. of rejected gap > t

0

20

40

60

80

100

120

140

0 2 4 6 8 10 12 14 16

No

. of

gap

s

Time

Intersection Far Side Critical Gap

No. of accepted gap < t No. of rejected gap > t

89

Figure 4.19: Intersection near side critical lag

The value of far side critical lag is 2.9 sec as shown in Figure 4.20

Figure 4.20: Intersection far side critical lag

-20

0

20

40

60

80

100

120

140

0 2 4 6 8 10 12 14 16

No

. of

lags

Time

Intersection Near Side Critical Lag

No. of accepted lag < t No. of rejected lag > t

-20

0

20

40

60

80

100

120

140

160

0 2 4 6 8 10 12 14 16

No

. of

lags

Time

Intersection Far Side Critical Lag

No. of accepted lag < t No. of rejected lag > t

90

The value of Intersection critical gap is 3.5 sec as shown in Figure 4.21

Figure 4.21: Intersection critical gap

The value of Intersection critical lag is 3.4 sec as shown in Figure 4.22

Figure 4.22: Intersection critical lag

-100

0

100

200

300

400

500

0 2 4 6 8 10 12 14 16

No

. of

gap

s

Time

Intersection Critical Gap

No. of accepted gap < t No. of rejected gap > t

-50

0

50

100

150

200

250

0 2 4 6 8 10 12 14 16

No

. of

lags

Time

Intersection Critical Lag

No. of accepted lag < t No. of rejected lag > t

91

The summary of all gap/lag values are illustrated in Table 4.13

Table 4.13: Gap/lag values summary

Item Gap Lag

Morning near side 3.8 4.0

Morning far side 2.8 3.0

Morning (near side + far side) 3.6 3.5

Afternoon near side 3.6 4.5

Afternoon far side 3.1 2.8

Afternoon (near side + far side) 3.4 3.4

Intersection near side (morning +

afternoon)

3.8 4.0

Intersection far side (morning +

afternoon)

2.9 2.9

Intersection value (morning +

afternoon)

3.5 3.4

From Previous Figures & Table it is clear that:

1. Although the traffic volume in major street at afternoon is higher than morning,

afternoon drivers accept lower gap/lag than morning, which perhaps returns to that this

the time of employee's and students' departure and returning home.

2. In morning, afternoon and total intersection values, drivers accept lower gap/lag for

near side than far side.

3. There is a probability for increasing accidents ratio in afternoon, as drivers accept

lower gaps/lags value.

4. Drivers accept lower lags than gaps values, perhaps that drivers were more willing to

accept a lag than a gap of the same size.

5.When considering the whole intersection gap values data, the value of the critical lag

is less than the critical gap, although when considering near side and far side data, the

92

critical gap in both of them is less than the critical lag, and this return to that increasing

the number of rejected short lags leads to reduce the value of critical lag, and driver's

usually reject short times lag, as it is the first choice he decide to accept or not when he

enters the intersection, and he hope that a better and a larger gap will come next.

5. It was noted that approximately 40% of the lag data were lag acceptance data, while

about 60% of the total data were lag rejection data, while 33% of the gap data were gap

acceptance data.

Average values of accepted/rejected gaps/lags are illustrated in Table 4.14

Table 4.14: Average gap/lag values

Item Average accepted(s) Average rejected(s)

Intersection gap 6.79 1.38

Near side gap 7.17 1.41

Far side gap 6.22 1.39

Intersection lag 6.62 1.62

Near side lag 8.43 1.76

Far side lag 5.69 1.23

From previous Table it is obvious that there is a significant difference between average

gap/lag and critical gap/lag, and driver behavior is better described using critical gap

rather than the average gaps.

4.4.6 Factors Affecting Critical Gap Values

Table 4.15 illustrates the values of critical gap for different levels of studied attributes

considered in this study that can affect driver gap acceptance decision.

Critical gap graphs are included in Annex 2.

93

Table 4.15: Critical gap at different levels of the studied variables

Item Level Gap value

Vehicle Type

Taxi 3.3

Private 3.6

Bus/Truck 3.8

# persons inside vehicle 1 to 2 3.5

>=3 3.7

Vehicle Model >2003 3.7

<2003 3.5

Vehicle ownership <=2 3.6

>2 3.7

Engine power <1600 3.4

>1600 3.7

Transmission Type Automatic 3.6

Manual 3.6

Trip Purpose

Work 3.6

Social/entertainment 3

Other 4

Trip Time

<10 3.6

10 to 30 3.6

>30 3.3

Sex Male 3.6

Female N.A

Age <35 3.5

>35 3.7

Driving experience

< 3years 3

3 to 8 3.5

> 8 3.7

Education level

Primary 3

Preliminary 3.5

University 3.7

Familiarity with site

<10 3.5

10 to 20 3.7

>20 3.8

Gap acceptance Criteria

Distance 3

Speed 4.2

Speed + distance 3.7

No. of accidents

0 3.6

1 4.1

>1 3.3

No. of traffic violations

0 3.7

1 2.7

> 1 3.2

94

The main comments on Table 4.15 include:

1. Derived critical gaps changes over the range from 2.7 seconds to 4.2 seconds.

2. Some variables don't show a steady trend of change (increase/decrease) in the critical

gap as their level increase like number of accidents and number of traffic violations.

3. The change in critical gap is steady in its direction and expected in nature like vehicle

age , engine power , driver age, driving experience, familiarity with site, and education

level as critical gap increase continuously as each of them increase.

4. The critical gap decrease as the trip time and years of vehicle ownership increase.

5. The value of critical gap for female drivers cannot be determined as there was only

one case.

4.5 Comparing Critical Gap Value

Depending on Highway Capacity Manual (HCM) 2000, the next equation is used to find

the value of critical gap (HCM, 2000)

3,LTt –c,T t –G c,G + tHV Pc,HV + tc,base = t c,xt

where:

tc,x= critical gap for movement x (s),

tc,base= base critical gap from HCM.

tc,HV= adjustment factor for heavy vehicles (1.0 for two - lane major streets and 2 for

four-lane major streets)

PHV= proportion of heavy vehicles for minor movements

tc,G=adjustment factor for heavy vehicles (1.0 for two-lane major streets and

2.0 for four-lane major streets) (s),

G= percent grade divided by 100

95

tc,T= adjustment factor for each part of a two-stage gap acceptance process (1 for first or

second stage, 0 if only one stage)

t3,LT= adjustment factor for intersection geometry ( 0.7 for minor-street left-turn

movement at three-leg intersection, 0 otherwise)

Table 4.16 illustrates the values of tc,base and tf,base from HCM 2000.

Table 4.16: Base critical gaps and follow-up times for TWSC intersections.

Base follow up

time

tf,base (s)

Base Critical Gap , tc,base (s) Vehicle Movement

Four lane Major

street

Two lane Major

street

2.2 4.1 4.1 Left turn from major

3.3 6.9 6.2 Right turn from

major

4.0 6.5 6.5 Through traffic on

major

3.5 7.5 7.1 Left turn from minor

4.5.1 Morning Critical Gap values

The near and far side critical gap value by using HCM equation is:

3,LTt –c,T t –G c,G + tHV Pc,HV + tc,base = t c,xt

tc,x = 6.9 + 1 * 0.145 + 0.2 * 0.04 - 1 - 0 = 6.05 sec

Assuming one stage gap acceptance process the morning intersection critical gap is

3,LTt –c,T t –G c,G + tHV Pc,HV + tc,base = t c,xt

tc,x = 6.9 + 1 * 0.145 + 0.2 * 0.04 - 0 - 0 = 7.05 sec

4.5.2 Afternoon Critical Gap values

The near and far side critical gap value by using HCM equation is:

3,LTt –c,T t –G c,G + tHV Pc,HV + tc,base = t c,xt

tc,x = 6.9 + 1 * 0.157 + 0.2 * 0.04 - 1 - 0 = 6.065 sec

96

Assuming one stage gap acceptance process the afternoon intersection critical gap is

3,LTt –c,T t –G c,G + tHV Pc,HV + tc,base = t c,xt

tc,x = 6.9 + 1 * 0.157 + 0.2 * 0.04 - 0 - 0 = 7.065 sec

From previous results there is a clear difference between values of practical critical gap

when computing it graphically and estimated critical gap when using HCM equation. As

the results from site is less than values by using HCM equation, which means that

critical gap HCM equation cannot be used on selected intersection due to the difference

of drivers behavior in Gaza Strip.

4.6 Comparing Potential Capacity Value

The potential capacity of each minor traffic stream can be computed by using HCM

2000 next equation

𝐶𝑝, 𝑥 = 𝑉𝑐, 𝑥𝑒−𝑉𝑐,𝑥 𝑡𝑐,𝑥/3600

1 − 𝑒−𝑉𝑐,𝑥 𝑡𝑐,𝑥/3600

where:

cp,x= potential capacity of minor movement x (veh/h),

vc,x= conflicting flow rate for movement x (veh/h),

tc,x=critical gap (i.e., the minimum time that allows intersection entry for one minor-

stream vehicle) for minor movement x (s), and

tf,x= follow-up time (i.e., the time between the departure of one vehicle from

the minor street and the departure of the next under a continuous queue

condition) for minor movement x (s).

The conflicting flow rate for movement is in Annex 3.

The follow-up time for minor movement is computed by using HCM next formula:

tf,x = tf,base + tf,HV PHV

where:

tf,x = follow-up time for minor movement x (s),

tf,base = base follow-up time from Exhibit 17-5 (s),

97

tf,HV= adjustment factor for heavy vehicles (0.9 for two-lane major streets and

1.0 for four-lane major streets), and

PHV= proportion of heavy vehicles for minor movement.

Table 4.17 illustrates the results of potential capacity values comparing between using

HCM critical gap value and using graphically critical gap value.

Table 4.17: Potential capacity compare.

Period tf,x Cp,x HCM Cp,x graphically

Morning 4.15 466.86 685

Afternoon 4.13 465.34 699.19

From previous Table, it is obvious that there is clear difference in potential capacity

when using HCM critical gap and graphically critical gap, which is evidence that HCM

gap acceptance equations and formulas cannot be implemented in Gaza Strip due to

differences in driver behavior, as the value of the critical gap decrease the value of

potential capacity increase.

This difference increases the capacity of the studied movement by an average about

48%.

4.7 Gap Acceptance and Driver Behavior Models

One of the objectives of this research is to develop a model for gap acceptance and to

investigate the effects of driver, vehicle, trip, and gap factors on driver gap acceptance

behavior.

Data collected at site was tried to be used in developing six separate models for gap. lag,

near side gap, near side lag, far side gap and far side lag, but the logistic regression

analysis get out with just one model for only gap acceptance.

The modeling procedure for this research is summarized as follow:

98

1. Calibrate and validate a model for each of the gap/lag types mentioned above, and

find out which of variables is significant in explaining driver gap acceptance behavior at

the desired level of significance which is 5%.

2. Validate the model calibrated using the data portion reserved for this purpose.

3. Test the assumption that drivers action to gaps is different from their response to lags.

4. Test the assumption that drivers response to near side gap/lag is different from their

response to far side gap/lag.

5. Some variables like queue size and delay are just used in gap models, and are not

used in lag models , as drivers evaluate lags in the moment they reach the stop line of

the intersection, so these variables will have no effect on lag acceptance.

4.7.1 Gap Model Calibration and Validation

The gap model is summarized in Table 4.18

99

Table 4.18: Gap Model Details.

Prob. (accept) =1/(1+exp[6.328 - 3.768 Gap Value + 0.065 Trip duration + 0.575

Delay + 3.306 aG Gee aGne epaa paG(speed) - 0.393 No. of traffic violations])

Variable/Statistic Coefficient

Significance Exp()

Constant -6.328 0.994

Gap Value 3.768 43.296 0.000

Trip duration -0.065 0.937 0.003

Delay -0.575 0.563 0.003

Gap acceptance criteria (speed) -3.306 0.037 0.032

No. of traffic violations 0.393 1.481 0.042

n (Number of observations) 480.000

-2 Log likelihood: Unrestricted model G2(M0) 612.431

-2 Log likelihood: Restricted model G2(M1) 49.387

Log Likelihood ratio G2(M0|M1) 563.043

Degrees of freedom for G2(M0|M1) 24

Sig. level for G2(M0|M1) 0.000

Hosmer and Lemeshow Test 3.440

Degrees of freedom for Hosmer and Lemeshow 7

Sig. level for Hosmer and Lemeshow 0.842

PCP (% corrected predicted observations) 98.50%

The main comments on the model include the following:

a. Based on the Significance. (P-value), each of the next independent variable is

statistically significant at 0.05 level since the p- value corresponding to each one is

smaller than the 0 05. (level of significance). The variables are listed according to

their impact on gap accepting from largest to smallest significant:

1. Gap value in seconds,

100

2. Trip duration in minutes,

3. Delay that driver experience in seconds,

4. Gap acceptance criteria, when the choice is speed,

5. Number of traffic violations in the last year.

The other independent variables are not statistically significant at 0.05.

b. The impact of Gap acceptance on factors is measured by the odds ratio Exp(()

,which are for the effective factors:

1. A one unit change in the Gap Value increases the odds of Gap acceptance by a factor

of 43.296; that is there is a 422.96% increase ((43.296-1)*100%).

2. A one unit change in the Trip duration decreases the odds of Gap acceptance by a

factor of 0.937; that is there is a 6.3% decrease ((0.937-1)*100%).

3. A one unit change in the Delay decreases the odds of Gap acceptance by a factor of

0.563; that is there is a 43.7% decrease ((0.563-1)*100%).

4. A one unit change in the Gap acceptance criteria (speed) decreases the odds of Gap

acceptance by a factor of 0.037; that is there is a 96.3% decrease ((0.037-1)*100%).

5. A one unit change in the Number of traffic violations increases the odds of Gap

acceptance by a factor of 1.481; that is there is a 48.1% increase ((1.481-1)*100%).

c. Signs of the variable coefficients agree with the expected driver gap acceptance

behavior as mentioned in Chapter 2. It is expected that the probability of accepting a

gap increases as each of the gap size and number of traffic violations increases and is

expected to decreases as the trip duration, delay and gap acceptance criteria ( speed )

increase.

The decrease in gap acceptance probability with the increase in trip duration indicates

that drivers making longer trips tend to wait for longer gaps.

d. The constant term in the model is called the accept choice-specific constant. A

positive constant indicates a relative preference to accept gaps, while a negative

101

constant indicates a relative preference to reject gaps. (Ben-Akiva and Lerman ,1985).

In this model the constant term is not significantly different at 5 %.

e. The high percentage of the correctly predicted observations 98.5% is an indicator of

the good capability of the model in replicating driver gap acceptance behavior.

The full model analysis detail is shown in Annex 4.

4.7.1.1 Goodness of Fit of a Likelihood-Ratio Test (Model Validation)

The likelihood-ratio statistic -2(L0-L1) tests whether certain model parameters are zero

by comparing the log likelihood L1 for the fitted model M1 with L0 for a simpler model

M0 to check the validity of model. Denote this statistic for testing M0, given that M1

holds, by G2(M0|M1).

G2(M0|M1) = -2(L0-L1) = G2(M0) - G2(M1)

= 612.431 - 49.387

= 563.043

The likelihood Ratio Test Statistic (Chi-Squared calculated) = 563.043

Chi-Squared tabulated value at (0.05, 24) = 36.42

To test whether the independent variables contribute significantly to model, we test

0 1 2 24 0:H L

Where βi is the coefficient of the ith variable in utility function. This states that the

probability of ( Gap acceptance) is not related of the independent variables. This means

there is no significant relationship between of the independent variables and whether the

Gap is rejected or accepted.

Since the Chi-Squared calculated = 563.043 is greater than Chi-Squared tabulated value

= 36.42, then we reject the null hypothesis H0. Similar result can be reached by using

Sig. (p-value) = 0 .000 which is smaller than the 0 05. (level of significance). This

result indicates that there is at least one of the independent variable is significantly

102

different from zero, i.e. there is at least one of the independent variable has significant

effect on the probability of ( Gap acceptance).

4.7.1.2 Hosmer-Lemeshow Goodness-of-Fit Statistic (Model Validation)

This goodness-of-fit statistic is more robust than the traditional goodness-of-fit statistic

used in logistic regression, particularly for models with continuous covariates and

studies with small sample sizes.

For the logistic regression fit to the Gap data with the mentioned independent variables,

the Sig. level for Hosmer and Lemeshow = 0.842 which is greater than the 0 05.

(level of significance), this result also indicates a decent fit.

4.7.1.3 The percentage of Observations

In the sample that a particular estimated equation explains correctly, 2pR , is given by:

2 Number of observations "predicted" correctly

Total number of observationspR

Note that 2pR = 0.985, indicating that the equation correctly "predicted" 96.5% of all

sample data based on the mentioned independent variables.

4.7.1.4 The Predicted Model

Prob. (accept) =1/(1+exp[6.328 - 3.768 Gap Value + 0.065 Trip duration + 0.575 Delay

+ 3.306 aG Gee aGne epaa paG(speed) - 0.393 No. of traffic violations]).

4.7.1.5 Gap Models Comparison

Table 4.19 presents the gap models results for the most significant variables that affect

driver's gap acceptance of some previous studies.

As shown in Table 4.19 the variables listed according to their impact on gap accepting

from largest to smallest significant, each of these independent variables is statistically

significant at 0.05 level.

103

Table 4.19: Significant Variables of Gap Models in Past Studies.

Reference Rossi et al.

(2012)

Bottom &

Ashworth

(2007)

Patil,

Patare &

Sangole

(2011)

Abu

Sheikh

(1997)

Variable 1 Gap size Speed of

oncoming

vehicle

Type of

gap

Gap size

Variable 2 Gender

Gap size

Age

Speed of

oncoming

vehicle

Variable 3 Driving style

( Anxious,

Angry)

Vehicle Type

Vehicle

occupancy

Delay

Variable 4 - Delay

Number of

rejected

gap

Queue size

Variable 5 - Engine

capacity

- No. of

accidents

Variable 6 - - - Driver

experience

Variable 7 - - - Trip

duration

By comparing the developed gap model results in this thesis with these results, There

is similarity in variables as:

1. The gap size variable is significant in three of these models.

2. The delay variable is significant in two of these models.

3.The speed of oncoming car variable is significant in two of these models .

4. The trip duration variable is significant in two of these models.

5. The number of traffic violations variable is not significant in any of these models.

Each model of them is developed for a different movement, and all models are for a

three leg intersection.

104

4.7.2 Other Gap/lag Models

As mentioned previously, we tried to develop other five models for gap/lag types

separately, but there were not enough significant variables to build models, which may

return to the following reasons:

1. Driver behavior for lag, near side and far side gap/lag is unpredicTable in Gaza due to

the reckless behavior of drivers.

2. Many factors were considered in the modeling process, minimizing the variables to

five or sex variables may led to better models, but it will minimizes the effectiveness

factors to a limit number.

The results of models are described below:

4.7.2.1 Result of the Logistic Regression Model for far side gap

Based on the Sig. (P-value), none of the independent variable is statistically significant

at 0.05 level since the p- value corresponding to each one is greater than the 0 05.

(level of significance). Complete results are shown in Annex 5.

4.7.2.2 Result of the Logistic Regression Model for near side gap

Based on the Sig. (P-value), Gap value is the only significant independent variable. The

other independents variable is statistically insignificant at 0.05 level since the p- value

corresponding to each one is greater than the 0 05. (level of significance). Complete

results are shown in Annex 6.

4.7.2.3 Result of the Logistic Regression Model for Lag

Based on the Sig. (P-value), Lag value is the only significant independent variable. The

other independents variable is statistically insignificant at 0.05 level since the p- value

corresponding to each one is greater than the 0 05. (level of significance). Complete

results are shown in Annex 7.

4.7.2.4 Result of the Logistic Regression Model for near side lag

Based on the Sig. (P-value), Lag value is the only significant independent variable. The

other independents variable is statistically insignificant at 0.05 level since the p- value

105

corresponding to each one is greater than the 0 05. (level of significance). Complete

results are shown in Annex 8.

4.7.2.5 Result of the Logistic Regression Model for far side lag

Based on the Sig. (P-value), none of the independent variable is statistically significant

at 0.05 level since the p- value corresponding to each one is greater than the 0 05.

(level of significance). Complete results are shown in Annex 9.

4.7.3 Driver Response to Near side/Far side Gaps/Lags

One of our concern is to study whether driver reaction in accepting gaps/lags is

significantly different or not, which will be described in next sections.

4.7.3.1 Driver Response to Gaps/Lags

Table 4.20 shows the result of independent samples T-test between lag and gap. The

mean for lag equals 6.63, with Standard deviation SD of 3.58, the mean for gap equals

6.79, with SD of 3.55. The value of the T-test equals -0.365, with p-value equals 0.716.

This implies that there is insignificant difference in the mean between lag and gap.

Table 4.20: Result of Independent Samples T- Test between Lag and Gap.

Type N Mean SD Test value P-value

Lag 96 6.63 3.58 -0.365 0.716

Gap 161 6.79 3.55

Another Test was done for the proportion of accepted/rejected gap/lag, Table 4.21

shows the following results:

106

Table 4.21: Proportions between "Lag" and "Gap" for Rejected/Accepted Gap.

Type of

Gap

type

Total

Test Statistic

Sig.(P-

value)

Lag Gap

Rejected Count 161 319 480

1.214

0.271

% within

type 62.4% 66.5% 65.0%

Accepted Count 97 161 258

% within

type 37.6% 33.5% 35.0%

Total Count 258 480 738

% within

type 100.0% 100.0% 100.0%

For rejected gap, the proportions of "Lag" and "Gap" are 62.4% and 66.5%. For

accepted gap, the proportions of "Lag" and "Gap" are 37.6% and 33.5%.

The Pearson Chi-squared value of 1.214 with p-value 0.271 indicates there is

insignificant difference for proportions of rejected/accepted between "Lag" and "Gap".

We conclude that gap acceptance (Rejected/ accepted) and gap type (Lag/Gap) are

independent of each other. In other words, these two variables are insignificantly

related.

4.7.3.2 Comparison between Far Side Gap and Near Side Gap

Table 4.22 shows the result of independent samples T-test between far side gap and near

side gap.

The mean for far side gap equals 6.22, with SD of 2.73, the mean for near side gap

equals 7.18, with SD of 3.97. The value of the T-test equals -1.685, with p-value equals

0.047. Since the p-value is smaller than 0.05 (level of significance), then there is

significant difference in the mean between far side gap and near side gap. Since the sign

of the T-test is negative, then mean of far side gap is significantly smaller than that for

near side gap.

107

Table 4.22: Result of Independent Samples T- Test between Far Side Gap and Near Side Gap.

Type N Mean SD Test value P-value

Far Side Gap 65 6.22 2.73

-1.685 0.047*

Near Side Gap 96 7.18 3.97

* The mean difference is significant at 0.05 level

4.7.3.3 Comparison between Far Side Lag and Near Side Lag

Table 4.23 shows the result of independent samples T-test between far side lag and near

side lag.

The mean for far side lag equals 5.69, with SD of 2.32, the mean for near side lag

equals 8.43, with SD of 4.73. The value of the T-test equals -3.135, with p-value equals

0.002. Since the p-value is smaller than 0.05 (level of significance), then there is

significant difference in the mean between far side lag and near side lag. Since the sign

of the T-test is negative, then mean of far side lag is significantly smaller than that for

near side lag.

Table 4.23: Result of Independent Samples T- Test between Far Side Lag and Near Side Lag.

Type N Mean SD Test value P-value

Far Side Lag F 64 5.69 2.32

-3.135 0.002* Near Side Lag F 33 8.43 4.73

* The mean difference is significant at 0.05 level

108

5 CHAPTER 5: CONCLUSIONS AND RECOMMENDATIONS

5.1 Introduction

This chapter summarizes the basic findings, and the main derived conclusion about the

effects of the studied vehicle, trip, driver, gap and traffic attributes on driver gap

acceptance at priority intersection. Also this chapter is listing the main

recommendations for future research in this field.

5.2 Conclusion

At the end of this study, the next main conclusions were derived:

1. Driver and trip attributes are the main factors that affect driver gap acceptance

behavior.

2. The value of critical gap that were obtained is lower than HCM values.

3. The value of far side gap/lag is less than the value of near side gap.

4. There is an insignificant difference between driver reaction to gaps and their reaction

to lags.

5. Drivers reaction to near side gap/lag is significantly different than their reaction to far

side gap/lag.

6. The gap value is the most significant variable in the gap model, followed by trip

duration, delay, gap acceptance criteria (speed), and number of traffic violations.

7. The use of logistic regression model has led to the following equation to study driver

behavior for accepting or rejecting a gap, and which can be used in different

applications in traffic engineering. The equation is:

Prob. (accept) =1/(1+exp[6.328 - 3.768 Gap Value + 0.065 Trip duration + 0.575 Delay

+ 3.306 aG Gee aGne epaa paG(speed) - 0.393 No. of traffic violations]).

8. There are not significant variables enough to build a model for driver's acceptance of

lag, near side and far side gap/lag.

109

5.3 Recommendations

At the end of this study, the following points can be recommended:

1- Development of similar models for similar intersections for different characteristics

to study the transferability of calibrated models.

2- HCM critical gap formulas & values used in traffic planning & designing in Gaza

are recommended to be changed as mentioned in the thesis with further investigation in

this regard is recommended.

3- It is recommended to extend this work to study different movements in the same

intersection, with same factors, and compare results with this study.

4- It is recommended to develop more models at different intersections, to get more

calibrated model to be used for Gaza.

5- It is recommended to study the lag, near side and far side lag/gap with more sample

size and less factors.

6. The methodology and approach used in this thesis open the gate for more traffic

modeling studies in Gaza city and other Palestinian cities.

110

REFERENCES

1) Abdul Kareem, A. (2001). 'A Comparative Study of Gap Acceptance at Priority

Intersections', University of Ilorin.

2) Adebisi , O. (1982) ' Driver gap acceptance phenomenon ', Journal of

Transportation Engineering , vol . 108 , no . TE6 , pp . 676 - 689.

3) Abdesi, O. & Sama, G.N. (1989),'Influence of stopped delay on driver gap

acceptance behavior', Journal of transportation engineering, vol. 115, no. 3, pp.

305-315.

4) Abu sheikh , A. (1997). ' Developing behavioral models for driver gap

acceptance at priority intersection ' Phd thesis, King Fahd University Of

Petroleum And Minerals.

5) Almasri, E. H. (2012), ' Improving traffic performance by coordinating traffic

signals using Transyt-7F model: Eljalaa Arterial Road in Gaza City as a Case

Study', The 4th International Engineering Conference, Gaza, Palestine.

6) Al-Jazzar, M. (2012). 'Evaluating and Modeling the Gaza Transportation System

Based on GIS and TransCAD Software' Master Thesis, Islamic University Of

Gaza.

7) Ben-Akiva, M., & Lerman, S.R. (1985),'Discrete choice analysis: Theory and

applications to travel demand,' Cambridge, Massachusetts.

8) Bottom, C. G. , & Ashworth, R. (2007),' Factors affecting the variability of

driver gap- acceptance behavior', Ergonomics, vol. 21, no.9, pp.721-734.

9) Brilon, W., Koeing, R. & Troutbeck, R.J. (1999),'Useful estimation procedures

for critical gaps', Transportation Research, Part A, vol. 33, pp. 161-186.

10) Dissanayake, S., Lu, J. J., & Yi, P. (2001), ' Driver age differences in day and

night gap acceptance capabilities', IATSS Research , vol.26, no.1, University

Nanjing, China.

11) Farah, H., Polus, A., Bekhor, S., & Toledo, T. (2007),' Study of passing gap

acceptance behavior using a driving simulator', Advances in Transportation

Studies an international Journal.

12) Gattis , J. L. & Sonny, T. Low. (1998) , ' Gap acceptance at nonstandard stop-

controlled intersections', University of Arkansas.

13) Guo, R. J., & Lin, B. L. (2011). 'Gap acceptance at priority – controlled

intersection ' , Journal of Transportation . Engineering , pp. 269 – 276 .

14) Hagring, O. ( 2000), 'Estimation of critical gaps in two major streams',

Transportation Research ,Part, B .34, pp. 293-313.

111

15) Hunt, M., Harper, D.N., Lie, C. (2011),' Mind the gap: Training road users to

use speed and distance when making gap-acceptance decisions', Accident

Analysis and Prevention, vol. 43, pp. 2015– 2023.

16) Hwang, S.Y., & Park C.H. (2005),' Modeling of the gap acceptance behavior at

at merging section of urban freeway', Eastern Asia Society for Transportation

Studies, vol. 5, pp. 1641 - 1656.

17) Kearney, J.K., Grechkin, T., Cremer, J., & Plamert, J. (2006),'Traffic generation

for studies of gap acceptance', The University of Iowa.

18) Mhna, A., Alkhaldy, H., Almshhrawi, S., & Mter, H. (2013),' Critical gap at

priority intersections for left-turn from major street' Bachelor Project, Islamic

University of Gaza.

19) Nabaee, S., Moore, D., & Hurwitz, D. (2011),' Revising driver behavior at

unsignalized intersections: Time of day implications for two-way left turn

lanes(TWLTL)', the Sixth International Driving Symposium on Human Factors

in Driver Assessment, Training and Vehicle Design.

20) Palestinian Central Bureau of Statistics (PCBS) 2007 , “Demographic and

Transportation Statistics”, Palestinian National Authority, Gaza.

21) Palestinian Central Bureau of Statistics (PCBS) 2010, “Annual census

Palestinian book”, Palestinian National Authority, Gaza.

22) Palestinian Central Bureau of Statistics (PCBS) 2012 , “Demographic and

Transportation Statistics”, Palestinian National Authority, Gaza.

23) Patil, G. P., Pataer, P., Sangole, J. p. (2011), ' Gap acceptance behavior of two-

wheelers at limited priority uncontrolled intersections', Transportation Research

Board 90th Annual Meeting, Washington, D. C.

24) Rene, L.A., Manoj, K.J. (2012).'Modeling gap acceptance and driver behavior at

stop controlled (priority) intersections in developing countries', Applied

Mathematics in Electrical and Computer Engineering, pp. 29-38.

25) Rossi, R., Gastaldi, M., Gecchele, G., & Meneguzzer, C. (2012), 'Comparative

analysis of random utility models and fuzzy logic models for representing gap-

acceptance behavior using data from driving simulator experiments',15th Edition

of the Euro Working Group on Transportation International Scientific

Conference. Padova, Italy.

26) Sarraj, Y. (2001).'Behavior of road users in Gaza, Palestine', Journal of the

Islamic University of Gaza, v.9, no. 2,pp.85-101.

27) The free encyclopedia, Available from the URL:

http://en.wikipedia.org/wiki/Gaza (accessed on December 2013)

28) Tian, Z, Troutbeck, R, Michael, K, Brilon, W, Vandehey, M, Kittelson W, &

Robinson B. (2000), 'A further investigation on critical gap and follow-up time',

112

Transportation Research Circular E-C018: 4th International Symposium on

Highway Capacity . pp397-408.

29) Transportation Research Board. Highway Capacity Manual 2000. Washington,

D.C., 2000.

30) Transportation Research Board. Highway Capacity Manual 1994. Washington,

D.C., 1994.

31) Transportation Research Board. Highway Capacity Manual 1985. Washington,

D.C., 1985.

32) Tupper, S.M., Jr Knodler, M.A., & Hurwitz, D.S. (2011),'Connecting gap

acceptance behavior with crash experience', 3rd International Conference on

Road Safety and Simulation, USA.

33) Velan, S.M., & Aerde, M.V. (1996),' Gap acceptance and approach capacity at

unsignalized intersections', ITE Journal, pp. 40-45.

34) Wu, N. (2006), 'A New model for estimating critical gap and its distribution at

unsignalized intersections based on their equilibrium of probabilities ', 5th

International Symposium on Highway Capacity and Quality of Service.

Yokohama, Japan.

113

ANNEX 1: QUESTIONNAIRE

Studying Driver Gap Acceptance Behavior At Priority Intersections

Driver's Field Interview Questionnaire

Interviewee:.................................... Date:..................... Day:..................... Time:.............

Part one: Vehicle's information

1- Registration no:

1-Vehicle usage: Private Taxi Bus/Truck

1-Vehicles' type: Color:

4- # persons in car(with driver):

5- Year of production:

2- Years of car ownership: Year

0- Engine power:

8- Transmission type: Automatic Manual

Part two: Trip's information:

9-Trip purpose: Work Social /Entertainment Other

10-Trip expected duration: Min

Part three: Driver's information:

11- Gender: Male Female

12- Age: years

13- Driving experience: Years

14- Education Level: Primary Secondary University

15- No. of times passing this intersection /week: Times

16- On what you took your decision to accept the gap you have crossed:

A- Opposing car speed B- Distance between you and the car C-Speed+ Distance

17- Estimation of opposing car speed you have crossed in front of it:

A- Fast B- Moderate C-Slow

18- Estimation of opposing car distance you have crossed in front of it:

A- Far B- Moderate distance C-Near

19- No. of traffic accidents per last two years:

18-No. of traffic violation you had through last year:

114

ANNEX 2: CRITICAL GAP GRAPHS FOR FACTORS

-10

0

10

20

30

40

50

60

70

80

0 2 4 6 8 10 12 14 16

No

. of

gap

s

Time

Critical Gap for Taxi

No. of accepted gaps < t No. of gaps rejected > t

-50

0

50

100

150

200

250

0 2 4 6 8 10 12 14 16

No

. of

gap

s

Time

Critical Gap for Private Vehicle

No. of accepted gaps < t No. of gaps rejected > t

115

-10

0

10

20

30

40

50

0 2 4 6 8 10 12 14 16

No

. of

gap

s

Time

Critical Gap for Heavy Vehicle

No. of accepted gaps < t No. of gaps rejected > t

-50

0

50

100

150

200

250

0 2 4 6 8 10 12 14 16

No

. of

gap

s

Time

Critical Gap for 1-2 Persons Inside Vehicle

No. of accepted gaps < t No. of gaps rejected > t

116

-20

0

20

40

60

80

100

120

140

0 2 4 6 8 10 12 14 16

No

. of

gap

s

Time

Critical Gap for >3 Persons Inside Vehicle

No. of accepted gaps < t No. of gaps rejected > t

-50

0

50

100

150

200

0 2 4 6 8 10 12 14 16

No

. of

gap

s

Time

Critical Gap for OLd Vehicle

No. of accepted gaps < t No. of gaps rejected > t

117

-20

0

20

40

60

80

100

120

140

160

0 2 4 6 8 10 12 14 16

No

. of

gap

s

Time

Critical Gap for New Vehicle

No. of accepted gaps < t No. of gaps rejected > t

-50

0

50

100

150

200

250

0 2 4 6 8 10 12 14 16

No

. of

gap

s

Time

Critical Gap for <=2 Years Vehicle Ownership

No. of accepted gaps < t No. of gaps rejected > t

118

-20

0

20

40

60

80

100

120

140

0 2 4 6 8 10 12 14 16

No

. of

gap

s

Time

Critical Gap for >2 Years Vehicle OwnershipNo. of accepted gaps < t No. of gaps rejected > t

-20

0

20

40

60

80

100

120

140

160

0 2 4 6 8 10 12 14 16

No

. of

gap

s

Time

Critical Gap for Normal Engine power No. of accepted gaps < t No. of gaps rejected > t

119

-50

0

50

100

150

200

0 2 4 6 8 10 12 14 16

No

. of

gap

s

Time

Critical Gap for Strong Engine Power No. of accepted gaps < t No. of gaps rejected > t

-20

0

20

40

60

80

100

0 2 4 6 8 10 12 14 16

No

. of

gap

s

Time

Critical Gap for Automatic Vehicle

No. of accepted gaps < t No. of gaps rejected > t

120

-50

0

50

100

150

200

250

0 2 4 6 8 10 12 14 16

No

. of

gap

s

Time

Critical Gap for Manual Vehicle

No. of accepted gaps < t No. of gaps rejected > t

-20

0

20

40

60

80

100

120

140

160

180

0 2 4 6 8 10 12 14 16

No

. of

gap

s

Time

Critical Gap for Work Trip

No. of accepted gaps < t No. of gaps rejected > t

121

-10

0

10

20

30

40

50

60

0 2 4 6 8 10 12 14 16

No

. of

gap

s

Time

Critical Gap for Other Trip

No. of accepted gaps < t No. of gaps rejected > t

-5

0

5

10

15

20

25

0 2 4 6 8 10 12 14 16

No

. of

gap

s

Time

Critical Gap for Social Trip

No. of accepted gaps < t No. of gaps rejected > t

122

-20

0

20

40

60

80

100

0 2 4 6 8 10 12 14 16

No

. of

gap

s

Time

Critical Gap for <10 min. Trip Duration

No. of accepted gaps < t No. of gaps rejected > t

-50

0

50

100

150

200

250

0 2 4 6 8 10 12 14 16

No

. of

gap

s

Time

Critical Gap for 10-30 min Trip Duration

No. of accepted gaps < t No. of gaps rejected > t

123

-5

0

5

10

15

20

25

30

0 2 4 6 8 10 12 14 16

No

. of

gap

s

Time

Critical Gap for >30 min trip Duration

No. of accepted gaps < t No. of gaps rejected > t

-50

0

50

100

150

200

250

300

350

0 2 4 6 8 10 12 14 16

No

. of

gap

s

Time

Critical Gap for Male Drivers

No. of accepted gaps < t No. of gaps rejected > t

124

-50

0

50

100

150

200

0 2 4 6 8 10 12 14 16

No

. of

gap

s

Time

Critical Gap for Young Drivers

No. of accepted gaps < t No. of gaps rejected > t

-20

0

20

40

60

80

100

120

140

160

0 2 4 6 8 10 12 14 16

No

. of

gap

s

Time

Critical Gap for Old Drivers

No. of accepted gaps < t No. of gaps rejected > t

125

-2

0

2

4

6

8

10

12

14

0 2 4 6 8 10 12 14 16

No

. of

gap

s

Time

Critical Gap for <3 Years Driving Experience

No. of accepted gaps < t No. of gaps rejected > t

-10

0

10

20

30

40

50

60

70

80

90

0 2 4 6 8 10 12 14 16

No

. of

gap

s

Time

Critical Gap for 3-8 Years Driving Experience

No. of accepted gaps < t No. of gaps rejected > t

126

-50

0

50

100

150

200

250

0 2 4 6 8 10 12 14 16

No

. of

gap

s

Time

Critical Gap for >8 Years Driving Experience

No. of accepted gaps < t No. of gaps rejected > t

-5

0

5

10

15

20

25

30

0 2 4 6 8 10 12 14 16

No

. of

gap

s

Time

Critical Gap for Drivers with Primary Degree

No. of accepted gaps < t No. of gaps rejected > t

127

-50

0

50

100

150

200

0 2 4 6 8 10 12 14 16

No

. of

gap

s

Time

Critical Gap for Drivers with Secondary Degree

No. of accepted gaps < t No. of gaps rejected > t

-20

0

20

40

60

80

100

120

140

0 2 4 6 8 10 12 14 16

No

. of

gap

s

Time

Critical Gap for Drivers with University Degree

No. of accepted gaps < t No. of gaps rejected > t

128

-20

0

20

40

60

80

100

120

140

160

0 2 4 6 8 10 12 14 16

No

. of

gap

s

Time

Critical Gap for <10 Times Intersection Experience

No. of accepted gaps < t No. of gaps rejected > t

-20

0

20

40

60

80

100

120

0 2 4 6 8 10 12 14 16

No

. of

gap

s

Time

Critical Gap for 10-20 Times Intersection Experience

No. of accepted gaps < t No. of gaps rejected > t

129

-20

0

20

40

60

80

100

0 2 4 6 8 10 12 14 16

No

. of

gap

s

Time

Critical Gap for >20 Times Intersection Experience

No. of accepted gaps < t No. of gaps rejected > t

-20

0

20

40

60

80

100

120

0 2 4 6 8 10 12 14 16

No

. of

gap

s

Time

Critical Gap for Acceptance on Distance

No. of accepted gaps < t No. of gaps rejected > t

130

-10

0

10

20

30

40

50

60

70

0 2 4 6 8 10 12 14 16

No

. of

gap

s

Time

Critical Gap for Acceptance on Speed

No. of accepted gaps < t No. of gaps rejected > t

-50

0

50

100

150

200

0 2 4 6 8 10 12 14 16

No

. of

gap

s

Time

Critical Gap for Acceptance on Distance + Speed

No. of accepted gaps < t No. of gaps rejected > t

131

-50

0

50

100

150

200

250

300

0 2 4 6 8 10 12 14 16

No

. of

gap

s

Time

Critical Gap for 0 Traffic Accidents

No. of accepted gaps < t No. of gaps rejected > t

-10

0

10

20

30

40

50

60

70

0 2 4 6 8 10 12 14 16

No

. of

gap

s

Time

Critical Gap for 1 Accidents

No. of accepted gaps < t No. of gaps rejected > t

132

-1

0

1

2

3

4

5

6

7

8

0 2 4 6 8 10 12 14 16

No

. of

gap

s

Time

Critical Gap for >1 Traffic Accidents

No. of accepted gaps < t No. of gaps rejected > t

-50

0

50

100

150

200

250

0 2 4 6 8 10 12 14 16

No

. of

gap

s

Time

Critical Gap for 0 Traffic Violations

No. of accepted gaps < t No. of gaps rejected > t

133

-5

0

5

10

15

20

25

30

35

40

45

0 2 4 6 8 10 12 14 16

No

. of

gap

s

Time

Critical Gap for 1 Traffic Violations

No. of accepted gaps < t No. of gaps rejected > t

-10

0

10

20

30

40

50

60

0 2 4 6 8 10 12 14 16

No

. of

gap

s

Time

Critical Gap for >1 Traffic Violations

No. of accepted gaps < t No. of gaps rejected > t

134

ANNEX 3: CONFLICTING FLOW RATE

135

ANNEX 4: Details of Gap Model

Case Processing Summary

Unweighted Cases(a) N

Percen

t

Selected Cases Included in Analysis 480 100.0

Missing Cases 0 0.0

Total 480 100.0

Unselected Cases 0 0.0

Total 480 100.0

a. If weight is in effect, see classification Table for the total number of cases.

Dependent Variable Encoding

Original Value Internal Value

Rejected 0

Accepted 1

Categorical Variables Codings

Frequen

cy

Parameter coding

(2) (1)

Gap acceptance criteria 0.000 1.000 88 س عة

1.000 0.000 215 س عة+ مساية

0.000 0.000 177 مساية

Vehicle type 0.000 1.000 109 اج ة

1.000 0.000 301 صغي ة خاصة

0.000 0.000 70 م كبة كبي ة/حايلة

ability of driver to estimate speed 0.000 1.000 8 ضعيةة

1.000 0.000 381 قوية

0.000 0.000 91 متوسطة

Trip purpose 0.000 1.000 82 اجتماعي/ت ييهي

1.000 0.000 66 اخ ي

0.000 0.000 332 عمل

educ 0.000 1.000 39 ايتدائي

1.000 0.000 244 اعدادي/ثانوي

0.000 0.000 197 جامعي

Transmission type 1.000 134 اوتوماتيك

0.000 346 يدوي

Block 0: Beginning Block

Classification Table(a,b)

Observed

Predicted

Type of Gap Percentage

Correct

Reject

ed

Accept

ed

Step 0 Type of Gap Rejected 319 0 100.0

Accepte

d 161 0 0.0

Overall Percentage

66.5

b. The cut value is .500

136

Variables in the Equation

B S.E. Wald df Sig.

Exp(

B)

Step 0 Constant -0.684 0.097 50.028 1

0.000

0.505

Variables B S.E. Wald df Sig. Exp(B)

Constant -6.328 910.500 0.000 1 0.994 0.002

Gap Value 3.768 0.962 15.340 1 0.000 43.296

Trip duration -0.065 0.022 8.823 1 0.003 0.937

Delay -0.575 0.196 8.573 1 0.003 0.563

gapa(1) -3.306 1.545 4.578 1 0.032 0.037

@#oftrafficviolati

ons 0.393 0.193 4.137 1 0.042 1.481

Enginepower -0.002 0.001 3.703 1 0.054 0.998

gapa 4.685 2 0.096

Queuesize -1.605 1.022 2.467 1 0.116 0.201

vectype(1) -3.511 2.236 2.464 1 0.116 0.030

trans(1) -2.270 1.448 2.457 1 0.117 0.103

@#ofaccidents -2.597 1.714 2.297 1 0.130 0.074

vectype(2) -2.574 1.747 2.172 1 0.141 0.076

educ(1) 3.827 2.798 1.870 1 0.171 45.927

Intersectionexperience

0.059 0.045 1.703 1 0.192 1.061

Drivingexperience -0.110 0.088 1.580 1 0.209 0.896

trippupos(2) 2.829 2.418 1.369 1 0.242 16.935

vectype 2.620 2 0.270

educ 2.068 2 0.356

educ(2) 0.947 1.143 0.687 1 0.407 2.579

Driverage 0.058 0.073 0.637 1 0.425 1.060

Vehicleage 0.052 0.067 0.617 1 0.432 1.054

trippupos 1.510 2 0.470

trippupos(1) 0.924 1.490 0.385 1 0.535 2.520

carownershipyears -0.062 0.156 0.158 1 0.691 0.940

@#personsinsidev

ehicle -0.081 0.236 0.119 1 0.730 0.922

gapa(2) -0.342 1.170 0.085 1 0.770 0.710

137

ability(2) -

101.693 919.181 0.012 1 0.912 0.000

ability 0.012 2 0.994

ability(1) -61.442

8,613.282

0.000 1 0.994 0.000

# rejected gap 0.068 0.079 0.675 1 0.843 1.078

Size of preceding gap

0.843 1.27 0.673 1 0.401 2.345

138

ANNEX 5: Details of Far Side Gap Model

Case Processing Summary

Unweighted Cases(a) N Percent

Selected Cases Included in Analysis

130 100.0

Missing Cases 0 0.0

Total 130 100.0

Unselected Cases 0 0.0

Total 130 100.0

a. If weight is in effect, see classification Table for the total number of

cases.

Dependent Variable Encoding

Original Value Internal Value

Rejected 0

Accepted 1

Categorical Variables Codings

Frequency

Parameter coding

(2) (1)

Gap acceptance

criteria

0.000 1.000 26 س عة

1.000 0.000 51 س عة+ مساية

0.000 0.000 53 مساية

Vehicle type 0.000 1.000 24 اج ة

1.000 0.000 87 صغي ة خاصة

0.000 0.000 19 م كبة كبي ة/حايلة

ability of driver to estimate speed

0.000 1.000 5 ضعيةة

1.000 0.000 89 قوية

0.000 0.000 36 متوسطة

Trip purpose 0.000 1.000 21 اجتماعي/ت ييهي

1.000 0.000 12 اخ ي

0.000 0.000 97 عمل

educ 0.000 1.000 12 ايتدائي

1.000 0.000 72 اعدادي/ثانوي

0.000 0.000 46 جامعي

Transmission type 1.000 40 اوتوماتيك

0.000 90 يدوي

Block 0:

Beginning Block

Classification Table(a,b)

Observed

Predicted

Type of Gap Percent

age Correct

Rejected

Accepted

Step 0 Type of Gap Rejected 0 65 0.0

Accepted 0 65 100.0

Overall Percentage

50.0

a. Constant is included in the model.

139

b. The cut value is .500

Variables in the Equation

B S.E. Wald df

Sig

. Exp(B)

Step 0 Constant 0.000 0.175 0.000 1

1.0

00 1.000

Variables not in the Equation

Score df Sig.

Step 0 Variables Delay 0.529 1 0.467

Queuesize 0.000 1 1.000

GapValue 75.708 1 0.000

@#personsinsid

evehicle 0.475 1 0.491

Vehicleage 0.002 1 0.966

carownershipye

ars 0.142 1 0.706

Enginepower 0.462 1 0.497

Tripduration 0.108 1 0.743

Driverage 0.739 1 0.390

Drivingexperience

0.700 1 0.403

Intersectionexpe

rience 0.254 1 0.614

@#ofaccidents 0.174 1 0.676

@#oftrafficviola

tions 0.368 1 0.544

ability 59.888 2 0.000

ability(1) 5.200 1 0.023

ability(2) 59.888 1 0.000

vectype 0.577 2 0.749

vectype(1) 0.000 1 1.000

vectype(2) 0.313 1 0.576

Trans(1) 0.000 1 1.000

TripPurpos 0.521 2 0.771

TripPurpos(1) 0.511 1 0.475

TripPurpos(2) 0.000 1 1.000

educ 3.396 2 0.183

educ(1) 0.367 1 0.545

educ(2) 1.992 1 0.158

gapa 2.329 2 0.312

gapa(1) 1.731 1 0.188

gapa(2) 0.032 1 0.857

Overall Statistics 91.804 24 0.000

Block 1: Method

= Enter

Omnibus Tests of Model Coefficients

Chi-square df Sig.

Step 1 Step 180.218 24 0.000

Block 180.218 24 0.000

Model 180.218 24 0.000

140

Model Summary

Step

-2 Log

likelihood

Cox & Snell R

Square

Nagelkerke R

Square

1 .000(a) 0.750 1.000

a. Estimation terminated at iteration number 20 because maximum iterations has been reached. Final solution cannot be found.

Hosmer and Lemeshow Test

Step Chi-square df Sig.

1 0.000 6 1.000

Contingency Table for Hosmer and Lemeshow Test

Type of Gap = Rejected Type of Gap =

Accepted

Tot

al

Observed

Expecte

d

Obser

ved

Expect

ed

Step 1 1 13 13.000 0 0.000 13

2 13 13.000 0 0.000 13

3 13 13.000 0 0.000 13

4 13 13.000 0 0.000 13

5 13 13.000 0 0.000 13

6 0 0.000 13 13.000 13

7 0 0.000 7 7.000 7

8 0 0.000 45 45.000 45

Classification Table(a)

Observed

Predicted

Type of Gap Percent

age

Correct

Rejecte

d

Accep

ted

Step 1 Type of Gap Rejected 65 0 100.0

Accepted 0 65 100.0

Overall Percentage

100.0

a. The cut value is .500

141

Variables in the Equation

B S.E. Wald df

Sig

. Exp(B)

95.0% C.I.for

EXP(B)

Lo

wer Upper

Step 1(a) Delay 2.781 987.269 0.000 1

0.998

16.140 0.00

0 .

Queuesize -84.328

924,025

.024 0.000 1

1.0

00 0.000

0.00

0 .

GapValue 27.965

2,631.9

65 0.000 1

0.9

92

#######

####

0.00

0 .

@#personsinsidevehicle

-4.644 1,863.0

79 0.000 1

0.998

0.010 0.00

0 .

Vehicleage 0.013 52.607 0.000 1

1.0

00 1.013

0.00

0

#######

####

carownershipye

ars 3.620

2,206.1

51 0.000 1

0.9

99 37.343

0.00

0 .

Enginepower 0.003 11.350 0.000 1

1.000

1.003 0.00

0 #######

####

Tripduration 0.382 950.013 0.000 1

1.0

00 1.465

0.00

0 .

Driverage 0.383

3,034.4

29 0.000 1

1.0

00 1.467

0.00

0 .

Drivingexperience

-1.822 3,019.7

33 0.000 1

1.000

0.162 0.00

0 .

Intersectionexpe

rience 0.145 931.022 0.000 1

1.0

00 1.156

0.00

0 .

@#ofaccidents 26.691

51,537.

864 0.000 1

1.0

00

#######

####

0.00

0 .

@#oftrafficviolations

-2.554 1,421.2

51 0.000 1

0.999

0.078 0.00

0 .

ability

0.000 2

1.0

00

ability(1) 2.610

31,120.

039 0.000 1

1.0

00 13.605

0.00

0 .

ability(2) -32.294

19,983.394

0.000 1 0.999

0.000 0.00

0 .

vectype

0.000 2

1.0

00

vectype(1) -20.024

35,690.413

0.000 1 1.000

0.000 0.00

0 .

vectype(2) 39.317

23,853.

731 0.000 1

0.9

99

#######

####

0.00

0 .

Trans(1) -28.259

17,468.

216 0.000 1

0.9

99 0.000

0.00

0 .

TripPurpos

0.000 2 1.000

TripPurpos(1) 15.831

22,784.

330 0.000 1

0.9

99

7,502,69

2.538

0.00

0 .

TripPurpos(2) -11.148

917,374

.057 0.000 1

1.0

00 0.000

0.00

0 .

educ

0.000 2 1.000

educ(1) 47.439

48,181.

783 0.000 1

0.9

99

#######

####

0.00

0 .

educ(2) -11.370

10,788.

507 0.000 1

0.9

99 0.000

0.00

0 .

gapa

0.000 2

1.0

00

gapa(1) -57.538

17,907.

533 0.000 1

0.9

97 0.000

0.00

0 .

gapa(2) -3.706

16,166.

127 0.000 1

1.0

00 0.025

0.00

0 .

Constant -105.229

124,660.389

0.000 1 0.999

0.000

142

ANNEX 6: Details of Near Side Gap Model

Case Processing Summary

Unweighted Cases(a) N Percent

Selected Cases Included in

Analysis 350 100.0

Missing Cases 0 0.0

Total 350 100.0

Unselected Cases 0 0.0

Total 350 100.0

a. If weight is in effect, see classification Table for the total number of

Dependent Variable Encoding

Original Value Internal Value

Rejected 0

Accepted 1

Categorical Variables Codings

Frequency

Parameter coding

(2) (1)

Gap acceptance

criteria

0.000 1.000 62 س عة

1.000 0.000 164 س عة+ مساية

0.000 0.000 124 مساية

Vehicle type 0.000 1.000 85 اج ة

1.000 0.000 214 صغي ة خاصة

0.000 0.000 51 م كبة كبي ة/حايلة

Trip purpose 0.000 1.000 61 اجتماعي/ت ييهي

1.000 0.000 54 اخ ي

0.000 0.000 235 عمل

educ 0.000 1.000 27 ايتدائي

1.000 0.000 172 اعدادي/ثانوي

0.000 0.000 151 جامعي

ability of driver to

estimate speed

0.000 1.000 3 ضعيةة

1.000 0.000 292 قوية

0.000 0.000 55 متوسطة

Transmission type 1.000 94 اوتوماتيك

0.000 256 يدوي

Driver sex 1.000 14 انري

0.000 336 ذك

Block 0:

Beginning Block

Iteration History(a,b,c)

Iteration -2 Log

likelihood

Coeffici

ents Constan

t

Step 0 1 411.579 -0.903

2 411.233 -0.972

3 411.233 -0.973

4 411.233 -0.973

143

a. Constant is included in the model.

b. Initial -2 Log Likelihood: 411.233 c. Estimation terminated at iteration number 4 because parameter

estimates changed by less than .001.

Classification Table(a,b)

Observed

Predicted

Type of Gap Percent

age Correct

Rejected

Accepted

Step 0 Type of Gap Rejected 254 0 100.0

Accepted 96 0 0.0

Overall Percentage

72.6

a. Constant is included in the model.

b. The cut value is .500

Variables in the Equation

B S.E. Wald df

Sig

. Exp(B)

Step 0 Constant -0.973 0.120

65.955

1 0.000

0.378

Variables not in the Equation

Score df Sig.

Step 0 Variables Delay 6.376 1 0.012

Queuesize 1.393 1 0.238

GapValue 195.564 1 0.000

@#personsinsid

evehicle 1.213 1 0.271

Vehicleage 3.043 1 0.081

carownershipye

ars 0.024 1 0.877

Enginepower 0.352 1 0.553

Tripduration 0.030 1 0.862

Driverage 0.003 1 0.956

Drivingexperien

ce 0.069 1 0.792

Intersectionexperience

0.000 1 0.990

@#ofaccidents 0.729 1 0.393

@#oftrafficviola

tions 0.078 1 0.780

ability 183.940 2 0.000

ability(1) 8.006 1 0.005

ability(2) 183.940 1 0.000

VecType 0.457 2 0.796

VecType(1) 0.418 1 0.518

VecType(2) 0.103 1 0.749

TransType(1) 0.359 1 0.549

TripPurpos 6.899 2 0.032

TripPurpos(1) 0.007 1 0.932

TripPurpos(2) 6.712 1 0.010

sex(1) 3.015 1 0.083

educ 0.989 2 0.610

144

educ(1) 0.398 1 0.528

educ(2) 0.839 1 0.360

Gapa 1.130 2 0.568

Gapa(1) 0.000 1 0.999

Gapa(2) 0.914 1 0.339

Overall Statistics 257.882 25 0.000

Omnibus Tests of Model Coefficients

Chi-square df Sig.

Step 1 Step 391.947 25 0.000

Block 391.947 25 0.000

Model 391.947 25 0.000

Model Summary

Step

-2 Log

likelihood

Cox & Snell R

Square

Nagelke

rke R

Square 1 19.285(a) 0.674 0.975

Hosmer and Lemeshow Test

Step Chi-square df Sig.

1 2.061 8 0.979

Contingency Table for Hosmer and Lemeshow Test

Type of Gap = Rejected

Type of Gap =

Accepted

Tot

al

Observed

Expecte

d

Obser

ved

Expect

ed Step 1 1 35 35.000 0 0.000 35

2 35 35.000 0 0.000 35

3 35 35.000 0 0.000 35

4 35 35.000 0 0.000 35

5 35 35.000 0 0.000 35

6 35 35.000 0 0.000 35

7 34 34.730 1 0.270 35

8 10 9.271 25 25.729 35

9 0 0.000 8 8.000 8

10 0 0.000 62 62.000 62

Classification Table(a)

Observed

Predicted

Type of Gap Percent

age

Correct

Rejecte

d

Accep

ted

Step 1 Type of Gap Rejected 253 1 99.6

Accepted 1 95 99.0

Overall Percentage

99.4

145

Variables in the Equation

B S.E. Wald df

Sig

. Exp(B)

95.0% C.I.for

EXP(B)

Lo

wer Upper

Step 1(a) Delay -0.318 0.195 2.662 1

0.103

0.728 0.49

7 1.066

Queuesize -2.204 2.003 1.211 1

0.2

71 0.110

0.00

2 5.594

GapValue 7.170 3.577 4.017 1

0.0

45

1,299.24

0

1.17

2

1,440,16

1.256

@#personsinsidevehicle

0.772 0.989 0.610 1 0.435

2.165 0.31

1 15.052

Vehicleage -0.096 0.217 0.197 1

0.6

57 0.908

0.59

3 1.390

carownershipye

ars -0.981 0.778 1.589 1

0.2

07 0.375

0.08

2 1.723

Enginepower -0.007 0.005 1.787 1

0.181

0.993 0.98

2 1.003

Tripduration -0.337 0.228 2.180 1

0.1

40 0.714

0.45

7 1.117

Driverage 0.144 0.225 0.407 1

0.5

24 1.155

0.74

2 1.796

Drivingexperience

-0.094 0.218 0.187 1 0.665

0.910 0.59

4 1.394

Intersectionexpe

rience 0.182 0.138 1.718 1

0.1

90 1.199

0.91

4 1.573

@#ofaccidents -19.010 13.332 2.033 1

0.1

54 0.000

0.00

0

1,236.44

8

@#oftrafficviolations

1.247 0.729 2.923 1 0.087

3.480 0.83

3 14.534

ability

0.003 2

0.9

99

ability(1) -12.708

17,196.

857 0.000 1

0.9

99 0.000

0.00

0 .

ability(2) -105.625

2,037.287

0.003 1 0.959

0.000 0.00

0 .

VecType

3.643 2

0.1

62

VecType(1) -16.503 8.689 3.608 1

0.058

0.000 0.00

0 1.693

VecType(2) -19.343 10.503 3.392 1

0.0

66 0.000

0.00

0 3.462

TransType(1) -2.635 2.714 0.942 1

0.3

32 0.072

0.00

0 14.661

TripPurpos

1.966 2 0.374

TripPurpos(1) 2.546 6.800 0.140 1

0.7

08 12.761

0.00

0

7,827,77

5.917

TripPurpos(2) 11.977 8.586 1.946 1

0.1

63

159,054.

269

0.00

8

#######

####

sex(1) -5.357

9,986.758

0.000 1 1.000

0.005 0.00

0 .

educ

0.212 2

0.8

99

educ(1) -0.929 9.671 0.009 1

0.9

23 0.395

0.00

0

#######

####

educ(2) -1.241 2.833 0.192 1

0.6

61 0.289

0.00

1 74.534

Gapa

2.275 2

0.3

21

Gapa(1) -6.221 4.990 1.554 1

0.2

13 0.002

0.00

0 35.162

Gapa(2) 1.214 3.589 0.114 1

0.735

3.368 0.00

3 3,824.04

1

Constant 305.574

2,089.7

94 0.021 1

0.8

84

#######

####

146

ANNEX 7: Details of Lag Model

Case Processing Summary

Unweighted Cases(a) N Percent

Selected Cases Included in

Analysis 258 100.0

Missing Cases 0 0.0

Total 258 100.0

Unselected Cases 0 0.0

Total 258 100.0

a. If weight is in effect, see classification Table for the total number of cases.

Dependent Variable Encoding

Original Value Internal Value

Rejected 0

Accepted 1

Categorical Variables Codings

Frequency

Parameter coding

(2) (1)

Gap acceptance

criteria

0.000 1.000 48 س عة

1.000 0.000 110 س عة+ مساية

0.000 0.000 100 مساية

Trip purpose 0.000 1.000 40 اجتماعي/ت ييهي

1.000 0.000 18 اخ ي

0.000 0.000 200 عمل

Educ 0.000 1.000 20 ايتدائي

1.000 0.000 138 اعدادي/ثانوي

0.000 0.000 100 جامعي

Vehicle type 0.000 1.000 60 اج ة

1.000 0.000 160 صغي ة خاصة

0.000 0.000 38 م كبة كبي ة/حايلة

Transmission type 1.000 68 اوتوماتيك

0.000 190 يدوي

Block 0: Beginning

Block

Classification Table(a,b)

Observed

Predicted

Type of Lag Percent

age

Correct

Rejected

Accept

ed Step 0 Type of Lag Rejected 161 0 100.0

Accepted 97 0 0.0

Overall Percentage

62.4

a. Constant is included in the model.

b. The cut value is .500

147

Variables in the Equation

B S.E. Wald df Sig.

Exp(

B)

Step 0 Constant -0.507 0.129 15.541 1

0.000

0.602

Variables not in the Equation

Score df Sig.

Step 0 Variables LagValue 127.314 1 0.000

@#personsinsidev

ehicle 0.052 1 0.820

Vehicleage 1.079 1 0.299

carownershipyears

2.278 1 0.131

Enginepower 0.198 1 0.656

Tripduration 0.128 1 0.721

Driverage 0.571 1 0.450

Drivingexperience 1.383 1 0.240

Intersectionexperience

0.863 1 0.353

@#ofaccidents 0.024 1 0.877

@#oftrafficviolations

0.797 1 0.372

VecType 2.167 2 0.338

VecType(1) 1.826 1 0.177

VecType(2) 1.864 1 0.172

TranType(1) 2.637 1 0.104

TripPurpos 3.196 2 0.202

TripPurpos(1) 2.057 1 0.152

TripPurpos(2) 0.795 1 0.373

Educ 1.668 2 0.434

Educ(1) 0.506 1 0.477

Educ(2) 0.645 1 0.422

Gapa 2.381 2 0.304

Gapa(1) 0.952 1 0.329

Gapa(2) 0.472 1 0.492

Overall Statistics 136.389 20 0.000

Block 1: Method =

Enter

Omnibus Tests of Model Coefficients

Chi-square df Sig.

Step 1 Step 213.644 20 0.000

Block 213.644 20 0.000

Model 213.644 20 0.000

Model Summary

Step -2 Log likelihood Cox & Snell R

Square

Nagelke

rke R Square

1 127.977(a) 0.563 0.767

a. Estimation terminated at iteration number 10 because parameter estimates

changed by less than .001.

148

Hosmer and Lemeshow Test

Step Chi-square df Sig.

1 110.817 8 0.000

Contingency Table for Hosmer and Lemeshow Test

Type of Lag = Rejected Type of Lag =

Accepted

Tot

al

Observed

Expecte

d

Observ

ed

Expecte

d

Step 1 1 26 25.895 0 0.105 26

2 26 25.635 0 0.365 26

3 26 25.281 0 0.719 26

4 25 24.766 1 1.234 26

5 23 23.674 3 2.326 26

6 21 19.299 5 6.701 26

7 9 11.428 17 14.572 26

8 4 4.527 22 21.473 26

9 0 0.485 26 25.515 26

10 1 0.009 23 23.991 24

Classification Table(a)

Observed

Predicted

Type of Lag Percent

age Correct

Rejected Accept

ed

Step 1 Type of Lag Rejected 149 12 92.5

Accepted 17 80 82.5

Overall Percentage

88.8

a. The cut value is .500

Variables in the Equation

B S.E. Wald df Sig. Exp(B)

95.0%

C.I.for

EXP(B)

Lower

Upper

Step 1(a) LagValue 1.317 0.180 53.543 1

0.0

00 3.733

2.62

3

5.31

2

@#personsinsidev

ehicle 0.036 0.092 0.158 1

0.6

91 1.037

0.86

6

1.24

2

Vehicleage 0.015 0.032 0.228 1

0.633

1.016 0.95

3 1.08

2

carownershipyear

s 0.090 0.057 2.545 1

0.1

11 1.094

0.98

0

1.22

3

Enginepower 0.001 0.001 2.377 1

0.1

23 1.001

1.00

0

1.00

2

Tripduration -0.006 0.015 0.175 1

0.6

76 0.994

0.96

5

1.02

4

Driverage 0.028 0.042 0.432 1

0.5

11 1.028

0.94

7

1.11

6

Drivingexperience -0.037 0.051 0.518 1

0.472

0.964 0.87

2 1.06

5

Intersectionexperi

ence -0.014 0.013 1.131 1

0.2

88 0.986

0.96

2

1.01

2

@#ofaccidents 0.512 0.491 1.088 1

0.2

97 1.669

0.63

7

4.36

9

@#oftrafficviolations

0.185 0.109 2.875 1 0.090

1.203 0.97

2 1.49

0

149

VecType

0.922 2

0.6

31

VecType(1) 0.837 1.021 0.672 1

0.4

12 2.311

0.31

2

17.1

03

VecType(2) 0.317 1.021 0.096 1

0.7

56 1.373

0.18

6

10.1

62

TranType(1) -1.193 0.753 2.511 1

0.113

0.303 0.06

9 1.32

7

TripPurpos

1.593 2

0.4

51

TripPurpos(1) 0.077 0.698 0.012 1

0.9

12 1.080

0.27

5

4.23

9

TripPurpos(2) -1.393 1.137 1.500 1

0.221

0.248 0.02

7 2.30

6

Educ

0.578 2

0.7

49

Educ(1) -1.122 1.533 0.535 1

0.4

64 0.326

0.01

6

6.57

6

Educ(2) -0.140 0.624 0.051 1

0.822

0.869 0.25

6 2.95

1

Gapa

0.347 2

0.8

41

Gapa(1) 0.065 0.665 0.010 1

0.9

22 1.067

0.29

0

3.92

7

Gapa(2) -0.330 0.621 0.282 1

0.596

0.719 0.21

3 2.43

0

Constant -38.325 64.800 0.350 1

0.5

54 0.000

150

ANNEX 8: Details of Near Side Lag Model

Case Processing Summary

Unweighted Cases(a) N Percent

Selected Cases Included in

Analysis 129 100.0

Missing Cases 0 0.0

Total 129 100.0

Unselected Cases 0 0.0

Total 129 100.0

a. If weight is in effect, see classification Table for the total number of cases.

Dependent Variable Encoding

Original Value Internal Value

Rejected 0

Accepted 1

Categorical Variables Codings

Frequency

Parameter coding

(2) (1)

Gap acceptance

criteria

0.000 1.000 24 س عة

1.000 0.000 55 س عة+ مساية

0.000 0.000 50 مساية

Educ 0.000 1.000 10 ايتدائي

1.000 0.000 69 اعدادي/ثانوي

0.000 0.000 50 جامعي

Trip purpose 0.000 1.000 20 اجتماعي/ت ييهي

1.000 0.000 9 اخ ي

0.000 0.000 100 عمل

Vehicle type 0.000 1.000 30 اج ة

1.000 0.000 80 صغي ة خاصة

0.000 0.000 19 م كبة كبي ة/حايلة

Transmission type 1.000 34 اوتوماتيك

0.000 95 يدوي

Block 0:

Beginning Block

Classification Table(a,b)

Observed

Predicted

Type of Lag Percent

age

Correct

Rejecte

d

Accep

ted Step 0 Type of Lag Rejected 96 0 100.0

Accepted 33 0 0.0

Overall Percentage

74.4

a. Constant is included in the model.

b. The cut value is .500

151

Variables in the Equation

B S.E. Wald df Sig.

Exp(

B)

Step 0 Constant -1.068 0.202 28.003 1

0.000

0.344

Variables not in the Equation

Score df Sig.

Step 0 Variables LagValue 67.228 1 0.000

@#personsinside

vehicle 0.009 1 0.925

Vehicleage 0.245 1 0.620

carownershipyea

rs 0.169 1 0.681

Enginepower 0.004 1 0.950

Tripduration 0.054 1 0.815

Driverage 0.462 1 0.497

Drivingexperienc

e 0.746 1 0.388

Intersectionexperience

0.037 1 0.848

@#ofaccidents 0.441 1 0.507

@#oftrafficviolations

0.125 1 0.723

VecType 0.527 2 0.769

VecType(1) 0.401 1 0.527

VecType(2) 0.037 1 0.847

TransType(1) 1.527 1 0.217

Educ 1.438 2 0.487

Educ(1) 1.184 1 0.277

Educ(2) 0.020 1 0.888

TripPurpos 1.537 2 0.464

TripPurpos(1) 1.392 1 0.238

TripPurpos(2) 0.057 1 0.811

Gapa 0.228 2 0.892

Gapa(1) 0.199 1 0.655

Gapa(2) 0.001 1 0.977

Overall Statistics 74.050 20 0.000

Block 1: Method

= Enter

Omnibus Tests of Model Coefficients

Chi-square df Sig.

Step 1 Step 102.054 20 0.000

Block 102.054 20 0.000

Model 102.054 20 0.000

Model Summary

Step -2 Log likelihood Cox & Snell R

Square

Nagelk

erke R Square

1 44.654(a) 0.547 0.805

a. Estimation terminated at iteration number 10 because parameter

estimates changed by less than .001.

152

Hosmer and Lemeshow Test

Step Chi-square df Sig.

1 1.333 8 0.995

Contingency Table for Hosmer and Lemeshow Test

Type of Lag = Rejected Type of Lag =

Accepted

Tot

al

Observed

Expecte

d

Obser

ved

Expect

ed

Step 1 1 13 13.000 0 0.000 13

2 13 12.998 0 0.002 13

3 13 12.983 0 0.017 13

4 13 12.931 0 0.069 13

5 13 12.774 0 0.226 13

6 12 12.388 1 0.612 13

7 10 10.907 3 2.093 13

8 7 6.556 6 6.444 13

9 2 1.460 11 11.540 13

10 0 0.003 12 11.997 12

Classification Table(a)

Observed

Predicted

Type of Lag Percent

age Correct

Rejected

Accepted

Step 1 Type of Lag Rejected 93 3 96.9

Accepted 5 28 84.8

Overall Percentage

93.8

a. The cut value is .500

Variables in the Equation

B S.E. Wald df Sig.

Exp(

B)

95.0% C.I.for

EXP(B)

Low

er Upper

Step 1(a) LagValue 1.582 0.392 16.281 1

0.000

4.864 2.25

6 10.489

@#personsinside

vehicle -0.354 0.235 2.270 1

0.1

32 0.702

0.44

3 1.113

Vehicleage 0.038 0.057 0.437 1

0.5

09 1.039

0.92

8 1.162

carownershipyears

0.174 0.149 1.360 1 0.244

1.190 0.88

8 1.593

Enginepower 0.002 0.001 2.172 1

0.1

40 1.002

0.99

9 1.005

Tripduration -0.006 0.062 0.009 1

0.9

23 0.994

0.88

1 1.122

Driverage 0.024 0.097 0.061 1

0.805

1.024 0.84

6 1.240

Drivingexperienc

e -0.008 0.111 0.006 1

0.9

40 0.992

0.79

8 1.232

Intersectionexperience

-0.028 0.034 0.690 1 0.406

0.972 0.91

0 1.039

@#ofaccidents 0.940 1.384 0.462 1

0.4

97 2.561

0.17

0 38.596

@#oftrafficviolat

ions -0.060 0.208 0.083 1

0.7

73 0.942

0.62

7 1.415

153

VecType

3.504 2

0.1

73

VecType(1) 6.691 3.782 3.130 1

0.0

77

805.1

58

0.48

6

1,333,348

.977

VecType(2) 4.879 3.406 2.052 1

0.1

52

131.5

39

0.16

6

104,293.1

15

TransType(1) -2.547 1.673 2.317 1

0.128

0.078 0.00

3 2.080

Educ

1.378 2

0.5

02

Educ(1) -1.879 2.802 0.450 1

0.5

02 0.153

0.00

1 37.036

Educ(2) -1.472 1.255 1.376 1

0.241

0.230 0.02

0 2.684

TripPurpos

0.871 2

0.6

47

TripPurpos(1) -1.602 1.738 0.849 1

0.3

57 0.202

0.00

7 6.078

TripPurpos(2) 0.195 1.775 0.012 1

0.912

1.215 0.03

8 39.380

Gapa

2.786 2

0.2

48

Gapa(1) -0.140 1.166 0.014 1

0.9

05 0.870

0.08

8 8.547

Gapa(2) -2.154 1.312 2.694 1

0.101

0.116 0.00

9 1.519

Constant -89.797 114.219 0.618 1

0.4

32 0.000

154

ANNEX 9: Details of Far Side Lag Model

Case Processing Summary

Unweighted Cases(a) N Percent

Selected Cases Included in

Analysis 129 100.0

Missing Cases 0 0.0

Total 129 100.0

Unselected Cases 0 0.0

Total 129 100.0

a. If weight is in effect, see classification Table for the total number of cases.

Dependent Variable Encoding

Original Value Internal Value

Rejected 0

Accepted 1

Categorical Variables Codings

Frequency

Parameter coding

(2) (1)

Gap acceptance

criteria

0.000 1.000 24 س عة

1.000 0.000 55 س عة+ مساية

0.000 0.000 50 مساية

Trip purpose 0.000 1.000 20 اجتماعي/ت ييهي

1.000 0.000 9 اخ ي

0.000 0.000 100 عمل

Educ 0.000 1.000 10 ايتدائي

1.000 0.000 69 اعدادي/ثانوي

0.000 0.000 50 جامعي

Vehicle type 0.000 1.000 30 اج ة

1.000 0.000 80 صغي ة خاصة

0.000 0.000 19 م كبة كبي ة/حايلة

Transmission type 1.000 34 اوتوماتيك

0.000 95 يدوي

Block 0:

Beginning Block

Classification Table(a,b)

Observed

Predicted

Type of Lag Percent

age

Correct

Rejecte

d

Accep

ted Step 0 Type of Lag Rejected 65 0 100.0

Accepted 64 0 0.0

Overall Percentage

50.4

a. Constant is included in the model.

b. The cut value is .500

155

Variables in the Equation

B S.E. Wald df

Sig

. Exp(B)

Step 0 Constant -0.016 0.176 0.008 1

0.930

0.985

Variables not in the Equation

Score df Sig.

Step 0 Variables LagValue 78.831 1 0.000

@#personsinsid

evehicle 0.053 1 0.818

Vehicleage 0.982 1 0.322

carownershipyea

rs 2.923 1 0.087

Enginepower 0.309 1 0.579

Tripduration 1.674 1 0.196

Driverage 0.196 1 0.658

Drivingexperien

ce 0.735 1 0.391

Intersectionexperience

4.845 1 0.028

@#ofaccidents 0.626 1 0.429

@#oftrafficviolations

0.836 1 0.361

VecType 2.916 2 0.233

VecType(1) 1.687 1 0.194

VecType(2) 2.895 1 0.089

TransType(1) 1.314 1 0.252

TripPurpos 2.152 2 0.341

TripPurpos(1) 0.875 1 0.350

TripPurpos(2) 1.026 1 0.311

Educ 1.075 2 0.584

Educ(1) 0.001 1 0.980

Educ(2) 0.955 1 0.329

Gapa 3.114 2 0.211

Gapa(1) 0.897 1 0.344

Gapa(2) 0.933 1 0.334

Overall Statistics 86.817 20 0.000

Block 1: Method

= Enter

Omnibus Tests of Model Coefficients

Chi-square df Sig.

Step 1 Step 178.824 20 0.000

Block 178.824 20 0.000

Model 178.824 20 0.000

Model Summary

Step -2 Log

likelihood Cox & Snell R

Square

Nagelk

erke R Square

1 .000(a) 0.750 1.000

a. Estimation terminated at iteration number 20 because maximum

iterations has been reached. Final solution cannot be found.

156

Hosmer and Lemeshow Test

Step Chi-square df Sig.

1 0.000 5 1.000

Contingency Table for Hosmer and Lemeshow Test

Type of Lag = Rejected Type of Lag =

Accepted

Tot

al

Observed

Expect

ed

Obser

ved

Expect

ed

Step 1 1 13 13.000 0 0.000 13

2 13 13.000 0 0.000 13

3 13 13.000 0 0.000 13

4 13 13.000 0 0.000 13

5 13 13.000 0 0.000 13

6 0 0.000 10 10.000 10

7 0 0.000 54 54.000 54

Classification Table(a)

Observed

Predicted

Type of Lag Percent

age

Correct

Rejecte

d

Accep

ted Step 1 Type of Lag Rejected 65 0 100.0

Accepted 0 64 100.0

Overall Percentage

100.0

a. The cut value is .500

Variables in the Equation

B S.E. Wald df

Sig

. Exp(B)

95.0% C.I.for

EXP(B)

Lo

wer Upper

Step 1(a) LagValue 99.292

3,501.1

07 0.001 1

0.9

77

#######

####

0.00

0 .

@#personsinsidevehicle

-0.152 7,368.7

69 0.000 1

1.000

0.859 0.00

0 .

Vehicleage -0.013 83.306 0.000 1

1.0

00 0.987

0.00

0

#######

####

carownershipyears

0.260 901.67

7 0.000 1

1.000

1.297 0.00

0 .

Enginepower 0.024 14.573 0.000 1

0.9

99 1.025

0.00

0

#######

####

Tripduration 1.129

177.74

2 0.000 1

0.9

95 3.091

0.00

0

#######

####

Driverage 4.669

899.167

0.000 1 0.996

106.618 0.00

0 .

Drivingexperien

ce -4.201

985.38

9 0.000 1

0.9

97 0.015

0.00

0 .

Intersectionexpe

rience 1.524 57.341 0.001 1

0.9

79 4.591

0.00

0

#######

####

@#ofaccidents -13.153

21,369.064

0.000 1 1.000

0.000 0.00

0 .

@#oftrafficviola

tions 16.692

597.79

4 0.001 1

0.9

78

#######

####

0.00

0 .

VecType

0.000 2

1.0

00

VecType(1) 23.628

51,960.112

0.000 1 1.000

###########

0.000

.

VecType(2) 75.264 41,811. 0.000 1 0.9 ####### 0.00 .

157

816 99 #### 0

TransType(1) -3.101

10,594.

072 0.000 1

1.0

00 0.045

0.00

0 .

TripPurpos

0.000 2

1.0

00

TripPurpos(1) -51.921

13,462.429

0.000 1 0.997

0.000 0.00

0 .

TripPurpos(2) -347.735

19,175.

870 0.000 1

0.9

86 0.000

0.00

0 .

Educ

0.000 2

1.0

00

Educ(1) 143.778

69,692.708

0.000 1 0.998

###########

0.000

.

Educ(2) -0.310

6,534.1

61 0.000 1

1.0

00 0.733

0.00

0 .

Gapa

0.000 2

1.0

00

Gapa(1) 0.678

5,815.719

0.000 1 1.000

1.971 0.00

0 .

Gapa(2) 32.244

3,094.5

01 0.000 1

0.9

92

#######

####

0.00

0 .

Constant -497.877

99,722.

935 0.000 1

0.9

96 0.000

158

159

160

161