PhD Thesis Full Version - Jezan Md Diah

Jezan bin Md Diah UNIVERSITI TEKNOLOGI MARA

DEVELOPMENT OF WEAVING SECTION
FLOW MODEL OF CONVENTIONAL
ROUNDABOUT

JEZAN BIN MD DIAH

PhD
October 2012

1

UNIVERSITI TEKNOLOGI MARA

DEVELOPMENT OF WEAVING SECTION
FLOW MODEL OF CONVENTIONAL
ROUNDABOUT

JEZAN BIN MD DIAH

Thesis submitted in fulfillment
of the requirements for the degree of

Doctor of Philosophy

Faculty of Civil Engineering
October 2012

2

AUTHOR’S DECLARATION

I declare that the work in this thesis was carried out in accordance with the regulations
of University Teknology MARA. It is original and is the result of my own work,
unless otherwise indicated or acknowledged as referenced work. This thesis has not
been submitted to any other academic institution or non-academic institution for any
degree or qualification.

I, hereby, acknowledge that I have been supplied with the Academic Rules and
Regulations for Post Graduate, Universiti Teknologi MARA, regulating the conduct of
my study and research.

Name of Student : Jezan Md Diah
Programme : Doctor of Philosophy in Civil Engineering
Faculty : Civil Engineering
Thesis Title : Development of Weaving Section Flow Model

Date of Conventional Roundabout
: October 2012

ii

ABSTRACT

Roundabout has been used and becomes popular in sub-urban residential areas as one
of a viable traffic control system at intersections. At roundabout vehicles need to make
a circulatory movement before exiting to their respective directions without having to
stop, thus minimize delay. Studies on roundabout capacity and performance mostly
focus on geometric configuration and flow at the entry, on the basis and acceptance of
offside priority rule. Studies had shown that offside priority is most appropriate and
efficient with small and mini roundabout. As for conventional roundabout or those
with inscribe diameter DI > 50 m, the approach may give rise to differences in
predicted capacities. This may be due to the phenomenon of flow interactions (driver
behaviour related to lane selection and changing) at the weaving section, and this
seems to be the ‘gap’ in present knowledge on roundabout capacity prediction.
Inefficient traffic movement within the weaving section may affect discharge flow,
and hence capacity at entry. As such it seems more appropriate to study and measure
flow at the weaving area. Thus, this research focuses to understand and study the
dynamic as well as complex traffic behaviour/interaction in the weaving section of
conventional roundabout, and to give a measure (model) of weaving flow capacity. A
typical 4-legs 2-circulatory lanes conventional roundabout was selected with video
recorder set-up to capture traffic movements on one of its weaving section. Field data
were collected during weekdays which cover both the morning and afternoon sessions.
Data reduction was done using semi-automatic vehicle analyser (SAVA) software.
Using Excel the raw data (vehicles types, pattern movement and time gap) were
organised and tabulated. Statistical tools from MiniTAB were used for data screening
and verification. Traffic flow at weaving section which exhibits dynamic and
complex behaviour/interaction can be modelled (Qwsf), that comprises through (non-
conflicting Qncf) and weaving (conflicting Qcf ) movements. These flow patterns are
critically governed by the available gaps between vehicles, thus time ideal safe gap
(Tisg ) been identified and retrieved. With the available data, data transformations and
rigorous statistical tests were done during the model development process. Statistical
tables and graph plots revealed the good correlations, relationships and significances
between the variables/parameters being considered. The developed model
(Qwsf = 2700 + 0.000028 Qncf3/2.Qcf - 1.22Tisg .Qcf), was calibrated, verified and
validated with independent field data (new data set). Comparison of weaving flow
capacity between the develop model and observed/field data was within
approximately 5% difference. Sensitivity analysis was done to check on the measured
of effectiveness (MOE) of the model. Integration between weaving section flow and
practical capacity flow enable level of service (LOS) chart being deduced. The LOS
chart is considered another significant contribution of this research to practising traffic
engineers and academicians. Knowledge on the mechanics of traffic flow interactions
at weaving section and the developed model are able to give better prediction on
weaving capacity as well as performance level and, hence, the objectives set for this
research works were accomplished.

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ACKNOWLEDGEMENTS

In the name of Allah, most gracious, most merciful. With His permission,
Alhamdulillah, this project was completed without any uncomfortable occurrence.
I would like to thank my supervisors Prof. Ir. Dr. Mohd Yusof Abdul Rahman and Dr.
Muhammad Akram Adnan for their continuous guidance, support and friendship. As
to the other members of my doctoral thesis committee, Prof. Karl-Lennart Bang, Prof.
Haris Koutsopoulos and Assoc. Prof. Dr. Ismail Atan for their valuable advice and
feedback are very much appreciated.
I thank Faculty of Civil Engineering staff and students, too many to list, which made
this an enjoyable experience. Special thanks to my fellow friends and staff at the
MiTRANS and KTH for their friendship. I also like to thank the UiTM Staff,
Scholarship and Research Management Institute (RMI) for their financial support.
Above all I am grateful to my wife Martini bt. Mohamad, my children Muhammad
Hanif Haikal, Jafni Adawiyah, Jannah Adriana, Muhammad Harraz Hamzi and my
parents Mr.Md Diah bin Madon, Mrs.Jahulah bt. Abd Aziz, Mr.Mohamad bin Salleh
and Mrs.Maznah bt Ahmad for their endless support and encouragement.

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TABLE OF CONTENTS Page
ii
AUTHOR’S DECLARATION iii
ABSTRACT iv
ACKNOWLEDGEMENTS v
TABLE OF CONTENTS ix
LIST OF TABLES xi
LIST OF FIGURES xv
LIST OF PLATES xvi
LIST OF EQUATIONS xvii
LIST OF SYMBOLS
LIST OF ABBREVIATIONS xviii

CHAPTER ONE : INTRODUCTION 1
1.1 Background of Studies 3
1.2 Problem Statement 4
1.3 Objectives of the Study 5
1.4 Scope and Limitation of the Study 5
6
1.4.1 Scope of the Study 6
1.4.2 Limitation of the Study
1.5 Summary 8
8
CHAPTER TWO : LITERATURE REVIEW 13
2.1 Introduction 20
2.2 Roundabout Design and Performance Analysis 21
2.3 Capacity Analysis and Related Issues 23
2.4 Flow and Gap Acceptance Theories 23
24
2.4.1 Traffic Flow of Roundabout 26
2.4.1.1 Non-Conflicting Flow 28
2.4.1.2 Conflicting Flow
2.4.1.3 Passenger Car Unit

2.4.2 Ideal Safe Gap of Roundabout
2.5 Weaving Area Capacity Estimation

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2.6 Summary 29

CHAPTER THREE : RESEARCH METHODOLOGY 31
3.1 Introduction 31
3.2 Overview of the Methodology 32
3.3 Site Selection 36
37
3.3.1 Site Selection Process 40
3.3.2 Site Identification 41
3.4 Data Collection 42
3.4.1 Roundabout Geometric Design 46
3.4.2 Traffic Flow 46
3.4.3 Gap 47
3.5 Data Reduction 48
3.5.1 Assigning a Film File 48
3.5.2 Loading an Existing Output File 49
3.5.3 Input of Road-User Events 49
3.5.4 Drawing Virtual-Lines 50
3.5.5 Output File Window and Associated Functions 59
3.6 Model Development 60
3.7 Model Validation 60
3.7.1 Validation from Other Fieldwork 61
3.8 Sensitivity Analysis of Model Development
3.9 Summary

CHAPTER FOUR : EXPERIMENTAL DATA, DATA ANALYSIS AND 62
RESULTS 63

4.1 Introduction 65
4.2 Traffic Volume and Time Gap in Weaving Section of Conventional 69
72
Roundabout 74
4.2.1 Traffic Volume for Non-Conflicting Flow (q11 and q22) 74
4.2.2 Traffic Volume for Conflicting Flow (q12 and q21)
4.2.3 Time Gap – Ideal Safe Gap
4.3 Analysis of Traffic Parameters at Weaving Section
4.3.1 Morning Period – Analysis of Traffic Flows at Weaving Section

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4.3.2 Evening Period – Analysis of Traffic Flow at Weaving Section 76
78
4.4 Analysis of Conflicting Flow versus Ideal Safe Gap and Weaving
Section Flow 80
81
4.5 Verification of Data Set – Checking the Outliers of the Variables

4.6 Summary

CHAPTER FIVE : MODEL DEVELOPMENT AND VALIDATION 82
5.1 Introduction 83
5.2 General Statistic Principle 84
5.3 Empirical Data Analysis on Conflicting Flow and Ideal Safe Gap 88
5.4 Empirical Data Analysis on Weaving Section Flow 92
5.5 Development of Weaving Section Flow Model, Qwsf 92
96
5.5.1 Descriptive Statistic for Qwsf Data 99
5.5.2 Scatter Plot of Residuals for Qwsf model 100
5.6 Collection of New Data and Method to Check Model Validity 100
5.7 Descriptive Statistics of the Validation Data Set from New Fieldwork 102
5.7.1 The Goodness of Fit for Model Qwsf
5.8 Summary

CHAPTER SIX : SENSITIVITY ANALYSIS AND APPLICATION OF 104
THE WEAVING SECTION FLOW MODEL 104
105
6.1 Introduction 113
6.2 Approach to Sensitivity Analysis 120
127
6.2.1 Analysis for Type A1, A2, A3, A4, A5 and A6
6.2.2 Analysis for Type B1, B2, B3, B4, B5 and B6 129
6.2.3 Analysis for Type C1, C2, C3, C4, C5 and C6 131
6.3 Integration between the Qwsf Model with the Arahan Teknik (Jalan) 137
11/87 (1987) Qp Model which adapted from Wardrop (1957) Model
146
6.3.1 Analysis of Weaving Section Flow Model, Qwsf 147
6.3.2 Analysis of Arahan Teknik (Jalan) 11/87 (1987) Model, Qp
6.4 Development of Level of Service (LOS) at Weaving Section of
Conventional Roundabout

6.4.1 Applications of the Developed Model and LOS Chart
6.5 Summary

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CHAPTER SEVEN : CONCLUSIONS AND RECOMMENDATIONS 149
7.1 Introduction 150
7.2 Conclusions 152
7.3 Recommendations for Future Study

REFERENCES 154

APPENDICES 161

viii

LIST OF TABLES

Table Caption Page
2.1 Characteristics of Six Roundabout Categories 10
2.2 Distinction of Roundabouts by Their Size 11
2.3 Studies of Roundabout Based on its L, W and e 12
2.4 The Research on Roundabout and Related Studies 16
2.5 PCU Conversion Factor 26
3.1 Site Selection – Physical Entity 33
3.2 Site Selection – Control Mechanism 34
3.3 Site Selection – Traffic Operation 35
3.4 Data of Roundabout Geometric Design 41
3.5 Data of Traffic Flow 45
3.6 General Definition for Level of Service (LOS) 45
3.7 Data of Ideal Safe Gap 46
4.1 Geometrical Configuration of Bulatan Bistari (Base on Roundabout 64
Geometric Design)
4.2
4.3 Total Vehicle at Inner Lane of Bulatan Bistari, q11 65
4.4 Total Vehicle at Outer Lane of Bulatan Bistari, q22 65
4.5 The Total Vehicle at Inner to Outer Lane of Bulatan Bistari, q12 69
5.1 The Total Vehicle at Outer to Inner Lane of Bulatan Bistari, q21 69
5.2 Summary of the Overall Descriptive Statistics 83
5.3 Descriptive Statistics for Qwsf Flow 93
5.4 The Statistics of Skewness and Kurtosis for Qwsf Flow 93
Output Iteration or Data Transformation Analysis in Calibrating 94
5.5 Qwsf Model

5.6 Data Transformation Analysis for Final Model Qwsf vs. Qncf, Qcf 95
5.7 and Tisg
5.8 96
5.9 Analysis of Variance for Final Model, Qwsf 99
100
6.1 Normality Test Results for Qwsf Model 101

Descriptive Statistics Validation Dataset for New Fieldwork

Statistical Evaluation of Paired t-Test between Qwsf.m and Qwsf.f
Model

Configuration of Default Value for Sensitivity Analysis in Type A1 106

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6.2 Configuration of Default Value for Sensitivity Analysis in Type A2 106

6.3 Configuration of Default Value for Sensitivity Analysis in Type A3 107

6.4 Configuration of Default Value for Sensitivity Analysis in Type A4 107

6.5 Configuration of Default Value for Sensitivity Analysis in Type A5 108

6.6 Configuration of Default Value for Sensitivity Analysis in Type A6 108

6.7 Configuration of Default Value for Sensitivity Analysis in Type B1 113

6.8 Configuration of Default Value for Sensitivity Analysis in Type B2 113

6.9 Configuration of Default Value for Sensitivity Analysis in Type B3 114

6.10 Configuration of Default Value for Sensitivity Analysis in Type B4 114

6.11 Configuration of Default Value for Sensitivity Analysis in Type B5 115

6.12 Configuration of Default Value for Sensitivity Analysis in Type B6 115

6.13 Configuration of Default Value for Sensitivity Analysis in Type C1 120

6.14 Configuration of Default Value for Sensitivity Analysis in Type C2 120

6.15 Configuration of Default Value for Sensitivity Analysis in Type C3 121

6.16 Configuration of Default Value for Sensitivity Analysis in Type C4 121

6.17 Configuration of Default Value for Sensitivity Analysis in Type C5 122

6.18 Configuration of Default Value for Sensitivity Analysis in Type C6 122

6.19 Model for Predicting Weaving Section Flow 128

6.20 Configuration of Trial Values for Comparison Analysis for Qwsf 130
and Qp

6.21 Effect of Different L, W and e Values for Weaving Section 133
Capacity Qp

6.22 Summarized Results of Different L , W and e Values for Qp 135

6.23 New LOS of Tisg at Weaving Section of Conventional Roundabout 139

6.24 LOS at Entry of Roundabout 139

6.25 The Ratio of Conflicting Flow to Non-Conflicting Flow Demand 140

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LIST OF FIGURES

Figures Caption Page
2.1 Description of Key Roundabout Features 9
2.2 Description of Key Roundabout Dimensions 9
2.3 Conventional Roundabout: Layout 11
2.4 The Traffic Movement of Roundabout 21
2.5 Entry Capacity versus Circulating Flow at Roundabout 23
2.6 Improper Turn Conflicts that Occur at Weaving Section of 24
Multilane Roundabouts

3.1 Methodology Flow Chart 32

3.2 Map of Roundabout in Shah Alam 37

3.3 Walking Measure 41

3.4 Method of Data Collection using Video-Capture Technique 42

3.5 The Set-up of PVBTA 43

3.6 The Location of Setting up the PVBTA 44

3.7 The SAVA-Program Window at Start-up 47

3.8 The Opened Film File 48

3.9 Input Road User Events 49

3.10 Creating a Virtual Line 49

3.11 The Output Window 50

3.12 Weaving Area and Weaving Diagram 51

3.13 Ideal Safe Gap from Inner to Outer Lane Diagram 52

3.14 Ideal Safe Gap from Outer to Inner Lane Diagram 52

3.15 Statistical Methodology 55

3.16 Checking the Outliers 56

3.17 Checking Descriptive Statistic 56

3.18 Checking Dependent or Independent Variables based on Scatter 57
Plot

3.19 Checking Dependent or Independent Variables based on Fitted 57
Line Plot

3.20 Develop Model based on Selected Variables 58

3.21 Validity Checks for Develop Model 58

3.22 Model Validation with other New Fieldwork 59

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4.1 The Minimum Required Sample Size for Multiple Regression 63
Study

4.2 Geometric Layout of Weaving Section at Bulatan Bistari 65

4.3 The Total Vehicle, q11 in Percentage at Bulatan Bistari 66

4.4 The Total Vehicle, q22 in Percentage at Bulatan Bistari 66

4.5 Total Non-Conflicting Flow per 1-Minute Interval at Bulatan 67
Bistari (Morning)

4.6 Total Non-Conflicting Flow per 1-Minute Interval at Bulatan 69
Bistari (Evening)

4.7 The Total Vehicle, q12 in Percentage at Bulatan Bistari 70

4.8 The Total Vehicle, q21 in Percentage at Bulatan Bistari 70

4.9 Total Conflicting Flow per 1-Minute Interval at Bulatan Bistari 71
(Morning)

4.10 Total Conflicting Flow per 1-Minute Interval at Bulatan Bistari 72
(Evening)

4.11 Ideal Safe Gap at Bulatan Bistari (Morning) 73

4.12 Ideal Safe Gap at Bulatan Bistari (Evening) 74

4.13 Combination of Non-Conflicting Flow per 1-Minute Interval at 75
Bulatan Bistari (Morning)

4.14 Combination of Conflicting Flow per 1-Minute Interval at Bulatan 75
Bistari (Morning)

4.15 Combination of Weaving Section Flow per 1-Minute Interval at 76
Bulatan Bistari (Morning)

4.16 Combination of Non-Conflicting Flow per 1-Minute Interval at 77
Bulatan Bistari (Evening)

4.17 Combination of Conflicting Flow per 1-Minute Interval at Bulatan 77
Bistari (Evening)

4.18 Combination of Weaving Section Flow per 1-Minute Interval at 78
Bulatan Bistari (Evening)

4.19 Ideal Safe Gap vs Conflicting Flow at Bulatan Bistari 79

4.20 Conflicting Flow vs Weaving Section Flow at Bulatan Bistari 79

4.21 Example of the Outliers using Boxplot Method 80

5.1 Measured Conflicting Flow Qcf vs Lane q12 84
5.2 Measured Conflicting Flow Qcf vs Lane q21 85
5.3 Measured Lane q12 vs Lane q21 85
5.4 Measured Lane q12 vs Ideal Safe Gap Tisg 86

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5.5 Measured Lane q21 vs Ideal Safe Gap Tisg 87

5.6 Measured Conflicting Flow Qcf vs Ideal Safe Gap Tisg 87

5.7 Measured Weaving Section Flow Qwsf vs Non-Conflicting Flow 88
Qncf

5.8 Measured Weaving Section Flow Qwsf vs Conflicting Flow Qcf 89

5.9 Measured Non-Conflicting Flow Qncf vs Conflicting Flow Qcf 89

5.10 Measured Non-Conflicting Flow Qncf vs Ideal Safe Gap Tisg 90

5.11 Measured Conflicting Flow Qncf vs Ideal Safe Gap Tisg 91

5.12 Measured Weaving Section Flow Qwsf vs Ideal Safe Gap Tisg 91

5.13 A Sample of Qwsf Reduced Data for 0.04s Frame by Frame 92
Analysis in Weaving Area for 1 Minutes Time Interval

5.14 Histogram Plot for Measured Weaving Section Flow in Weaving 93
Area

5.15 Residual vs. the Fitted Values for Final Model Qwsf 97

5.16 Normal Probability Plot of Qwsf Residual based on Anderson- 97
Darling Test

5.17 Normal Probability Plot of Qwsf Residual based on Kolmogorov 98
Smirnov Test

5.18 Histogram of the Residual for Final Model Qwsf 98

5.19 Predicted Flow Qwsf.m from Eq. 5.3 versus Observed Flow Qwsf.f 101
from New Fieldwork Validation Database

5.20 Histogram of Differences between Qwsf.m and Qwsf.f Model 102
6.1 Sensitivity Analysis Output for Type A1 109

6.2 Sensitivity Analysis Output for Type A2 110

6.3 Sensitivity Analysis Output for Type A3 110

6.4 Sensitivity Analysis Output for Type A4 111

6.5 Sensitivity Analysis Output for Type A5 112

6.6 Sensitivity Analysis Output for Type A6 112

6.7 Sensitivity Analysis Output for Type B1 116

6.8 Sensitivity Analysis Output for Type B2 117

6.9 Sensitivity Analysis Output for Type B3 118

6.10 Sensitivity Analysis Output for Type B4 118

6.11 Sensitivity Analysis Output for Type B5 119

6.12 Sensitivity Analysis Output for Type B6 119

6.13 Sensitivity Analysis Output for Type C1 123

xiii

6.14 Sensitivity Analysis Output for Type C2 124

6.15 Sensitivity Analysis Output for Type C3 125

6.16 Sensitivity Analysis Output for Type C4 126

6.17 Sensitivity Analysis Output for Type C5 126

6.18 Sensitivity Analysis Output for Type C6 127

6.19 Output of Integration from Trial Values 131

6.20 The Geometric Parameters of Conventional Roundabout from 132
Previous Researchers

6.21 Sensitivity Analysis Output for Various L 134

6.22 Sensitivity Analysis Output for Various W 134

6.23 Sensitivity Analysis Output for Various e 135

6.24 Summarized of Sensitivity Analysis Output for Various L 136

6.25 Summarized of Sensitivity Analysis Output for Various W 136

6.26 Summarized of Sensitivity Analysis Output for Various e 137

6.27 LOS Chart for Weaving Section with Ratio Qcf to Qncf Equal to 143
0.06

6.28 LOS Chart for Weaving Section with Ratio Qcf to Qncf Equal to 143
0.09

6.29 LOS Chart for Weaving Section with Ratio Qcf to Qncf Equal to 144
0.12

6.30 LOS Chart for Weaving Section Flow Qwsf 144
6.31 Example for Determining Length (L) at Weaving Section 145
6.32 Process Flow Chart - Model and LOS Applications 147

xiv

LIST OF PLATES

Plates Caption Page
3.1 38
3.2 Satellite Image for Roundabout at Bulatan Bistari 38
3.3 39
Satellite Image for Roundabout at Bulatan Sejahtera
3.4
Traffic Flow at Weaving Section of Bulatan Sejahtera during
Morning Peak Hours

Typical Pattern Movements at Weaving Section of Bulatan Bistari 39

xv

LIST OF EQUATIONS

Equations Caption Page
2.1 Practical Capacity of the Weaving Section of a Conventional 11
Roundabout, Qp
2.2 21
2.3 Flow or Flow rate, q 22
3.1 Flow rate (veh/h) 51
3.2 Weaving Section Flow from Fieldwork, Qwsf 52
3.3 Conflicting Flow from Fieldwork, Qcf 52
3.4 Non-Conflicting Flow from Fieldwork, Qncf 53
3.5 ISGIO – Ideal Safe Gap from Inner to Outer Lane 53
3.6 ISGOI – Ideal Safe Gap from Outer to Inner Lane 53
5.1 Ideal Safe Gap, Tisg 94
5.2 Qwsf Model – Step 1 94
5.3 Qwsf Model – Step 2 95
6.1 Qwsf Model – Final 137
6.2 Weaving Section Flow Model, Qwsf 139
Delay, d

xvi

LIST OF SYMBOLS

% percent
& and
DI Diameter of Inscribe Circle
DC Diameter of Centre Circle
1/3p the proportion of weaving traffic
9/5h the proportion of heavy vehicles
e average entry width (m)
g1 Time movement of B.V to back of S.V
g2 Time movement of B.V from back of S.V to infront of S.V
g3 Time movement of B.V from infront of S.V to back of I.V
L length of weaving section (m)
m meter
q11 Non-Conflicting Flow in Inner lane (pcu/hr)
q12 Conflicting Flow from Inner to Outer lane (pcu/hr)
q21 Conflicting Flow from Outer to Inner lane (pcu/hr)
q22 Non-Conflicting Flow in Outer lane (pcu/hr)
Qcf Conflicting Flow (pcu/hr)
Qcf.f Conflicting Flow of weaving section (pcu/hr) from new fieldwork
Qcf.m Conflicting Flow of weaving section (pcu/hr) from model development
Qncf Non-Conflicting Flow (pcu/hr)
Qp capacity of weaving section (pcu/hr)
Qp(max) Maximum capacity of weaving section (pcu/hr)
Qp(min) Minimum capacity of weaving section (pcu/hr)
Qwsf Weaving Section Flow (pcu/hr)
Qwsf.f Weaving Section Flow (pcu/hr) from new fieldwork
Qwsf.m Weaving Section Flow (pcu/hr) from model development
Tisg Ideal Safe Gap (second)
W width of weaving section (m)

xvii

(adj) LIST OF ABBREVIATIONS
B.V / I.V
am / pm Adjusted
DVD Back Vehicle / In front Vehicle
FHWA before noon / after noon
Hgv Digital Video Disc
h or hr Federal Highway Administration
i.e. Heavy good vehicles
ISGIO Hour
ISGOI In example
km/hr or kph Ideal Safe Gap from Inner to Outer Lane
LAN Ideal safe gap from Outer to Inner Lane
Lgv Kilometer per hour
LOS Local area network
min / max Light good vehicles
MOE Level of service
n.a Minimum / Maximum
PCU / PCE Measures of effectiveness
PVBTA Not available
RMDT Passenger Car Unit / Passenger Car Equivalent
R-sq or R2 Portable Vision Based Traffic Analyser
S Regression model of data transformation
S.V Coefficient of determination
SAVA Standard deviation
sec Subject Vehicle
TRB Semi-Automatic Video Analyser
VEVID second
veh or vh Transportation Research Board
VL Vehicle Video-Capture Data Collector
vs vehicles
WSFCR Virtual line
Versus
Weaving Section Flow of Conventional Roundabout

xviii

CHAPTER ONE
INTRODUCTION

1.1 BACKGROUND OF STUDIES

Roundabout is an intersection that provides a circular traffic pattern with
significant reduction in the crossing conflict points. Arahan Teknik (Jalan) 11/87
(1987) categorised roundabout as conventional, small and mini depending on the size
of the inscribe diameter. As for conventional roundabout the prescribe inscribe
diameter should be DI > 50 m. Roundabouts are more appropriate where traffic
volume are about constant and below capacity with all-legs have approximately equal
amount of flow. Thus, this form of intersection is quite common in sub-urban
residential areas that have less restriction on land and may add aesthetic to the
environment.

Studies of roundabout have been done by many researchers and most works
focus at the entry with respect to its flow, gap and geometric design. To-date it was
found that very few studies have directly addressed the flow, gap and geometric
design issue at the circulatory roadway especially at the weaving section of
roundabout. However, recent studies from Hagring et al. (2003) did mentioned that
“the lane allocation of circulating flow did have a significant impact on capacity,
particularly at large circulating flow rates.” Current study would investigate the
phenomena of circulating flow at weaving section on the capacity.

Chik et al. (2004) mentioned that in the early stage, Wardrop (1957) had
developed the roundabout capacity formula based on a weaving section of roundabout.
Wardrop (1957) formula only consider geometric design parameter and proportion of
weaving section flow, without any explanation on the complex activities (lane
selection and lane changing) that involve in the weaving section. It can be expected
that inefficiency of these manoeuvres in the weaving section may create slow down in
flow to the discharge or exit points, hence affect the entire system such as ‘lock’
movement. Thus, knowledge and understanding of the mechanic of movements at
weaving section is crucial for effective movement at roundabout system, and this is
what this study would like to address.

1

In Wardrop (1957) equation, besides geometric parameters the traffic flow
parameters are being considered as the proportion of weaving traffic and heavy
vehicles. The Equation uses 1/3p and 9/5h for the proportion of weaving traffic and
heavy vehicles respectively. This value (proportion) is not very clear to its rationale
application and further more, it does not differentiate between non-conflicting flow
and conflicting flow. The proportion value which is being assumed, empirical or
engineering judgement does not really reflect the conditions at the weaving section. In
other words it does not reflect the characteristics as well as differentiate between non-
conflicting flow and conflicting flow which could affect smoothness of movement. As
such, Kimber (1980) studies later showed that the proportion of weaving traffic stream
is no longer a satisfactory predictor of capacity due to the introduction of the offside
priority rule. In his study, the theory of gap-acceptance is assumed to be passive where
the circulating traffic is assumed not to react to the presence of entering traffic. This
approach (offside priority) is very efficient where minimal or non-conflicting flow
exists, like single circulatory lane. Thus, roundabouts according to Kimber (1980)
may be classified into two types which are conventional roundabout and offside
priority roundabout. These roundabouts are designed according to geometric
principles and behave differently due to operational mechanisms, where weaving for
conventional designs and gap-acceptance for offside priority designs. Thus, their
characteristics geometric features and sizes are different, where conventional
roundabouts will have large central islands and can have parallel sided weaving
sections, whereas offside priority designs have smaller, usually circular central island.
Hence, Kimber (1980) findings showed that a satisfactory predictor of the capacity
and the application gap acceptance for offside priority roundabout designs can be used
to develop a much smaller designs such as both mini and small roundabout. As for
roundabout whose diameter of inscribe circle, DI > 50m is distinguish between the
categories offside priority and conventional may gave rise to differences in the
predicted capacities.

With the acceptance of offside priority rule, other researchers and publications
like Tan (1997), Akcelik et al. (1997), Transportation Research Board, TRB (2000),
Chik et al. (2004), Kabit et al. (2006), Tracz and Chodur (2006), Khatib (2006), Wu
(2006) and Macioszek (2007), where most of their works were based on capacity
model related to traffic at the approach / entry of roundabout become of offside
priority rule. Hagring (1997) studies related to traffic on weaving section at

2

roundabout, but his research was based on critical gaps model which depend on the
length and width of the weaving section of roundabout. However, his follow-up
studies, Hagring (1998) and Hagring et al. (2003) indicated that “lane allocation of
circulating flow did have a significant impact on capacity, particularly at large
circulating flow rates.” The circulating flow referred in his study was flow at the
weaving section.

As to Malaysia scenario, the Wardrop’s equation had being modified and
adapted by Arahan Teknik (Jalan) 11/87 (1987) for use in geometric design but
excluded the traffic flow parameters. This may be considered as simplified version for
easy practical application but would lead to over-design. This had been supported by
studies from Wan Ibrahim and Hamzah (1999) and Chik et al. (2004) suggested that it
needed to be reviewed to include traffic parameters for capacity estimation of
roundabouts in Malaysia. Thus, this research is relevant and timely as to investigate
and re-evaluate the weaving capacity design to take into consideration the dynamic
and complex flow interactions at the weaving section of conventional roundabout. The
findings from this research will be of much benefit to the understanding of flow
interactions phenomenon at the weaving section and its effect on capacity as well as
performance level. Further more, it can be of much use in the geometric design
application, where conventional roundabout is still quite common and popular in use
in sub-urban residential areas in Malaysia.

1.2 PROBLEM STATEMENT

With the acceptance of offside priority rule at roundabout, most studies on
roundabout capacity focus on entry capacity, Kimber (1980). Currently, there is very
limited documentation on weaving capacity except that of Arahan Teknik (Jalan)
11/87 (1987), a modification of Wardrop (1957) formula, however Hagring et al.
(2003) indicated that “lane allocation of circulating flow did have a significant impact
on capacity, particularly at large circulating flow rates.” The circulating flow referred
in his study was flow at the weaving section. Current study investigates and develops
a weaving section flow model which takes into consideration the dynamic interaction
of traffic movement in the area. Capacity by definition relates to the maximum
number of traffic/vehicles a facility can accommodate in unit time, which is constant

3

and can be based on geometric dimension only. Whereas, flow or volume is the
number of vehicles that passes a point in unit time. Flow varies from no vehicle to
maximum number of vehicles that the facility can accommodate that is, to say
maximum flow equal to capacity. This study attempts to develop an empirical model
of flow at weaving section of conventional roundabout that able to give flow
measurement. In developing such model, consideration should be given to the
dynamic pattern of traffic interactions in the weaving section, where almost non
previous studies has considered or recorded. Driver behaviour and complex decision
making on lane changing in the weaving area is crucial and a challenge to this study.
A technique needs to be developed to record or capture these complex manuoverabilty
processes and analyse the data. Basically, the data involve are non-conflicting flow,
conflicting flow and the ideal safe gap time that are video recorded and image
processing using semi-automatic vehicle analyser software. With the integration of
developed model of weaving section flow with weaving section capacity, level of
service (LOS) chart to measure or assess performance was deduced. The developed
model together with the LOS chart can be a useful tool for practising traffic engineers
to be used for the design and monitoring of conventional roundabout performance
under Malaysian traffic and road conditions application.

1.3 OBJECTIVES OF THE STUDY

The primary objective of this research is to develop weaving section flow
(Qwsf) model at weaving area of conventional roundabout.

Specific objectives set in order to achieve the above primary objective are as follows;

i. To acquire and analyse field data for determining non-conflicting flow,
conflicting flow and gap at weaving section of conventional roundabout using
video (image) capture technique,

ii. To develop weaving section flow (Qwsf) model with functions of conflicting
flow (Qcf), non-conflicting flow (Qncf) and ideal safe gap (Tisg) at weaving area
of conventional roundabout.
4

iii. To validate and verify the model with other fieldwork or independent data set for
estimating Qwsf model at weaving area of conventional roundabout.

iv. To develop performance level (level of service) chart through an integration of
the weaving section flow (Qwsf ) model and Arahan Teknik (Jalan) 11/87 (1987)
weaving capacity (Qp ) which adapted from Wardrop (1957) model.

1.4 SCOPE AND LIMITATION OF THE STUDY

In order to achieve the stated objectives of this study as specified in section
1.3, the scope and limitation of this research are as follows:

1.4.1 Scope Of The Study

i. i. This research is an empirical study involve a typical bituminous surface
Malaysia conventional roundabout of inscribe diameter DI > 50 m with 2-
circulating lanes as case study.

ii.
ii. Raw data were organised, statistically verified and analysed using MiniTAB
software.

iii. Empirical model (weaving section flow model) was developed using the
statistical software and later verified with independent set of data.

iv. Based on the model developed and standard performance criteria,
performance chart was developed for predicting traffic conditions (level of
service) at the weaving section of roundabout.

5

1.4.2 Limitation Of The Study

i. Traffic data are under stable flow condition and were captured using
camera/video recording technique.

ii. The data collected does not include pedestrian, bicyclist movement and more
sites may need to be investigated in the future.

iii. The data reveal the driver behaviour as regard to lane selection and lane
changing (conflicting and non-conflicting movement) at the weaving section
of conventional roundabout. Semi-automatic vehicle analyser (SAVA)
software was used to retrieve the information to give numerical measurement
such as conflicting flow, non-conflicting flow and gap.

1.5 SUMMARY

This chapter highlights the needs and significance of the current research on
the development of weaving section flow model, after reviewed the works of previous
researchers, especially those of Wardrop (1957), Kimber (1980) and Hagring et al.
(2003) that indicated “lane allocation of circulating flow did have a significant impact
on capacity, particularly at large circulating flow rates.” With the introduction and
acceptance of offside priority rule at roundabout, most research works focused on
traffic data collected at entry and geometric parameters. However, offside priority is
most appropriate and efficient with small and mini roundabout. As for conventional
roundabout or those with inscribe diameter DI > 50 m, the approach may give rise to
differences in predicted capacities. This probably due to the phenomenon of flow
interactions (driver behaviour related to lane selection and changing) at the weaving
section, and this seems to be the ‘gap’ in present knowledge on roundabout capacity
prediction. Modified Wardrop’s equation used in Arahan Teknik (Jalan) 11/87 (1987),
ignore the traffic parameters and used geometrics parameter only, which can lead to
over-design. Thus, it is the focus of this research to understand and highlight the
dynamic and complex traffic behaviour/interaction in the weaving section.
Understanding the mechanics of flow interactions at weaving section may enable a

6

better model being developed to predict capacity as well as performance level and
these are among the objectives set for this research works.

7

CHAPTER TWO
LITERATURE REVIEW

2.1 INTRODUCTION

Studies related to roundabout are categorized under two (2) categories, that are
studies at the entry and at the weaving area. Basic parameters considered in these
studies are the geometric of the roundabout and the traffic that traversed through it.
This chapter reviewed and presented available literatures which are related to this
study.

2.2 ROUNDABOUT DESIGN AND PERFORMANCE ANALYSIS

The [Federal Highway Administration (FHWA) 2000] stated that roundabouts
are circular intersections with specific design and traffic control features which
include yield control of all entering traffic, channelized approaches, and appropriate
geometric curvature to ensure that travel speeds on the circulatory roadway are
typically less than 50 km/h.

Roundabouts are categorized into six (6) classes based on the size and
environment in which they are located (FHWA 2000, Garber and Hoel 2002). Figures
2.1 and 2.2 illustrate the features and dimensions of roundabout. Table 2.1 shows the
characteristics of the six categories of roundabout. The six (6) classes are mini-
roundabouts, urban compact roundabouts, urban single-lane roundabouts, urban
double-lane roundabouts, rural single-lane roundabouts and rural double-lane
roundabouts.

8

FIGURE 2.1
Description of Key Roundabout Features

(Source: Federal Highway Administration, 2000)
FIGURE 2.2

Description of Key Roundabout Dimensions

(Source: Federal Highway Administration, 2000)

9

TABLE 2.1
Characteristics of The Six Roundabout Categories

Design Mini Urban Urban Single- Urban Double- Rural Single- Rural Double-
Lane
Element Roundabout Compact Lane Lane Lane
50 km/h
Recommended 25 km/h 25 km/h 35 km/h 40 km/h 40 km/h (30 mph)

maximum (15 mph) (15 mph) (20 mph) (25 mph) (25 mph) 2

entry design 55 to 60 m
(180 to 200 ft)
speed
Raised and
Maximum 1 1 1 21 extended, with
crosswalk cut
number of
Refer to the
entering lanes source

per approach

Typical 13 m to 25 m 25 to 30 m 30 to 40 m 45 to 55 m 35 to 40 m

inscribed (45 ft to 80 ft) (80 to 100 ft) (100 to 130 ft) (150 to 180 ft) (115 to 130 ft)

circle

diameter1

Splitter island Raised if Raised, with Raised, with Raised, with Raised and

treatment possible, crosswalk crosswalk cut crosswalk cut extended, with

crosswalk cut if cut crosswalk cut

raised

Typical daily 10,000 15,000 20,000 Refer to the 20,000

service source

volumes on 4-

leg roundabout

(veh/day)

1. Assumes 90-degree entries and no more than four legs.

(Source: Federal Highway Administration, 2000)

The design and categorization of roundabouts in Malaysia is documented in
Arahan Teknik (Jalan) 11/87 (1987), which are conventional roundabout, small
roundabout and mini roundabout. Basically, Arahan Teknik (Jalan) 11/87 (1987)
roundabout formula was adopted and simplified from those of Wardrop’s formula, by
considering the geometric parameters only. Thus, it was named as practical capacity
of roundabout. Table 2.2 shows the different classes of roundabouts based on their
diameter of the inscribed (DI) and diameter of the centre circle (DC) as specified in
the Arahan Teknik (Jalan) 11/87 (1987). The practical capacity of conventional
roundabout is given as in Equation 2.1, based on the procedures of Arahan Teknik
(Jalan) 11/87 (1987). It has been specified that the reserve capacity should not be less
than 15% from the observed traffic volume (from fieldwork). Otherwise, the
roundabout is no more appropriate and should be replaced with other form of
intersection type.

10

TABLE 2.2
Distinction of Roundabouts by Their Size

Type of Diameter of Diameter of
Roundabout
Inscribed Circle, DI (m) Centre Circle, DC (m)

Conventional DI > 50 DC > 25
Small 50 > DI > 20 25 > DC > 4
Mini
20 > DI 4 > DC

(Source: Arahan Teknik (Jalan) 11/87 (1987) adapted from Wardrop’s Formula)

Equation 2.1 is the practical capacity of the weaving section of a conventional
roundabout, which is based on the geometrical characteristics (see Figure 2.3);

160W (1 + e )
W
Qp = 1+ W (2.1)

L

where: = capacity of weaving section (veh/h)
Qp = width of weaving section (meter)
W = ½ (e1 + e2): average entry width (meter)
e = length of weaving section (meter)
L
FIGURE 2.3
Conventional Roundabout: Layout
Entry Radius
(Min. 200m.)

DI

Circulatory
Roadway

DC

(Source: from Arahan Teknik (Jalan)11/87, 1987)

11

It is thought that the roundabout design as used in Malaysia (Arahan Teknik
(Jalan) 11/87 (1987) simplified version) needs to be improved in order to enhance the
performance analysis based on its capacity and safety.

Hagring (1997) had developed roundabout capacity model based on length,
width and gap acceptance of the weaving section and named CAPCAL2. From his
study, the capacity predicted by his model with CAPCAL2 was not accurate at 70
km/h because the travel speeds on the circulatory roadway were typically less than 50
km/h (FHWA, 2000). Table 2.3 shows several studies of roundabout based on L, W
and e. Surprisingly, Arahan Teknik (Jalan) 11/87 (1987) (Malaysia) has been using
the equation for quite some times but no works being done as to date to verified the
equation or evaluate the performance of the designed roundabout using the equation.

TABLE 2.3
Studies of Roundabout Based on its L, W and e

Roundabout Geometric Design (All unit in meter)

Studies Length of Width of Average Entry Width, e(m)
weaving weaving section, e1 e2
section, L(m) e
W(m)

Kimber (1980) min = 9 m min = 7 m min = 3.6 m min = 4.9 m min = 4.25 m
max = 16.5
Arahan Teknik Jalan 11/87 max = 86 m max = 26 m m max = 22.7 m max = 19.6 m
(1987) which adapted from min = n.a min = n.a min = n.a min = n.a
max = n.a max = 15 m min = n.a max = n.a max = n.a
Wardrop (1957)
max = n.a

Hagring (1998) min = 26 m min = 8 m min = n.a min = n.a min = n.a
max = 64 m max = 14 m max = n.a max = n.a max = n.a

Wan Ibrahim and Hamzah min = 39 m min = 9.5 m min = n.a min = n.a min = 8.95 m
max = 11 m max = n.a max = n.a max = 11.05 m
(1999) max = 47.11 m

FHWA (2000) min = n.a min = n.a min = 6.0 m min = 8.7 m min = 7.35 m
max = n.a max = n.a max = n.a max = n.a max = n.a
n.a. - not available

Akcelik (2002) presented a model which was based on roundabout negotiation
radius, distance and speed. The model shows some benefits in terms of reduction in
delay, operating cost, fuel consumption and pollutant emissions performance
measures. From this study, he indicated that the traverse speed should be less than 50
km/h is significant for through and turning vehicles at roundabout. While as, Katz et
al. (2005) and Land Transport (2005) studies were more concerned about the
navigation signing and guideline for marking roundabouts respectively.

12

2.3 CAPACITY ANALYSIS AND RELATED ISSUES

In general, capacity is defined by the Transportation Research Board, TRB
(2000) as “the maximum flow of vehicles that can reasonably be expected to traverse
a point or uniform section of a lane or roadway during a given time period under
prevailing roadway, traffic, and control conditions.”

Studies done on roundabout capacity (see Table 2.4) were mostly based on the
approach or entry of roundabout. Except Bergh (1997), Guicet (1997) and Botma
(1997), their studies deliberated about the current practice and research in their
countries. However, relevant research papers on issues related to capacity have been
identified and are discussed in the following paragraphs.

Kimber (1980) had proposed a model based on empirical methods in
predicting the capacity of roundabout at entries. In this study, he highlighted the great
significance factors that affect the capacity are the entry width and flare. However, in
this study he did not take into consideration parameters of the weaving section. Before
the year 1966, there was no regulation on priority of traffic flow movement at
roundabout. With the introduction of the offside priority rule, where traffic in
circulation and those on the right-hand side being given the priority right of way,
Kimber and many other researchers ignored the existence of problems in weaving
area, with the taught that traffic will always exit from the roundabout and the
phenomenon of locking, thus disappeared.

From this study also, Kimber had stated that the offside priority rule was more
appropriate and applicable for development of a much smaller designs of roundabout.
It may be anticipated that, the problem in weaving area may no longer exist if the
roundabout has single lane. As for the case of conventional roundabout, problems do
exist because with the double or triple lanes roundabout, priority rule might solved the
problem at entry but not at the weaving section. Thus, the issue of lane changing and
complex movement at weaving section needs to be address. Flow problems at
weaving section may affect the smoothness of discharge at exit and consequently, the
capacity as well as the amount of entries. In Malaysia, where conventional
roundabouts are quite common especially in sub-urban residential areas, Arahan
Teknik (Jalan) 11/87 (1987) formula used in roundabout design needs to be revised to
consider traffic parameters in the weaving section. This is more critical with the

13

amount of vehicles found to be increase drastically (Mustafa 2006) and had difference
behaviour of Malaysian’s driver (Ismail et al. 2005).

Tan (1997) had continued to develop new formula based on Kimber’s formula
on estimating traffic queues and delays at roundabout entries. He found that Kimber’s
formula can only be used for undersaturated but not for oversaturated traffic
conditions. The study was verified/indicated using simulation process.

TRB (2000) had proposed capacity estimation for the critical lane of multilane
roundabout entries based on capacity of the critical lane on the approach and
conflicting flow. Only in such cases where the overall capacity may be underestimated
due to a likely increase in the number of vehicles in the outer lanes entering adjacent
to non-conflicting vehicles circulating in the inner lanes. In such case, the situation
does not seem real or reflects real situation because motorists tend to use the
outermost lane mostly as to avoid conflicting maneuver.

Chik et al. (2004) studies were more related to the comparison of the
maximum entry flow between his works and Arahan Teknik (Jalan) 11/87 (1987).
There is a question on how the multi-lane derivation which is from circulating flow
can be related to weaving capacity of Arahan Teknik (Jalan) 11/87 (1987), which only
has geometric parameters?. The study approach seems to consider and count the
circulating flow only when there were conflicts between entry flow and circulating
flow. If this is so, it is not quite right to make a comparison between capacity at entry
as similar to capacity calculation from Arahan Teknik (Jalan) 11/87 (1987), as the
location as well as traffic situations between the two were totally difference.

Normally, the design of conventional roundabout in Malaysia is based on
Arahan Teknik (Jalan) 11/87 (1987) which consider only geometric design and does
not include the traffic parameters such as traffic flow and gap. This had been
commented by Wan Ibrahim and Hamzah (1999) and Chik et al. (2004), and they
suggested that it should and need to be reviewed to include traffic parameters for
capacity estimation of roundabouts in Malaysia.

Akcelik (1997, 2002, 2004) had developed and used Sidra Software in the
evaluation of roundabout performance. Akcelik (1997) had estimated roundabout
entry-lane capacity using delay, queue length, proportion queued, queue clearance
time. In year 2002, Akcelik developed a new method for estimating the side friction
factor as a function of speed and introduced in Sidra Software. The interrelation
between capacity and driver behaviour was made through Akcelik (2008) when he

14

incorporated the variables of headway, driver response time during queue and speed in
his model. Akcelik’s studies were mostly at roundabout entry and hence, is different
from the current research being undertaken which focuses at the weaving section of
the roundabout.

Studies on roundabout required geometric and traffic data. Geometric data is
easy to acquire through physical linear measurement, while as, traffic data is relatively
easy to capture if taken at entry as compared to at weaving section. That why, it might
be possible that due to technological limitation in data acquisition, that most previous
studies focused at entry as compared to at weaving section, where flow movement is
more complicated. With advancement of scientific equipment and technologies, Heng
Wei et al. (2005) had elaborated a technique of data reduction from video captures
using software known as Vehicle Video-Capture Data Collector (VEVID), which was
developed to help extract trajectory data from the video. The method used in his data
reduction was semi-auto and he did not highlight or discussed difficulties that were
encountered during the process. However, problems related to the used of semi-auto
data reduction were mentioned by Wan Ibrahim and Hamzah (1999), where the
process of data reduction from video camera was considered as time consuming
process. While List and Eisenman (2006) had used video captured from the omni-
directional Digital Video Disc (DVD) where the data were retrieved using a
timestamp-based method in evaluating the turning movements at the roundabouts. In
determining capacity, researches need the data collection of traffic parameters (i.e.
flow, gap and speed) in order to develop their own model. Md Diah et al. (2008c) had
investigated and used the data collection through the application of video recording
method and extracted the data through the data reduction software. A mentioned
earlier, researchers like Wan Ibrahim and Hamzah (1999), Kaysi and Alam (2000),
Al-Omari et al. (2004), Heng Wei et al. (2005), Bartin et al. (2005), List and
Eisenman (2006) and Kabit et al. (2006) had also use this technique which had made
data collection process safer and efficient, and some of the researchers had developed
models out from their studies.

15

TABLE 2.4
The Research on Roundabout and Related Studies

RESEARCHER EQUATION & PARAMETER REMARKS
/ PUBLISHER &

YEARS

105w (1 + e )(1 − 3w)(1 − p )
q = w 4l 3

(l + 1.8h)

Wardrop Where Wardrop (1957) had developed the
(1957) – adopted q = capacity of weaving section (pcu/h) roundabout capacity formula based on
w = width of weaving section (m) a weaving section of roundabout which
from Chik et al. e = average effective entry width (m) consider geometric design and
l = length of weaving section (m) proportion of weaving section only
(2004) p = proportion of the weaving traffic
h = proportion of heavy vehicles

Qe = k(F – fc Qc)

Kimber Where The development of a unified formula
(1980) Qe = entry capacity for predicting the capacity of
Qc = the circulating flow across the entry roundabout entries.
Hagring F & fc = are positive constant that depend on
(1997) the geometry of the entry

T =3.95−0.0286 L +0.12− w+0.65(NL −1)

Where Critical gaps were found to depend on
the length and width of the weaving
L = the length of the weaving section section and on whether the entry lane
w = the width of the weaving section was situated to the left or to the right.

N L = the lane number (1=right lane, 2=left

lane) in a two-lane roundabout.

Bergh None Description about current Swedish
(1997) practice and research

Pursula et al. None Includes a discussion of the advantages
(1997) of simulation and a comparison of
HUTSIM with a Swedish
mathematical model called CAPCAL2
and the new Swedish roundabout
model (CAP).

This comparison provides new insights
to the validity of both models and will
lead to further development of each
one.

16

RESEARCHER EQUATION & PARAMETER REMARKS
/ PUBLISHER &

YEARS

Tan T Develop new formula based on
(1997) Kimber’s formula on estimation of
D =  L (t)dt traffic queues and delays at roundabout
Guicet entries.
(1997) 0
Description about current France
Where practice and research.

L = queue length
T = is the area under the curve relating

queue length and time (t).

None

Qe = max ( f od Qg Qm ) - from SIDRA

Akcelik et al. Where: Present an analytical method for
(1997) estimating roundabout entry-lane
f od = factor to adjust the basic gap- capacity and performance measures.
Botma Formulae are presented for the
(1997) acceptance capacity for roundabout origin estimation of stop-line (control) delay,
destination flow pattern and approach queuing queue length, proportion queue, queue
effects clearance time and queue move-up
rate.
Qg = Capacity estimate using the gap-
Description about current Netherlands
acceptance method practice and research.

Qm = Minimum capacity of the opposed

stream (veh/hr)

None

160W 1+ e  - from JKR
 W
Qp =
1+  W 
L

Qe = max ( f od Qg Qm ) - from SIDRA

Wan Ibrahim and Where Presented to illustrate the differences
Hamzah between the two capacity estimating
(1999) Q p = Practical capacity of a weaving section techniques between Arahan Teknik
(Jalan) JKR 11/87 and Sidra 5. It was
(veh/hr) observed that the results obtained from
Sidra 5 gives higher storage
W = Width of weaving section (m)
e = Average entry width (m)
L = Length of weaving section (m)
Qe = Capacity of a lane

f od = factor to adjust the basic gap-acceptance

capacity for roundabout

Qg = Capacity estimate using the gap-acceptance

Qm = Minimum capacity of the opposed stream

(veh/hr)

17

RESEARCHER EQUATION & PARAMETER REMARKS
/ PUBLISHER &

YEARS

Ccrit = 1230e (-0.0009 Vc)

TRB (2000) Where Develop the capacity of the critical
Ccrit = capacity of the critical lane on the lane of a multilane roundabout entry.
approach, veh/hr
Vc = conflicting flow, veh/hr

Capacity = max (VFF + VRF + VRR + VFR)

Lertworawanich Where Develop a method for estimating
and Elefteriadou VFF = represents the through traffic flow rate capacity of ramp weaves based on gap
(2003) from freeway to freeway, at capacity. acceptance and linear optimization.
VRR = represents the ramp to ramp traffic flow
rate, at capacity.
VRF = represents the merging traffic flow rate
from the ramp to freeway, at capacity.
VFR = represents the merging traffic flow rate
from the freeway to ramp, at capacity.

Chik et al. (2004) Multi-lane: Qe = -0.7743Qc + 2,044.9 Examined roundabout formula stated
in Arahan Teknik (Jalan) 11/87. Found
Where that capacity calculation has not taken
Qe = is the maximum entry flow in pcu/hr into consideration the vehicle
Qc = is the maximum circulating flow in interaction.
pcu/hr

Zhang None Validates the INTEGRATION model
(2005) for estimating the capacity of weaving
sections. Comparisons are made to
field data and the Highway Capacity
Manual (HCM) procedures.

Kabit et al. Qe = 38.2 – 2.2Qc To investigate the effect of non-
(2006) circulating dominant flows on the
Where roundabout entry capacity. The results
Qe = entry capacity indicate that the non-circulating
Qc = the circulating flow across the entry dominant flow is not a significant
predictor of the entry capacity.

Cp,el = 3600.exp[-vc,el. (tc – tf + 0.3)]

Tracz and Chodur Where Presents research on the capacities of
(2006) Cp,el = inicial capacity of a lane l at entry e single-lane roundabout and enabled the
(pcu/hr) development of model in the case of
two-lane roundaboutsat entry.
vc,el. = major circulating flow on the

circulatory carriageway for a given lane l at
entry e (veh/hr)

Khatib Qe = 4953 – 1.51Qc (3 lanes) Presents capacity field measurements
(2006) Qe = 3462 – 0.87Qc (2lanes) for three-lane roundabouts. The
capacity of each entering and
Where circulating lane was calculated based
Qe = entry capacity on field observation.
Qc = the circulating flow across the entry

18

RESEARCHER EQUATION & PARAMETER REMARKS
/ PUBLISHER &

YEARS

cF = q1 + q2

nF + 1  q1  nF +1 +  q2  nF +1
c1 c2

Wu Where Presents a method to deal with the
(2006) enhancements/reductions on capacity
c F = capacity of the considered entry (veh/hr) at roundabouts with double-lane or
Macioszek c1/ 2 = capacity of lane 1/2 as a separate lane flared areas at the entries and capacity
(2007) restraints at the exits.
(veh/hr)

qn = total traffic flow at the entry (veh/hr)
q1/ 2 = traffic flow of lane 1/2 (veh/hr)
nF = length of the short lane (veh)
q p = circulating traffic flow (veh/hr)

x = saturation degree = q/c



C = q p .  f (t). (t)dt
t =0

Where Studies on capacity based on gap
acceptance at Small Roundabout.
C = minor approaches capacities Just identifying the parameter and still
 (t) = the number of minor street vehicles not develop the model, the author
review the model from Siegloch
that can enter the conflict area during one (1973)
minor stream gap size t.

f (t) = statistical density function of all gaps

(or headways) in the major stream.
q = the expected number of gaps of size t
within the major stream (or volume of major
stream)

Capacity = max (VFF + VRF + VRR + VFR)

Lertworawanich Where Generalized Capacity Estimation
and Elefteriadou VFF = represents the through traffic flow rate Model for Weaving Areas – additional
(2007) from freeway to freeway, at capacity.
VRR = represents the ramp to ramp traffic flow weaving section length parameter.
rate, at capacity.
VRF = represents the merging traffic flow rate
from the ramp to freeway, at capacity.
VFR = represents the merging traffic flow rate
from the freeway to ramp, at capacity.

Akcelik Q=us The relationship between capacity and
(2008) Where driver behaviour at roundabout entry
Q = capacity (veh/h), u = proportion of the
vehicles can depart from queue, s = saturation
flow rate (vh/h)

19

2.4 FLOW AND GAP ACCEPTANCE THEORIES

Basically, traffic flow and gap acceptance data are required to develop
capacity model either at roundabout entry or at roundabout weaving area. As for
capacity at roundabout entry the model (calculation) is based on entry flow and
circulating flow at the entry. While as, capacity model at weaving area is based on
weaving section flow and conflicting flow. An illustration of traffic behaviour at
entry, circulating, weaving section and exit related to flow and gap at roundabout is
shown in Figure 2.4.

Studies from Kimber (1980), Al-Omari et al. (2004), Bartin et al. (2005),
Khatib (2006) and Kabit et al. (2006) are mostly at the entry and circulating of
roundabout where the fieldwork data of flow and gap that obtained were used to
develop their own model. While Hagring (1997) and Hagring et al. (2003), studies
were more on the significant of the weaving section at the roundabout which based on
flow and gap.

Normally, the flows which come from entry flow and circulating flow is
combined when entering the weaving section of roundabout. This combination of
flows is called as weaving section flow and if the vehicles are trying to weave (reason
to change lane either to exit from the roundabout or move in the next circulating) at
the weaving section of the roundabout, the conflicting flow is occurred. Consequently,
the gap is also occurred when there is conflicting flow at the weaving section of
roundabout. Whereas the non-conflicting flow are occurred if the vehicles are still
moving in the same lane at the weaving section of roundabout.

20

FIGURE 2.4
The Traffic Movement of Roundabout

Arm 3 Legend:
Circulating Flow
Entry Flow
Weaving Section Flow
Exit Flow

Arm 2 Arm 4

Exit
Weaving Section

Entry

Arm 1

2.4.1 Traffic Flow Of Roundabout

Based on Garber and Hoel (2002), the definition of the flow or flow rate is
defined as the equivalent hourly rate at which vehicles pass a point on highway during
a time period less than one hour. It can be determined by Equation 2.2.

q = n  3600 (veh / h) (2.2)
T

where: = the equivalent hourly flow (veh/h)
q = the number of vehicles passing a point in the roadway
n = time duration (sec)
T

21

Flow rate is also can be related to the average headway of the traffic stream as
shown in Equation 2.3.

Flow rate (veh/h) = 3,600 (2.3)
headway (sec/veh)

where:

flow rate = the equivalent hourly flow (veh/h)
headway = the time between successive vehicles as they pass a

point on a lane or roadway (sec/veh)

The traffic flow is normally determined within 15 minutes time interval (TRB
2000). However, some researchers used 1 or 5 minutes in determining flow rate at
roundabout such as Kimber (1980) and Al-Omari et al. (2004). Tracz and Chodur
(2006) used 1 minute time interval to develop their flow model at roundabout. The
reason for using 1 minute time interval was the significant spread of measured
capacity which cause by the randomness of the short process analyzed. Wu (2006)
also used 1 minute as a good representation of the average of the 1-minute capacities
of roundabout. While Camus et al. (2004) mentioned that 1 minute is sufficient to
model traffic conditions to perform an acceptable description of conflicting flows
behaviour in the merge area.

While as, researchers like Wan Ibrahim and Hamzah (1999) and Abdul Aziz
Chik et al. (2004) used 60 minute or 1 hour in their studies of roundabout. Either 1
minute (Wu, 2006) or 60 minute (Chik et al., 2004) sampling, there is no much
different between them and have shown similar pattern as indicated in Figure 2.5,
graph of entry capacity versus circulating flow at roundabout. As can be anticipated as
the conflicting flow increases, the entry capacity is decreases.

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FIGURE 2.5
Entry Capacity versus Circulating Flow at Roundabout

Entry Capacity, Qe (pcu/hr) 3000
2500
2000 250 500 750 1000 1250 1500 1750 2000
1500
1000 Conflicting Flow, Qc (pcu/hr)
500

0
0

AbCdhuilkAeztiazlC. (h2i0k0e4t). al (2004) WWuu(2(02060)6)

2.4.1.1 Non-Conflicting Flow

“The flow that vehicles are not going to merge, diverge or weaved
where the vehicles goes straight without changing the lane is basically can be
considered as non-conflicting flow” (Md Diah et al., 2010). For roundabout,
there are only four types of flow which are entry flow, circulating flow,
weaving section flow and exit flow (refer Figure 2.4). Besides, there are few
researches that had mentioned about non-conflicting flow such as Adnan
(2007) and Lertworawanich (2003) where the researchers use non-conflicting
flow in their studies.

2.4.1.2 Conflicting Flow

According to TRB 2000, conflicting flow is “the flow rate of traffic
that conflicts with a specific movement at an unsignalised intersection.” While
as, according to FHWA 2000 conflicting flow is related with “a conflict point
of two motor vehicles, or a vehicle and a bicycle or pedestrian queue, diverge,
merge, or cross each other. Besides conflicts with other road users, the central
island of a roundabout presents a particular hazard that may result in over-

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representation of single-vehicle crashes that tend to occur during periods of
low traffic volumes. At cross intersections, many such violations may go
unrecorded unless a collision with another vehicle occurs.” As illustration
Figure 2.6 indicates the improper turn conflicts that occur at weaving section
of multilane roundabouts.

FIGURE 2.6
Improper Turn Conflicts that Occur at Weaving Section of Multilane Roundabouts

(Source: FHWA, 2000)

2.4.1.3 Passenger Car Unit
“The flow rate of homogeneous passenger car traffic can be expressed

in terms of vehicles per lane per hour. In mixed traffic, this expression is not
appropriate as different vehicle types cause different disturbances to the traffic.
Hence, the concept of Passenger Car Unit (PCU) or Passenger Car Equivalent
(PCE) is used to convert the vehicle counts in mixed traffic to an equivalent
passenger car flow” (Lee et al., 2010).

According to Lee et al. (2010), Passenger Car Unit (PCU) or
Passenger Car Equivalent (PCE) is “The PCU value of a passenger car that is
defined to be 1.0. Each vehicle type is assigned a single PCU equivalent to

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represent its relative disturbance to the flow under the prevailing traffic
condition. Sometimes a set of PCU values is assigned to a vehicle type to
represent the various disturbances its presence invokes in different traffic
environments.”

Researchers like Tiwari et al. (2000), Leong et al. (2006) and Aggarwal
(2008), using several methods in order to indicate different types of vehicles
with different intersection regarding with PCU for their studies.

REAM (2002) give values of PCU factor for various vehicle types and
location as shown in Table 2.5. Values in Table 2.5 shows the conversion
factor (PCU) for each typical vehicle types as classified in Arahan Teknik
(Jalan) to be used for converting number of vehicles to equivalent PCU for
design and other traffic engineering analysis purposes. The appropriate
roundabout design PCU was determined based on passenger car, motorcycles,
light vans, bus, medium and heavy lorries. Classified traffic volume data
collected at site were converted to equivalent PCU values using Table 2.5 (e.g.
bus: 1 x 2.8 = 2.8), and later computed the average PCU rate to be used or
input in the subsequent analysis. [Mathematical calculation: Number of
vehicles were converted to corresponding PCU equivalent, then the total
equivalent PCU is divided with total number of vehicles, which gave the
average PCU rate = (unit as pcu/vh)].

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TABLE 2.5
PCU Conversion Factor

Equivalent Value in PCU

Type of Rural Urban Roundabout Traffic Signal
Vehicles
Standard Standard Design Design

Passenger Car 1.00 1.00 1.00 1.00
Motorcycles 1.00 0.75 0.75 0.33
Light Vans 2.00 2.00 2.00 2.00

Medium 2.50 2.50 2.80 1.75
Lorries
Heavy Lorries 3.00 3.00 2.80 2.25
Buses 3.00 3.00 2.80 2.25

(Source adapted from: REAM 2002)

2.4.2 Ideal Safe Gap of Roundabout

Garber and Hoel (2002) define “gap as the headway in major stream, which is
evaluated by a vehicle driver in a minor stream who wishes to merge into the major
stream and expressed either in units of time (time gap) or in units of distance (space
gap)”.

Krogscheepers and Roebuck (2000) from their studies had found that the
critical gap is only one unit either 4.2 or 4.5 second based on Sidra calibrated and
observed values respectively. The limitation from the studies is that it may not be able
to determine the value of gap during various traffic flow situation in period of time.

Hence, Lertworawanich (2003) had identified and defined gap as the time
interval between two consecutive vehicles travelling in the same lane. From his study,
he used Drew’s method that had been modified as a method of ideal safe gap. He also
had explain that the ideal safe gap is defined as the gap that would not cause the
merging vehicle to collide with the leading and the following vehicles of the main
traffic stream including time loss due to acceleration processes during the lane

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changing. In his study, the ideal safe gap was used rather than critical gaps and his
rationales for doing so were;

a) “no extensive traffic data are available to estimate critical gaps for merging
processes and the critical gaps from one site are different from those of the
other sites where the results in a situation that a general equation for estimating
critical gaps for any sites will never be obtained”.

b) “ideal safe gaps can be estimated for various weaving sites without requiring a
large amount of data to calibrate”.

c) “ideal safe gaps are adequate for merging vehicles to change lanes without
making or causing any harmful disruptions to the main traffic streams”

Lertworawanich (2003) also mentioned that speed prediction procedures are
not good method to estimate the capacity of weaving areas.

Tracz and Chodur (2006) studied and developed capacity model of roundabout
entry. Using the gap acceptance theory, traffic flow distributions between lanes on the
circular carriageway and at entry of two-lane roundabouts were the two very
important parameters being considered, the model developed had established well.
However it needed certain modification in order to have better representation of real
situations due to empirical capacities. As for Khatib (2006) and Wu (2006), they also
had explored the studies of gap acceptance in order to develop appropriate capacity
models at roundabout entry.

The works by Akcelik and Besley (2004) and Polus et al. (2003) had found
that with the increasing of circulating flow and entry capacity, there will be a
corresponding decreasing of the critical gap at the roundabout. Similarly, Macioszek
(2007) had investigated the critical gaps but on three small roundabouts where he
found that the determination of critical gap is complicated which cannot be measured
directly and there is inconsistency of capacity based on inconsistent driver’s behaviour
measurement. For this reason Lertworawanich and Elefteriadou (2007) had used an
ideal safe gap for their studies, and also based on the reason there is no extensive
traffic data available to estimate critical gaps for merging processes as critical gaps are
different with other sites.

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2.5 WEAVING AREA CAPACITY ESTIMATION

Based on Hagring (1998), the definition from Highway Capacity Manual
(HCM) published by the Transportation Research Board, TRB (1994) where
definition of weaving on freeway can be applied for roundabouts, thus is defined as:-

“the crossing of two or more traffic streams travelling in the same general
direction along a significant length of highway, without the aid of traffic control
devices. Weaving segments are formed when a merge area is closely followed by a
diverge area.”

Roess et al. (2004) mentioned that “weaving occurs when one movement must
cross the path of another along a length of facility without the aid of signals or other
control devices, with the exception of guide and/or warning signs.” There is an
unclear relationship between weaving and separate merging and diverging
movements. From their studies, it was found that “weaving occurs when a merge is
closely followed by a diverge.” For understanding of merging and diverging, they had
defined as “merging occurs when two separate traffic streams join to form a single
stream and diverging occurs when one traffic stream separates to form two separate
traffic streams”.

Kimber (1980), the explanation on offside priority rule which introduced in
November 1966, where the priority was given to vehicles which approaching to
entering drivers from their left at roundabout. The study at roundabout entry gives
circulating flow as major flow while entry flows as minor flow. Kimber (1980) did
specified/classified two types of roundabout as conventional roundabout and offside
priority roundabout. Conventional roundabout has inscribed diameter > 50 m, while
as to those less may be considered as small or mini. According to Kimber, the
designed are according to geometric principles and behave differently due to
operational mechanisms where weaving for conventional designs; and gap-acceptance
for offside priority designs. The consideration of the entire roundabout is taken as a
complete system where the capacity of the entry of the roundabout affects level of
service (LOS) of the entire roundabout system, while the weaving section flow
studies is one part that need to be consider for the entire roundabout system. To-date
studies on the current practice of LOS at roundabout were done at the entry and can
be found through TRB (2000), where the parameters used were flow and delay. There

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is no record on LOS being prescribed based on studies at weaving section of
roundabout.

Fundamentally, Wan Ibrahim and Hamzah (1999) told that the capacity of a
weaving section had been developed by Wardrop in 1957 and used until 1970’s. Only
late 1980’s, Kimber’s formula had been used to predict the capacity of roundabout
entry which does not consider weaving section of roundabout. However, in Malaysia,
the increasing of the vehicle per year and an inconsistent driver behavior’s
measurement regarding with lane selection and lane changing, the traffic study is
needed at weaving section of roundabout.

Another study on assessing the capacity of the weaving section at freeway had
been done by Lertworawanich and Elefteriadou (2003 and 2007) and Zhang (2005).

2.6 SUMMARY

This chapter reviewed, made remarked and commented critically on capacity
studies especially related to conventional roundabout. Wardrop’s equation
formulation and application was understood and the rational of it been simplified and
adopted as design standard in Malaysia and been documented in Arahan Teknik
(Jalan) 11/87 (1987). Noted and appreciated works done by Kimber and others which
made irrelevant the works of Wardrop with the introduction of the off-side priority
rule. As such, most subsequent works were concentrated at the entry of the
roundabout. However, Kimber cautious the uses of his model and off-side priority
rule which he mentioned most appropriate and effective for small roundabout. As for
conventional roundabout with inscribe diameter > 50 m, and 2 or more travel lanes,
thus smooth flow at the weaving section is crucial to enable easy flow entries and
enhance/improve capacity. As to local (Malaysia) scenario, the simplified version
equation of Wardrop as used in Arahan Teknik (Jalan) 11/87 (1987) which omitted
the traffic parameter components and uses the geometric parameters only, and then
named it as practical capacity of the weaving section. This omission had been
highlighted and critised by many researchers and recommended for detail technical
studies. As to date there is no research or studies to model and evaluate capacity at
weaving section per say. Thus, it is the focus of current research to model and
evaluate weaving section capacity of a conventional roundabout by considering the

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complex traffic manoeuvrability activities at the weaving area. Consequently,
findings from this study may enable better understanding on the complex process of
selecting and changing lanes within the weaving area of the roundabout. This study
may also able to improve the current design guideline for local traffic engineer and
local authority in Malaysia for computing roundabout capacity and performance.
Next chapter discusses on the methodology for this study.

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CHAPTER THREE
RESEARCH METHODOLOGY

3.1 INTRODUCTION

The capacity at the entry of roundabout would be much affected by the nature
and flow characteristics as well as effectiveness movement at the weaving sections. It
is much appreciated that blockage/locked flow at the weaving sections would unable
vehicles to enter the roundabout. This study investigated the flow at the weaving
section of roundabout and this chapter would elaborate on the methodology of
weaving section flow model of conventional roundabout that based on empirical
fieldwork study. To undergo this field model development, the processes are
discussed in the following paragraphs.

3.2 OVERVIEW OF THE METHODOLOGY

Figure 3.1 of this section gives an overview of the methodology used in this
study. The methodology begins with identification and selection of a representative
study site, followed with fieldwork data collection, data verification and analysis, then
comes the model development and sensitivity analyses. Basically, there are three
different types of field data that being gathered; roundabout geometric design, traffic
flow and gap (time gap). The physical geometry measurements were taken using tru-
meter, while as the traffic flow and gap were capture through video recording. The
geometry parameters recorded were used to model capacity (practical capacity) using
model equation of Arahan Teknik (Jalan) 11/87 (1987) (noted adapted from Wardrop
(1957)). As for this study, the traffic flow consideration is under stable flow regime.
The traffic field data were verified before being used for Field Model Development.
The capacities derived from these approaches were compared. The developed model
was subjected to detail analyses and through sensitivity analysis. Last but not least,
criteria for level of service (LOS) were formulated/set and based on the developed
model the LOS at the weaving section of conventional roundabout was deduced.

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