OPTIMISATION OF LANE-CHANGING DISTRIBUTIONS FOR A … · 2018-01-29 · OPTIMISATION OF...

OPTIMISATION OF LANE-CHANGING DISTRIBUTIONS

FOR A FREEWAY WEAVING SEGMENT

A THESIS SUBMITTED TO

THE SCIENCE AND ENGINEERING FACULTY

OF QUEENSLAND UNIVERSITY OF TECHNOLOGY

IN FULFILMENT OF THE REQUIREMENTS FOR THE DEGREE OF

MASTER OF ENGINEERING (RESEARCH)

David SulejicBachelor of Engineering (Civil)

Principal Supervisor: Professor Edward Chung

Associate Supervisor: Dr Nasser R. Sabar

School of Civil Engineering and Built Environment

Science and Engineering Faculty

Queensland University of Technology

2018

Copyright in Relation to This Thesis

c© Copyright 2018 by David Sulejic. All rights reserved.

Statement of Original Authorship

The work contained in this thesis has not been previously submitted to meet requirements for an

award at this or any other higher education institution. To the best of my knowledge and belief,

the thesis contains no material previously published or written by another person except where

due reference is made.

Signature:

Date:

i

11/01/2018

QUT Verified Signature

This thesis is dedicated with love to my dearest family and my

beloved wife, Lisa.

iii

Abstract

Empirical studies have observed a lane-changing concentration problem in freeway weaving

segments which can cause flow break down and congestion. This research focuses on the

lane-changing concentration problem in weaving segments. A cooperative intelligent transport

system advisory has been shown to alleviate such a problem. The advisory aims to distribute

the lane-changing along the weaving segment. Unlike previous methods in the literature, where

weaving vehicles are assigned according to fixed distributions, this thesis proposes an algo-

rithm to optimise the lane-changing distributions. The proposed optimisation algorithm was

developed based on particle swarm optimisation.

The research applies a microscopic simulation in Aimsun to evaluate the optimised lane-

changing distribution for a one-sided freeway weaving segment. The simulation results show

that the proposed particle swarm optimisation algorithm can be used as a successful optimisa-

tion method for the lane-changing distributions.

The proposed C-ITS advisory, using the optimised lane-changing distributions, effectively

distributes lane changes along the freeway weaving segment to improve the performance. The

evaluation revealed that the proposed strategy has the potential to reduce delay, to increase

traffic speed and smooth traffic flow dynamics.

v

Keywords

particle swarm optimisation, cooperative intelligent transport systems, freeway weaving seg-

ment, lane-changing advisory, traffic simulation, Aimsun.

vii

Acknowledgments

The author would like to acknowledge the Department of Transport and Main Roads, Queens-

land, for providing the support to perform this research under the Study and Research Assisted

Scheme.

I would like to express my sincere gratitude to my principal supervisor, Professor Edward

Chung, for giving me the opportunity to complete the master’s degree. Thank you for your

continuous support and mentorship in my academic studies and professional career. I would

like to thank my associate supervisor, Dr Rui Jiang, for his guidance and instruction during the

first half of my graduate studies. I would also like to thank my associate supervisor, Dr Nasser

Sabar, for his guidance and expertise in completing my studies; your knowledge and support

has been valuable to me.

Professional editor Jennifer Beale provided copy-editing and proofreading services, accord-

ing to the guidelines laid out in the university-endorsed national ‘Guidelines for editing research

theses’.

ix

Table of Contents

Abstract v

Keywords vii

Acknowledgments ix

Nomenclature xv

List of Figures xviii

List of Tables xix

1 Introduction 1

1.1 Background . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1

1.2 Research problem . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3

1.3 Research objectives . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4

1.4 Research Significance . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5

1.5 Thesis Outline . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5

2 Literature Review 7

2.1 Weaving segments . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7

2.1.1 Weaving segment definition . . . . . . . . . . . . . . . . . . . . . . . 7

2.1.2 Factors influencing weaving capacity . . . . . . . . . . . . . . . . . . 8

2.1.3 Driving behaviour at weaving segments . . . . . . . . . . . . . . . . . 10

xi

2.1.4 Weaving segment management techniques . . . . . . . . . . . . . . . . 12

2.2 Cooperative intelligent transport systems . . . . . . . . . . . . . . . . . . . . . 13

2.2.1 Connected vehicles . . . . . . . . . . . . . . . . . . . . . . . . . . . . 14

2.2.2 C-ITS applications . . . . . . . . . . . . . . . . . . . . . . . . . . . . 14

2.3 Heuristic optimisation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 17

2.3.1 Particle swarm optimisation . . . . . . . . . . . . . . . . . . . . . . . 18

2.3.2 Particle swarm optimisation: traffic and transportation engineering ap-

plications . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 20

2.4 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 21

3 Methodology 23

3.1 Research design . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 23

3.2 Basic concept and assumptions . . . . . . . . . . . . . . . . . . . . . . . . . . 25

3.3 Proposed optimisation algorithm . . . . . . . . . . . . . . . . . . . . . . . . . 29

3.3.1 Proposed PSO . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 29

3.3.2 Solution representation . . . . . . . . . . . . . . . . . . . . . . . . . . 31

3.3.3 Co-evolutionary optimisation . . . . . . . . . . . . . . . . . . . . . . 31

3.3.4 Initialisation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 34

3.3.5 Objective function . . . . . . . . . . . . . . . . . . . . . . . . . . . . 34

3.3.6 Constraints . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 37

3.3.7 Velocity . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 37

3.3.8 Position . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 37

3.3.9 Termination criteria . . . . . . . . . . . . . . . . . . . . . . . . . . . . 38

3.4 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 38

4 Case Study 39

4.1 Simulation test bed . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 39

4.2 Performance indicators . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 41

xii

4.3 Evaluation of the proposed PSO algorithm . . . . . . . . . . . . . . . . . . . . 42

4.4 Simulation results and discussion . . . . . . . . . . . . . . . . . . . . . . . . . 44

4.4.1 Performance evaluation . . . . . . . . . . . . . . . . . . . . . . . . . . 45

4.4.2 Impact of different OD demands . . . . . . . . . . . . . . . . . . . . . 47

4.4.3 Sensitivity analysis . . . . . . . . . . . . . . . . . . . . . . . . . . . . 52

4.4.4 Application domain analysis . . . . . . . . . . . . . . . . . . . . . . . 57

4.4.5 Discussion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 61

4.5 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 62

5 Conclusions 63

5.1 Research findings . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 63

5.2 Recommendations for future work . . . . . . . . . . . . . . . . . . . . . . . . 64

A Sensitivity tests – traffic demand 67

B Lane-changing distribution 69

References 78

xiii

List of Abbreviations

API Application programming interface

C-ITS Cooperative intelligent transport systems

DSRC Dedicated short range communications

FF Freeway to freeway

FR Freeway to ramp

LC Lane-changing

O–D Origin–destination

PSO Particle swarm optimisation

RF Ramp to freeway

RM Ramp metering

RSU Roadside unit

RR Ramp to ramp

V2I Vehicle to infrastructure communication

V2V Vehicle to vehicle communication

xv

List of Figures

2.1 Formation of a weaving segment . . . . . . . . . . . . . . . . . . . . . . . . . 8

2.2 One-sided ramp weave . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8

2.3 Weaving management scenario: longitudinal solid pavement line marking (Al-

Jameel, 2013) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 12

3.1 Research methodology . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 24

3.2 One-sided weaving segment . . . . . . . . . . . . . . . . . . . . . . . . . . . 26

3.3 The process chart for the lane-changing advisory application . . . . . . . . . . 27

3.4 In-vehicle visual display unit (Transport for NSW, 2015) . . . . . . . . . . . . 29

3.5 Solution representation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 31

3.6 Co-evolutionary optimisation method . . . . . . . . . . . . . . . . . . . . . . 32

3.7 PSO cycle process . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 34

3.8 The flowchart of PSO . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 35

4.1 M60 Motorway test bed . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 40

4.2 Proposed PSO results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 43

4.3 Speed profile on critical weaving lanes . . . . . . . . . . . . . . . . . . . . . . 46

4.4 Contour speeds of lane 3 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 49

4.5 Contour speeds of auxiliary lane . . . . . . . . . . . . . . . . . . . . . . . . . 50

4.6 Average delay results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 51

4.7 Auxiliary lane speed . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 54

4.8 Lane 3 speed . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 55

xvii

4.9 Lane-changing distributions (Base case) . . . . . . . . . . . . . . . . . . . . . 56

4.10 Lane-changing distributions (Optimised case) . . . . . . . . . . . . . . . . . . 56

4.11 Density across all lanes (Test 311) . . . . . . . . . . . . . . . . . . . . . . . . 60

xviii

List of Tables

3.1 Notations of parameters and variables . . . . . . . . . . . . . . . . . . . . . . 30

4.1 Weaving segment parameters . . . . . . . . . . . . . . . . . . . . . . . . . . . 41

4.2 Proposed PSO test runs . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 42

4.3 Fitness values . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 43

4.4 Average delay comparison between base case and optimised case . . . . . . . . 45

4.5 Different demand setting (veh/h) . . . . . . . . . . . . . . . . . . . . . . . . . 47

4.6 Traffic demand . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 52

4.7 Lane-changing distribution (Base case) . . . . . . . . . . . . . . . . . . . . . . 57

4.8 Lane-changing distribution (optimised case) . . . . . . . . . . . . . . . . . . . 58

A.1 Sensitivity tests – traffic demand . . . . . . . . . . . . . . . . . . . . . . . . . 67

B.1 Lane-changing advisory distributions . . . . . . . . . . . . . . . . . . . . . . . 69

B.2 Number of lane changes – Base case . . . . . . . . . . . . . . . . . . . . . . . 70

B.3 Number of lane changes – Optimised case . . . . . . . . . . . . . . . . . . . . 71

xix

Chapter 1

Introduction

1.1 Background

Traffic congestion has become a significant problem in major world cities with the increase in

travel demand and private vehicle usage, as well as constrained roadway infrastructure capacity.

According to the Australian Government Bureau of Infrastructure, Transport and Regional

Economics (BITRE) (2015), the avoidable cost of congestion for Australian capital cities was

estimated to be around $16.5 billion for the 2015 financial year and is projected to rise to around

$30 billion by 2030.

A freeway network is a core component of a transportation system, as it provides an un-

hindered, high-speed, high-capacity flow of traffic. Freeway networks regularly experience

congestion due to peaks in traffic demand and incidents. Typically, traffic congestion leads to an

underutilisation of existing infrastructure assets, thus contributing to an accelerated increase in

congestion that results in excess delays, reduced safety and increased environmental pollution.

The traditional approach of continuously expanding infrastructure supply to meet the in-

creasing transportation demand of developed cities is becoming more difficult due to environ-

mental concerns, limited physical capacity and tightening fiscal constraints. Responsible road

authorities are beginning to realise that expensive freeway infrastructure, intended to deliver a

nominal capacity, is significantly underutilised due to congestion, usually, at times, maximum

capacity is most needed. This can be attributed to the lack of efficient, comprehensive traffic

control systems (Papageorgiou et al., 2003).

1

2 CHAPTER 1. INTRODUCTION

The solution to traffic congestion, therefore, requires the optimal use of existing infras-

tructure by traffic control systems. Intelligent transportation systems (ITS) have a variety of

traffic control applications for effective freeway management such as ramp metering, variable

speed limits and variable message signs. In particular, rapid developments in cooperative intelli-

gent transport systems (C-ITS), based on vehicle-to-vehicle (V2V) and vehicle-to-infrastructure

(V2I) communication technologies, have enabled new control strategies for the improvement of

traffic safety and efficiency.

Recent advancements in the field of C-ITS have enabled connected vehicles to send and

receive real-time information (Weiß, 2011). Vehicle to vehicle (V2V) and vehicle to roadside

infrastructure (V2I) communications have been extensively tested in real-world applications. In

recent field trials, C-ITS applications have been shown to provide traffic safety, efficiency and

environmental benefits (Green et al., 2014).

C-ITS provides a platform for active traffic flow management (Alexander et al., 2011).

C-ITS connectivity can provide detailed individual vehicular data including speed, accelera-

tion/deceleration, position and so on and a capability to relay personalised messages to drivers,

that is, information customised for each individual driver, such as speed adjustment or lane-

change advisories (Park and Smith, 2012). C-ITS allows better control than that of traditional

traffic control applications, such as ramp metering and variable speed limits, which depend on

passive point sensors that collect aggregated data and general advisory traveller information

tools (Park and Smith, 2012). C-ITS applications will benefit in supporting traffic control

operations and can be implemented to control and guide individual vehicles.

Several communications platforms such as the 3G or 4G mobile phone network and ded-

icated short-range communications (DSRC) can be used to carry communications between

vehicles and roadside units (Wall et al., 2014). Infrastructure-to-vehicle communications can

enable variable speed limits and advisories provided directly to drivers (Shladover, 2017). For

this study, the individual driver advisory for the lane-changing is not considered a time-critical

or safety-critical application, as such, it does not need the very low latency of DSRC; 3G or 4G

communications would suffice.

Traffic control is a complex subject, and its parameters are uncertain, non-linear and dy-

namic. Complex traffic problems call for the development of modern systems that merge

knowledge, techniques, and methodologies from various scientific areas (Teodorovic, 2008).

1.2. RESEARCH PROBLEM 3

The development of various algorithms, inspired by nature and designed for many real-life

problems, could be fundamental in solving traffic engineering problems, such as urban traffic

congestion.

1.2 Research problem

Traffic congestion, a major problem, reduces efficiency on the highway network by 20% to

50% (Chen et al., 2001). A major cause of congestion is the inefficient operation of highways

during periods of high demand. Congestion on freeways often occurs at specific locations such

as on-ramps, lane drops, crests, sags and sharp bends (Scarinci and Heydecker, 2014). Freeway

weaving segments are a frequent source of traffic bottleneck congestion, whose complex traffic

patterns and capacity variations present significant operational problems on freeways (Kwon,

2003). Increasing the operational efficiency at vulnerable locations of the highway network is a

practical method to reduce traffic congestion.

Weaving segments, a common design for freeways, are formed when merge segments are

closely followed by diverge segments (TRB, 2010). The Highway Capacity Manual (TRB,

2010, ch. 12) defines weaving as “the crossing of two or more traffic streams travelling in the

same direction along a significant length of freeway without the aid of traffic control devices.”

Weaving segments require intense lane-changing (LC) manoeuvres for drivers to access the lane

appropriate for their desired exit. They involve complex vehicle interactions, which presents

safety and operational problems. The traffic in a weaving segment is subject to more LC

turbulence than that normally present on basic freeway segments (TRB, 2010). Empirical

studies have shown that drivers tend to perform lane changes soon after they enter the weaving

segment, especially under capacity conditions (Cassidy and May, 1991). This behaviour, known

as the LC concentration problem, causes a bottleneck around the merge gore area which can lead

to congestion.

A C-ITS advisory, using V2I communications, is a potential application that can solve

the LC concentration problem in a freeway weaving segment by distributing LC along the

weaving segment to better utilise the existing roadway infrastructure. Recent efforts have

been made to model driving behaviours in a connected vehicle environment (Talebpour et al.,

2015). For instance, Mai et al. (2016) used a C-ITS-based LC advisory to improve the LC


concentration problem on weaving segments by distributing the LC over the segment length.

Their concept proposed an advisory that relies on V2I communications, independent from V2V

communications. Hence, the control strategy seeks to change LC behaviour while avoiding the

complexities of anticipated vehicle dynamics (acceleration, speed, deceleration). The proposed

strategy has the potential to improve average delay by up to 46%. In the study, the advisory

assumed a predefined set of LC advisory distributions; however, the LC distributions were not

optimised to improve the traffic performance of the weaving segment.

The proposed work closely follows the work done by Mai et al. (2016), mainly, the basic

concept and assumptions of the C-ITS advisory control strategy and the case study. In their

study, three combinations of the lane-changing distributions were tested. For each combination,

the advisory distributed lane-changes based on the percentages assigned to each section (total

of four sections). Their study focussed on the feasibility and effectiveness of the lane-changing

application, rather than seeking the optimal solution for the advisory distribution. In this study,

the C-ITS advisory distributes lane-changing into eight sections of the weaving segment to

achieve better utilisation. The main contribution of this study is to develop an algorithm to

optimise the lane-changing distributions at a freeway weaving segment. The methodology is

based on a C-ITS advisory control strategy.

1.3 Research objectives

This research proposed that an optimisation algorithm, based on particle swarm optimisation

(PSO), be implemented to improve the LC advisory distribution. The proposed method was

evaluated for a basic, one-sided ramp freeway weaving segment with a short-length weaving

configuration of 400 m between merging and diverging segments. Traffic simulation was used

to evaluate the traffic performance of the weaving segment.

This research aims to:

1. Present an improved C-ITS-based advisory strategy for weaving vehicles (section 3.2)

2. Propose an optimisation algorithm to improve the LC-advisory distribution for weaving

vehicles (section 3.3)

3. Present the results of the proposed PSO algorithm (section 4.3)

1.4. RESEARCH SIGNIFICANCE 5

4. Present the analysis of the LC distributions based on traffic simulation (section 4.4).

The major objective of this research is to develop a modified PSO algorithm to distribute

LC along a freeway weaving segment to improve traffic performance.

1.4 Research Significance

The significance of this research is its contribution to the field of traffic engineering optimisa-

tion. The research will focus on a C-ITS-based advisory strategy for freeway weaving segments.

Traffic simulation will be used as the method of evaluation. The research is expected to have

both a scientific and practical significance.

• Scientific significance: to the best of the author’s knowledge, this research is the first

attempt to develop an optimisation algorithm to improve the LC distribution at a freeway

weaving segment

• Practical significance: the optimised LC advisory distributions can provide useful insight

for road operators to implement and improve traffic control strategies at existing one-sided

ramp weaves; particularly, with the emergence and adoption of C-ITS-based technologies.

1.5 Thesis Outline

The thesis is outlined as follows:

Chapter 2 reviews the existing literature on freeway weaving segments, C-ITS and heuristic

optimisation.

Chapter 3 details the research methodology, presents the advisory control concept and its

assumptions and proposes an optimisation algorithm.

Chapter 4 describes the case study and tested scenarios.

Chapter 5 summarises the main findings of the research and recommends future works.

Chapter 2

Literature Review

This chapter provides the theoretical and methodological contributions underlying the study.

The chapter firstly reviews the freeway weaving segment: factors influencing freeway weaving

capacity, empirical research on the lane-changing concentration problem and weaving manage-

ment techniques. The chapter then briefly introduces cooperative intelligent transport systems

and C-ITS applications, followed by an overview of heuristic optimisation algorithms and their

application in traffic optimisation problems.

2.1 Weaving segments

2.1.1 Weaving segment definition

The Highway Capacity Manual 2010 (TRB, 2010) defines weaving as:

“the crossing of two or more traffic streams travelling in the same direction along a signifi-

cant length of highway without the aid of traffic control devices (except for guide signs). Thus,

weaving segments are formed when merge segments are closely followed by diverge segments.”

The weaving segment is subject to significant LC activity, as drivers manoeuvre from their

arrival leg to the desired departure leg. Hence, traffic in a weaving segment is subject to LC

turbulence more than that normally present on basic freeway segments (TRB, 2010).

Figure 2.1 displays the general formation of a weaving segment. Drivers entering on Leg A

and exiting on Leg D must cross the path of vehicles entering on Leg B and exiting on Leg C.

Flows A–D and B–C are, therefore, referred to as weaving movements. Flows A–C and BD,

7

8 CHAPTER 2. LITERATURE REVIEW

referred to as non-weaving movements, do not have to cross the path of any other flow. The

movements are defined as follows:

• A–C: Freeway-to-freeway (FF)

• A–D: Freeway-to-ramp (FR)

• B–D: Ramp-to-ramp (RR)

• B–C: Ramp-to-freeway (RF).

Figure 2.1: Formation of a weaving segment

The configuration of a weaving segment affects its operating characteristics. This research

focuses only on a one-sided ramp-weave configuration (figure 2.2), whereby no weaving ma-

noeuvres require more than two lane changes to be completed successfully, and all weaving

drivers must execute a lane change across the lane line separating the auxiliary lane from the

left lane of the mainline.

Figure 2.2: One-sided ramp weave

2.1.2 Factors influencing weaving capacity

Capacity is typically expressed as the maximum flow rate of vehicles that can reasonably be

expected to travel through a given facility. Numerous factors affect the capacity of freeway

2.1. WEAVING SEGMENTS 9

weaving segments: number of lanes in the weaving segment, length of weaving segment,

traffic composition, driver characteristics, lane widths, geometric configuration, volume ratio

and weaving ratio (Shoraka and Puan, 2010). This section outlines some of these factors.

Volume ratio

Volume ratio (VR) is the ratio of the weaving demand flow rate to the total demand flow rate in

the weaving segment, V R = V(AD+BC)/Vtotal.

Weaving ratio

The weaving ratio (R) is defined as the ratio of the smaller weaving demand flow rate to the total

weaving demand flow rate in the weaving segment, R = VAD/V(AD+BC) or VBC/V(AD+BC).

Weaving segment length

The weaving segment length is the distance between points in the respective gore areas where

the right edge of the ramp-travelled lane and the left edge of the freeway-travelled lane meet

(TRB, 2010).

The weaving segment length influences LC intensity. For any given demand situation,

longer segments allow weaving vehicles more time and space to find an acceptable gap to

execute lane changes. Consequently, this reduces the density of lane changing and, therefore,

the turbulence.

However, the simulation study by Vermijs (1998) showed that although the weaving length

helps increase weaving capacity, it has minimal effect on the capacity beyond a certain length.

It showed that a weaving segment length more than 400 m does not help to increase weaving

capacity.

Zhang and Rakha (2008) also demonstrated by simulation results that as the weaving seg-

ment length increases, its impact on the weaving segment capacity decreases.

The empirical comparison by He and Menendez (2016a) between longer and shorter weav-

ing segments concluded that the length of the weaving segment has limited influence on the

capacity and operation of the freeway weaving segment.


Weaving segment width

“The width of a weaving segment is measured as the number of continuous lanes with the

segment, that is, the number of continuous lanes between the entry and exit gore areas” (TRB,

2010, ch. 12).

Additional lanes provide more space for weaving and non-weaving vehicles; however, they

encourage additional optional LC activity. Thus, while reducing overall densities, additional

lanes can increase LC and intensity.

Traffic flow composition

Traffic flow composition affects weaving capacity. Heavy vehicles, such as trucks, buses and

recreational vehicles, often occupy more space and require more time to execute a lane change

due to their limited manoeuvrability, compared with passenger cars (Vermijs, 1998).

2.1.3 Driving behaviour at weaving segments

This subsection briefly reviews the literature related to driver behaviour in weaving segments

that cause a LC concentration problem. The problem has been observed in several empirical

studies.

Early research by Cassidy and May (1991) analysed the traffic flow behaviour in the in-

dividual lanes of a weaving segment. Their research showed that a high concentration of LC

manoeuvres occurred near the weaving entrance. The majority of lane changes were made

before a reference point, 76 m from the merge gore of a 445 m section. Their analysis suggested

that, as the weaving flow increased, weaving vehicles become more anxious to change lanes

over shorter travelled distances. They suggested that this increased feeling of pressure may

encourage motorists to perform lane-change manoeuvres as soon as possible. Hence, this

behaviour may result in increased turbulence in the weaving area: decreasing weaving area

capacity and becoming more vulnerable to congestion.

Research by Kwon et al. (2000) showed similar weaving behaviour for a short, one-sided

weaving section of 129 m. They observed that “most merging and diverging vehicles complete

their lane changes before they reach approximately the middle point of the weaving zone” (p.

2.1. WEAVING SEGMENTS 11

136). They found that as the weaving flow began to increase, the diverging vehicles began to

change to the auxiliary lane as soon as they entered the weaving zone.

Denny and Williams (2005) conducted a pilot study on a freeway weaving segment in

Houston. They observed from field studies that weaving manoeuvres were not uniformly

distributed along the weaving segment at capacity. In fact, their observations showed that about

85% of the manoeuvres took place in the first 120-150 m of a 400 m segment.

Lee (2008), who investigated the traffic behaviour in freeway weaving bottlenecks, found

that a high concentration of diverging manoeuvres near the on-ramp triggered bottlenecks,

resulting in vehicle slow-downs. Lee, (p. 59) concluded that “it is not only the amount of

lane changes that influence weaving bottleneck discharge flows, but also the concentrations of

these manoeuvres”.

Al-Jameel (2013) has recently investigated driver behaviour in weaving segments as part of

an empirical study. In that study, investigation of LC locations within a 400 m weaving segment

found that 80% of merging vehicles and up to 90% of diverging vehicles performed lane changes

in the first 100 m of the section. Observations found that the location of the bottleneck would

start at about 70 m and would oscillate between this location and the entrance point of the merge

segment, propagating congestion upstream from the entrance area.

In a recent empirical study to compare longer and shorter weaving sections, He and Menen-

dez (2016b) found that 70% of the total lane changes happen within the first 19% of the 570 m

weaving section length. They found that this, which caused the speed to be lower at the merge

location due to the intense lane change activities, was the likely cause of the weaving section

bottleneck.

The C-ITS strategy proposed by Mai et al. (2016) used an LC advisory to distribute lane-

changes along an entire weaving segment. Their study showed that such an advisory could

potentially reduce delay significantly.

According to the literature, the LC concentration problem can be observed to occur in

weaving segments, particularly when the weaving flow increases. This behaviour can lead to

congestion, reducing the weaving capacity. The problem can be alleviated by distributing lane

changes along the entire weaving segment. This can be achieved by using a C-ITS advisory to

better distribute lane changes along the weaving segment.


2.1.4 Weaving segment management techniques

The bottleneck that is formed by the LC concentration of weaving vehicles is a problem: better

management of the existing infrastructure is an effective solution.

Techniques for alleviating the LC concentration close to the merge gore areas have been

proposed in the literature. Al-Jameel (2013) proposed a management scenario to shift the

diverging vehicles to a certain distance downstream of the entrance point. The management

scenario, as depicted in figure 2.3, used a solid line marking to prevent diverging vehicles from

making a lane change early, while a parallel broken line permitted merging vehicles to change

lanes. Different solid line lengths were tested and 150 m (for a 500 m weaving length) provided

the best case for maximum throughput (from 7050 veh/h to 7400 veh/h).

Zhao et al. (2016) proposed a control method, combining lane assignment and on-ramp

Figure 2.3: Weaving management scenario: longitudinal solid pavement line marking (Al-Jameel, 2013)

2.2. COOPERATIVE INTELLIGENT TRANSPORT SYSTEMS 13

signal control, for improving traffic performance in a weaving segment. Furthermore, an op-

timisation model, based on a mixed-integer-non-linear program was formulated to select the

control strategies. The results showed capacity improvement for the weaving segment. This

study proposes an optimisation algorithm for the LC advisory distributions.

Mai et al. (2016) proposed a weaving management scenario based on C-ITS to distribute

lane-changes along an entire weaving segment. Their study demonstrated that the C-ITS-based

advisory could improve the LC concentration problem and alleviate bottlenecks. This study

adopts and refines the C-ITS-based advisory proposed by Mai et al. (2016).

2.2 Cooperative intelligent transport systems

Cooperative intelligent transport systems (C-ITS) is a platform that can be applied to vehicles

and roadside infrastructure to enable direct two-way communication. C-ITS enables real-time

information sharing between vehicles and roadside infrastructure, as well as with wireless

consumer devices (Austroads, 2012a). Austroads (2012a) define ‘cooperative’ in C-ITS as the

provision of connectivity through wireless communication:

• Vehicle to vehicle (V2V)

• Vehicle to infrastructure (V2I) and vice versa (I2V)

• Vehicle to other entities with wireless communications (V2X); for example, pedestrians

and cyclists.

The critical concept of C-ITS is to provide a platform within the vehicle that will expand

on available cellular based connectivity and provide dedicated short-range communications

(DSRC) connectivity (Austroads, 2015). DSRC is assigned a 5.9 GHz bandwidth for transport

applications. Using 5.9 GHz DSRC communications, a vehicle can link with a roadside unit

(RSU) to send and receive information. For example, a RSU can forward personalised messages

to targeted groups of vehicles for more refined traffic management.

Recent developments in C-ITS applications aim to deliver environmental, efficiency and

safety benefits to road users (Green et al., 2014). C-ITS allows the exchange of real-time

information between vehicles and infrastructure; therefore, producing richer traffic data at a


finer resolution. This has implications for traffic control. V2I communications enable an

additional layer of benefits that can enhance traffic management and relieve congestion.

2.2.1 Connected vehicles

Automated vehicles have attracted keen media attention because of their many potential bene-

fits. The Society of Automation Engineers (SAE) (United States Department of Transportation,

2017) have identified five levels of vehicle automation: driver assistance, partial automation,

conditional automation, high automation and full automation. At each level progression, the

vehicle is capable of performing more driving functions than the previous level, depending

on the driving conditions. Automation is a tool for solving transportation problems, such as

alleviating congestion, reducing emissions and improving safety.

Regardless of the various predictions, ambitious or conservative, concerning the timeline

for the introduction of vehicle automation, it is crucial for the vehicles to be connected. C-

ITS-enabled vehicles, also known as connected vehicles, can ‘talk’ and ‘listen’ as well as ‘see’

by using 5.9 GHz DSRC communications. They communicate individual vehicle data directly

rather than sensing indirectly; providing faster, richer and more accurate information.

The author believes the introduction of level 5 automation is unlikely, based on technological

feasibility, in the near future. Therefore, a C-ITS-based advisory has been implemented in this

study.

2.2.2 C-ITS applications

Key themes in the development of C-ITS applications are those that provide safety, efficiency

and environmental outcomes. This section summarises these applications.

Safety

Road safety is an essential issue for road authorities and the broader community. The cost of

road crashes on the road is significant, in terms of death, injury and cost. The annual economic

cost of road crashes in Australia is estimated at $27 billion per annum (Bureau of Infrastructure,

2.2. COOPERATIVE INTELLIGENT TRANSPORT SYSTEMS 15

Transport and Regional Economics (BITRE), 2015). Austroads (2012b) estimates that, hypo-

thetically, with full penetration of C-ITS technology in vehicles, serious casualty crashes could

be reduced by 25% to 35%. Hence, C-ITS applications for safety can provide significant cost

savings to the economy and can help reduce road crashes and fatalities.

C-ITS applications, with their increased connectivity between road users and their envi-

ronment, offer capabilities beyond that of sensor-based applications. C-ITS enables vehicles

to monitor and be warned of potentially dangerous situations and hazardous conditions on the

road (Austroads, 2013). C-ITS will become more integrated with wireless technologies, which

will increase the safety of the interactions between vehicles and bicycles, pedestrians and trains.

Safety alerts and warnings can be communicated to the driver using the onboard equipment.

Kanazawa et al. (2010) provided an overview of field operations tests of C-ITS technologies

used on Japan’s next-generation roadways (SmartWay). The ‘forward obstacle information

provision’ application was tested to prevent sharp braking and rear-end collisions at a site where

a vertical crest approaching an intersection reduced the visibility of stopped vehicles. The

application used both roadside sensors, to detect stopped vehicles, and V2I communication to

relay information, through an onboard unit, to alert approaching vehicles.

Efficiency

The transport system currently faces challenges, with increasing traffic demand and more con-

gestion. Forecasts estimate that congestion will considerably increase in the future. According

to a report by The Department of Infrastructure and Regional Development (2015), “the cost

of congestion in our capital cities, estimated at $13.7 billion in 2011, is expected to increase

to around $53.3 billion in 2031, or around 290 per cent, in the absence of additional capacity

and/or demand management.” C-ITS has the potential to enable capacity improvements.

ITS applications are deployed to alleviate and manage the impact of congestion on the

transport network. Conventional ITS devices, such as variable message signs, variable speed

limits, and ramp metering, rely on aggregated, flow-level traffic control. Conversely, C-ITS

provides rich traffic information, including speed, acceleration, location and direction of C-

ITS-enabled vehicles. Hence, C-ITS can be implemented to control traffic at a more refined

level. C-ITS-enabled vehicles may cooperate with the infrastructure to increase connectivity

and provide control at an individual level. This level of control can result in a reduction of


flow break down and delays. Tientrakool et al. (2011) estimates that if all of the vehicles use

sensors alone, the increase in highway capacity is about 43%; however, if all of the vehicles use

both sensors and V2V communication, the increase is about 273%. C-ITS applications, used to

inform road users of real-time traffic information, may better utilise the network and improve

the efficiency.

A ‘merging assistance’ application, tested in Japan, provided vehicles in the main lane with

information on the existence of merging vehicles (Kanazawa et al., 2010). Weiß (2011) provides

an overview of C-ITS applications, tested in Europe, covering three categories: traffic efficiency,

driver assistance/safety and commercial services. Traffic efficiency applications include alerting

drivers to changed traffic situations, traffic flow information, and traffic management.

Environmental

Emissions from transport pollute the environment affecting air quality, particularly in urban

areas. In recent decades, the automobile industry has increased their attention to more “eco-

friendly” vehicles (such as electric and hybrid vehicles) that produce fewer emissions than petrol

vehicles. Their efforts have improved the environmental credentials of passenger cars; however,

increasing transport demand will only perpetuate the emissions produced by the transport sector.

According to the Bureau of Infrastructure, Transport and Regional Economics (BITRE) (2009),

the passenger car fleet, in 2020, will remain the single most significant contributor to transport

sector emissions (around 47 percent of domestic transport output). Hence, there is a demand

for C-ITS applications with positive environmental outcomes.

Efficiency applications are closely related to environmental applications. C-ITS applications

that improve traffic flow and reduce delays will reduce overall network emissions. For example,

V2I applications, that coordinate vehicle speed with signal phasing, have been modelled to

deliver fuel savings and reduce emissions. C-ITS applications that enable road users to make

informed decisions and that provide advisory control will result in higher network efficiency,

reducing congestion and, hence, overall emissions.

2.3. HEURISTIC OPTIMISATION 17

2.3 Heuristic optimisation

This section provides a general overview of heuristic optimisation and how it is used to solve

traffic optimisation problems.

The primary task in an optimisation problem is to find the optimal solution by using some

optimisation technique. Applications of heuristic search algorithms inspired by natural phe-

nomena are rapidly growing in diverse scientific fields to solve tough optimisation problems.

Researchers have successfully applied heuristic algorithms to a wide variety of civil engineering

optimisation problems because heuristic algorithms are not problem-specific, do not require

the objective function to be continuous or differentiable (unlike gradient-based optimisation

algorithms like the quasi-Newton method), can incorporate constraints, can search vast spaces

of candidate solutions (Gopalakrishnan et al., 2013). Heuristic algorithms find quality solutions

to tough optimisation problems in a reasonable amount of time, but there is no guarantee that

optimal solutions are reached (Yang, 2010).Heuristic algorithms are characterised by some

balance between exploration (global search) and exploitation (local search).

Heuristic algorithms are preferred for problems that require good quality solutions which

are easily attained, rather than the best solutions. A heuristic algorithm is suited specifically

for the lane-changing concentration problem because the C-ITS advisory only requires a good

quality solution to improve the fitness function. This is more important than the guarantee of

an optimal solution because of the relatively high cost in computational effort, to attain the best

solution, compared to the marginal improvement in the fitness function.

Many modern heuristic algorithms that have been developed for computer science research:

for example simulated annealing, tabu search, genetic algorithms, ant colony optimisation, bee

algorithms, differential evolution, particle swarm optimisation, harmony search, big bang-big

crunch, the firefly algorithm, cuckoo search and bat-inspired algorithms.

Nature-inspired algorithms are based on the behaviour of so-called swarm intelligence,

which forms the foundation of heuristics (Yang, 2014). This research focuses on using swarm

intelligence models, mainly PSO, to solve the optimisation problem.


2.3.1 Particle swarm optimisation

PSO, a heuristic algorithm, has become one of the most widely used algorithms based on swarm

intelligence due to its simplicity and flexibility (Yang, 2014). It is a stochastic search and

optimisation technique that has been applied to many problem domains which are difficult to

solve by conventional methods.

The PSO concept, originally introduced by Eberhart and Kennedy (1995), was inspired by

the social behaviour of bird flocking or fish schooling. In PSO, a problem is optimised by

iteratively trying to improve a potential solution with respect to an objective function. It solves

a problem by having a swarm of particles, or population of potential solutions, which are flown

in a high-dimensional search space. Each particle has an adaptable velocity, according to which

it flies through the solution space. The movement of the particle is updated according to its own

best position in history, and to the current global best position, which is found by the swarm,

at the same time it tends to move randomly. When a particle finds a location better than any

previously found, it updates that location as the new current best for the particle. The swarm of

particles is expected to fly toward an optimal solution through the feasible solution space.

The original PSO algorithm has two variants: global best, gbest, and local best, lbest, PSO.

The global variant, widely used in literature, is used in this research (Gopalakrishnan et al.,

2013). Hence, the following describes the global best PSO algorithm.

Consider aD-dimensional search space, where the ith particle of a swarm can be represented

by a D-dimensional vector, Xi = (xi1, xi2, . . . , xiD)T . The velocity of the particle can be

represented by a D-dimensional velocity vector Vi = (vi1, vi2, . . . , viD)T . The particle, xi, has

a memory of its previously visited personal best position, denoted as yi = (yi1, yi2, . . . , yiD)T .

The social information is the best position found by the swarm, referred to as y. Let t denote

discrete time steps or the iteration number. Each particle updates its position based on its own

best experience, the best swarm overall experience, and its previous velocity vector, according

to equations 2.1 and 2.2 (Eberhart and Kennedy, 1995).

vt+1ij = ωvtij + c1r

t1j(y

tij − xtij) + c2r

t2j(y

tj − xtij) (2.1)

xt+1ij = vt+1

ij + xtij (2.2)

2.3. HEURISTIC OPTIMISATION 19

where j = 1, 2, . . . , D; i = 1, 2, . . . , ns and ns is the size of the swarm. The stochastic nature

of the algorithm is determined by rt1j , rt2j ∼ U(0, 1), which are random values, sampled from

a uniform distribution in the range [0, 1]. These random numbers are scaled by acceleration

coefficients c1 and c2, called cognitive and social parameters, respectively, where 0 ≤ c1, c2 ≤ 2.

The performance of each particle is measured by the objective function, which is related to the

problem under consideration. The inertia weight ω was added by Shi and Eberhart (1998)

to improve the convergence rate. Gopalakrishnan et al. (2013) added a maximum velocity

parameter, vmax, to improve the efficiency of the PSO in the region of the optimum by allowing

a finer step-size velocity.

The termination criterion for the PSO can be one of the following: a fixed number of

iterations, the maximum number of iterations without improvement, and the minimum error

requirement in the objective function.

The swarm behaviour in basic PSO is influenced by the number of particles, the inertia

weight, the maximum velocity, and the acceleration coefficients to modify the velocity. These

parameters are considered for the speed, convergence and efficiency of the algorithm. The

influence of the previous velocity on the current velocity, which affects the trade-off between

exploration (global search) and exploitation (local search), can be controlled by the inertia

weight, ω. A larger inertia weight facilitates the exploration; a smaller inertia weight tends

to facilitate the exploitation of the current search area. Hence, a suitable selection of the inertia

weight achieves the right balance between exploration and exploitation (Shi and Eberhart,

1998).

There are several key advantages of PSO over other optimisation techniques: derivative-

free algorithm unlike many conventional techniques, only a few parameters to adjust, ability

to handle objective functions with stochastic nature, ease of implementation, does not require

a decent initial solution to start its iteration process (AlRashidi and El-Hawary, 2009). Since

its original development, PSO has been modified into many different variants (Gopalakrishnan

et al., 2013). As a heuristic algorithm, PSO does not guarantee to find the optimum solution;

therefore, the practitioner may need to modify the algorithm to work efficiently for a given

problem.


2.3.2 Particle swarm optimisation: traffic and transportation engineering applications

Swarm intelligence techniques, including PSO, have been successfully applied for transporta-

tion and traffic engineering applications, including transportation network design, traffic flow

forecasting, traffic control, traffic accident forecasting and vehicle routing problem (Teodorovic,

2008; Gopalakrishnan et al., 2013).

Srinivasan and Seow (2003) proposed a new approach to automatic incident detection on

traffic highways using PSO. Their research used PSO to train a neural network in place of back-

propagation. The simulation results show that PSO performed better than the back-propagation

algorithm.

The vehicle routing problem with time windows accounts for a significant portion of the

work of many distribution and transportation systems. Zhu et al. (2006) developed an algorithm,

based on the principles of PSO, for the vehicle routing problem. The authors tested the proposed

approach on a few numerical experiments and compared the results with the results obtained

by the genetic algorithm approach. The PSO algorithm discovered optimal solutions in 82% of

cases, while the genetic algorithm discovered optimal solutions in 36% of cases. The simulated

results indicated that the PSO algorithm could efficiently and quickly achieve a resolution to the

vehicle routing problem.

Traffic flow forecasting is a key problem in the real-time adaptive control of urban traffic.

Zhao et al. (2006) proposed the radial basic function and neural network based forecasting

model for two adjacent intersections. They used PSO algorithm to optimise the hidden layer

and the output layer weights of the forecasting model. The proposed approach enhanced the

training speed and accuracy of the traffic flow forecast.

Chen and Xu (2006) proposed a PSO algorithm for solving the traffic optimisation prob-

lem by optimising the average delay and the average number of stops for adjacent junctions.

The simulation results showed that the delay per vehicle could be substantially reduced under

constant traffic demands and time-varying traffic demands.

Dong et al. (2006) proposed a chaos-PSO algorithm, which is a modified PSO algorithm

to allow chaotic searching, used to optimise the signal timing for urban area traffic control.

The experimental results for traffic networks consisting of nine intersections showed that signal

timing optimisation based on chaos-PSO could reduce average delay per vehicle by 41.6%.

2.4. SUMMARY 21

Wang et al. (2007) used a modified PSO for optimal coordination of the traffic signals in a

simulated artery system.

Peng et al. (2009) introduced isolation niches embedded in PSO for traffic lights control.

The proposed algorithm was used to optimise the time of green and red lights to make the

average waiting time for vehicles shorter. The simulation results showed that it was a valid

method.

Lianyu et al. (2009) proposed a method based on a quantum-behaved PSO algorithm to

obtain optimal origin–destination (OD) matrix calculation used in urban traffic management

and control.

Kachroudi and Bhouri (2009) proposed an urban traffic control strategy that uses traffic

lights to regulate private vehicle traffic and the progression of public transport vehicles. The

authors used a modified PSO algorithm to optimise the multi-modal traffic responsive strategy

on a large virtual urban network.

Cao et al. (2010) proposed a two-direction green wave control algorithm of the traffic signal

based on PSO. The PSO optimised the signal split and the phase offset. The simulation result,

using traffic data collected from Liansheng Road and Dongguan City, showed the method

significantly reduced average delay and average queue length.

Lertworawanich (2012) proposed a PSO algorithm for the sequential highway network re-

covery problems. The study used a model to determine the optimal highway network restoration

sequence after disasters.

These results from research have shown that the PSO is a promising technique capable of

solving complex traffic and transportation problems. As there have been few studies relating

to the use of PSO in freeway traffic control, this research aims to use PSO algorithm in the

lane-changing optimisation problem in a freeway weaving segment.

2.4 Summary

The literature review revealed that a bottleneck problem in freeway weaving segments, caused

by the lane-changing concentration of merging and diverging vehicles. Hence, the entire weav-

ing segment length is not effectively utilised.


A C-ITS-based LC advisory for weaving segments was proposed by Mai et al. (2016) using

V2I communications. The LC advisory was shown to alleviate the lane-changing concentration

problem effectively by distributing lane changes along the weaving segment length. However,

the study did not investigate how to optimise the LC distribution. An appropriate optimisation

technique must be implemented to satisfy the constraints of the problem. PSO has been used

extensively in literature to optimise diverse problem sets with various constraints.

In short, although the C-ITS lane changing advisory for weaving segments has been shown

to improve the LC concentration problem, no optimisation technique has been applied to the LC

distribution. The heuristic PSO algorithm provides an opportunity to optimise the LC advisory

distribution.

Chapter 3

Methodology

3.1 Research design

This chapter describes the research methodology used to achieve the aims and objectives stated

in chapter 1 based on the information gleaned from the literature review in chapter 2. The

research methodology involves both the basic concept and assumptions of the C-ITS-based LC

advisory (section 3.2) and the proposed PSO algorithm used in this study (section 3.3). The

overall research design, in the following four steps, is shown in figure 3.1.

Step 1: Literature review (Chapter 2)

The first stage of the literature review focused on weaving segments: the factors influ-

encing their capacity, the driver behaviour and the traffic management techniques at these

segments. The second stage of the literature review gave an overview of C-ITS and its

applications. The third section focussed on heuristic algorithms and on the application of

PSO in traffic engineering problems. Briefly, the literature review:

• Provided evidence of a lane-changing concentration problem causing bottlenecks at

freeway weaving segments

• Provided an overview of C-ITS and an example of how a LC advisory, based on V2I

communications, could alleviate the weaving lane-changing concentration problem,

and

• Provided examples of heuristic optimisation in traffic engineering applications.

23

24 CHAPTER 3. METHODOLOGY

Chapter 2: Literature Review

Cooperative IntelligentTransport Systems:

Investigate how C-ITS canprovide advisory traffic

control at weaving segments

Weaving segments:Investigate lane-changing

concentration problem andtraffic control limitations

at weaving segments

Heuristic optimisation:Identify opportunity toimplement an algorithm

to optimise lane-changingadvisory distribution

Chapter 3: Methodology

Propose an algorithm, based on particle swarmoptimisation, to optimise the distribution

for the C-ITS-based lane-changing advisory

Chapter 4: Case Study

Microscopic traffic simulation platform with Aimsun:

1. Model test site

2. Simulate C-ITS advisory traffic control

3. PSO interface with simulation

4. Evaluate optimisation results

Python code withPSO-Aimsunconnection

CompareObjective function

Chapter 5: Conclusion

Summarise thefindings by answeringthe research questions

and recommendfuture works

Figure 3.1: Research methodology

Step 2: Methodology and proposed algorithm (Chapter 3)

The methodology firstly involved a C-ITS-based LC advisory in distributing lane chang-

ing along the weaving segment (see section 3.2), and secondly, involved an algorithm,

based on PSO, to optimise the LC advisory distribution (see 3.3).

Step 3: Case Study (Chapter 4)

A case study was designed to implement and evaluate the proposed strategy. The C-

ITS advisory was implemented in a microscopic traffic simulation software, Aimsun by

using an application programming interface (API) that connected with external Python

3.2. BASIC CONCEPT AND ASSUMPTIONS 25

scripts. The proposed PSO algorithm, coded in Python, was executed in an integrated

development environment.

The objective function was examined and chosen based on current literature revealed in

the review. The results were used to evaluate different tests; these tests were compared

with the base case (no intervention) and the optimised case. Chapter 4 presents the details

of this step. The evaluation of this case study revealed outcomes relevant for answering

the research questions.

Step 4: Conclusion and recommendations for future work (Chapter 5)

The final step of the research design was to present the research findings discovered in

answering the research questions. This step also identified and explained the research

limitations and gave recommendations for further research work (see chapter 5).

3.2 Basic concept and assumptions

In this research, a C-ITS advisory was considered (see figure 3.2). This strategy aimed to

distribute weaving vehicles over the existing infrastructure by advising them, via V2I commu-

nications, from which point they could start to change lanes. Hence, the strategy sought to

alleviate the LC concentration problem, caused by excessive LC activity close to the merge

gore, in a freeway weaving segment (see 3.2(b) in figure 3.2).

The C-ITS advisory relied on the following assumptions:

• The communication signal strength was 100% guaranteed.

• All vehicles were assumed to be equipped with 5.9 GHz DSRC.

• DSRC connectivity was available (commonly used for C-ITS projects (Green et al., 2014)).

• Each vehicle complies with the guidance provided by the advisory.

• Each vehicle is tracked by a RSU to identify its lane.

• Each vehicle’s origin and destination are known; thus, a weaving vehicle could be identi-

fied.

• Traffic is composed of cars only and does not consider the impact of heavy vehicles.


(a) Weaving segment configuration

(b) Lane-changing concentration problem zone

(c) Weaving segment divided into eight sections

Figure 3.2: One-sided weaving segment

The five steps applying the advisory control strategy (see figure 3.3) are discussed in further

detail below.

Step 1: Data Collection

In this step, the OD information of each vehicle was collected via V2I communications.

Assuming an RSU located upstream of the weaving segment, vehicles equipped with

C-ITS capability would send their OD path information.

Step 2: Vehicle movement group classification

The vehicles were classified into weaving and non-weaving groups based on their OD

information. For the non-weaving group, no further actions were required so they pro-

ceeded as usual.

Step 3: Weaving group classification

3.2. BASIC CONCEPT AND ASSUMPTIONS 27

Obtain vehicle OD information

Weaving vehicle?

Do nothingClassify

weaving vehicle

No Yes

Merging or diverging?

Mergingvehicle group

Divergingvehicle group

RF FR

Assign section 1 Assign section 2Assign

section . . .Assign section j

distribution %

Lane-changingfrom section 1

Lane-changingfrom section 2

Lane-changingfrom section . . .

Lane-changingfrom section j

Step 1:Collect data

Step 2:Classifyvehiclemovementgroup

Step 3:Classifyweaving group

Step 4: Assignsections forweavingvehicles

Step 5: Sendlane-changingadvisory

Figure 3.3: The process chart for the lane-changing advisory application

The weaving vehicles were classified into merging and diverging subgroups, based on

their OD information, to allocate separate LC distributions. Movements of merging and

diverging are referred to as ramp-to-freeway and freeway-to-ramp movements, respec-

tively.

Step 4: Assignment of sections for weaving vehicles

A section was assigned to each weaving vehicle, from which point they were permitted to

start to perform a lane change. In this study, the weaving segment was divided into eight

sections to simulate C-ITS control at a detailed level (see figure 3.2(c)). Considering the

simulation step of 0.8 seconds, eight sections with lengths of 50 m would be suitable for

a vehicle travelling at a speed of 100 km/h. For example, at 100 km/h, a vehicle travels a

distance of approximately 28 m/s or 22 m per simulation step. Hence, the length of each


section ensured vehicles would be captured during a simulation time step. It also ensured

that the distance travelled did not exceed the section length over a simulation time step.

As part of step 4, the LC distributions were used separately for the RF and FR vehicle

groups. Hence, a weaving vehicle is assigned section j, where j ∈ n sections, according

to the LC distribution of its weaving group, RF and FR respectively.

Step 5: Lane-changing advisory sent

Each vehicle was sent a LC advisory to indicate where they were permitted to commence

their lane change. The strategy was assumed to provide advisory control; thus, LC was

not forced. Instead, the C-ITS application advised drivers when to commence LC based

on their location. For example, vehicles assigned to section one were permitted to change

lanes when they entered the weaving segment with a suitable gap, whereas a vehicle

assigned to section five was advised not to change lanes until the fifth section in the

weaving segment. The advisory restricted the LC until the vehicle reached its assigned

section, at which point the Aimsun LC model governed the LC characteristics of the

vehicle (Barcelo, 2010).

The individual weaving vehicles received LC guidance in the form of an audio and

visual alert, as is commonly implemented in real-world C-ITS applications, such as those

reviewed by Kanazawa et al. (2010) in Japan. Figure 3.4, for example, shows an in-

vehicle visual display unit for C-ITS applications. The LC advisory application, for

example, would display two different messages, as appropriate:

• ‘Distance until lane change’ (countdown of the distance until the assigned section)

• ‘Seek gap and perform lane change’ (alerting the driver to commence a lane change

where a suitable gap is found)

The purpose of the advisory was to distribute lane changes along the weaving segment

length to better utilise the infrastructure. This was achieved by optimising the LC distributions

for RF and FR vehicles in step 4. The actual LC behaviour may differ in a real-world scenario.

3.3. PROPOSED OPTIMISATION ALGORITHM 29

Figure 3.4: In-vehicle visual display unit (Transport for NSW, 2015)

3.3 Proposed optimisation algorithm

In a previous study by Mai et al. (2016), the distribution percentage was fixed, and optimal

solutions were not explored using sophisticated optimisation techniques. This study involves

particle swarm optimisation to seek optimal solutions for the LC advisory distribution.

A methodology for the optimisation of the LC advisory distribution is proposed in this

section. The proposed algorithm is discussed in further detail below.

Table 3.1 summarises the notations used in this section.

The basic PSO algorithm (summarised in algorithm 1) needed to be modified to handle

the constraints in the optimisation problem. Accordingly, section 3.3.1 provides the proposed

extension to the basic PSO.

3.3.1 Proposed PSO

The PSO algorithm was modified to generate solutions for the LC advisory distribution. Genetic

algorithms were attempted for this problem, but the crossover and mutation functions proved

difficult when dealing with the given constraints. Conversely, PSO could iteratively improve

each decision variable in the potential solution while remaining within the feasible search space.

Hence, a PSO algorithm was proposed for this problem because the fitness evaluations could be

used to guide the search directly (Paquet and Engelbrecht, 2003). Because the problem could be

defined as a continuous optimisation problem with constraints, PSO was a suitable algorithm.


Table 3.1: Notations of parameters and variables

PSO parametersf(x) Function to minimiseS Total number of particles in the swarmD Number of dimensions in a particlei Index for particle in swarm, Sj Index for dimension in particle, xixi Particle representing a potential solution, xi ∈ <n

xlb Lower bound limit for xijxub Upper bound limit for xijω Inertia weight, ω = 0.7

φp Cognition parameter, φp = 1.4

φg Social parameter, φg = 1.4

vi(t) Velocity vector, vi ∈ <n

vc Velocity clamping, vc = 0.2

Objective FunctionS Minimum detector speedM Missed turns penalty factor

Algorithm 1: The pseudocode of basic particle swarm optimisationInput: PSO parametersResult: The best particle found by the algorithm.

1 for each particle i = 1, . . . , ns do2 Initialise particle’s position and velocity3 end4 while maximum iterations or stopping criteria is not met do5 for each particle i = 1, . . . , ns do6 Calculate fitness value7 if the fitness value is better than the best fitness value (pbest) in history then8 pbest = fitness value9 end

10 end11 Choose the particle with best fitness value of all the particles as the gbest12 for each particle i = 1, . . . , ns do13 Calculate particle velocity according to equation 2.114 Update particle position according to equation 2.215 end16 end

The proposed PSO, for a constrained optimisation problem, has been adapted to search

within the feasible solution space. Constraints, in heuristic algorithms, may cause the search

to compromise on the optimal solution by just seeking a feasible solution Coello and Montes


(2002). So the PSO algorithm needs a mechanism to deal with the constraints of the problem

while maintaining its focus on optimisation.

PSO proved to be a useful algorithm to optimise unconstrained functions; however, if some

constraints were added to the objective function, the problem became more complicated (Paquet

and Engelbrecht, 2003). A modified PSO algorithm was developed specifically to include the

constraints in the optimisation problem. The following sections outline the modifications to the

basic PSO.

3.3.2 Solution representation

To optimise the LC-advisory distribution, the potential solution must be encoded in a suitable

form, such as a one-dimensional array jointly comprising the RF and FR LC advisory distribu-

tions. Figure 3.5 depicts a simple potential solution.

RF FR

xRF1 xRF2 xRF3 xRF4 xRF5 xRF6 xRF7 xRF8 xFR1 xFR2 xFR3 xFR4 xFR5 xFR6 xFR7 xFR8

Figure 3.5: Solution representation

3.3.3 Co-evolutionary optimisation

A decomposition approach was implemented to improve the potential solution iteratively. The

proposed PSO improved the potential solutions by improving the lane-changing advisory dis-

tribution made up of the RF and FR distributions.

Figure 3.6 provides an example of the steps for this co-evolutionary optimisation approach.

Assume there is a swarm size of ten particles, each with 16 decision variables, each column

representing one dimension (one decision variable); the swarm of solutions (particles) will be a

matrix of D × S (16× 10), as shown in step 1. In the matrix, each row represents one solution

(particle), the columns represent the set of decision variables. The initial population is randomly

generated within the predefined constraints.

The set of decision variables is divided into the RF and FR subset arrays in step 2; these are

denoted by the yellow and green colour, respectively. The size of each subset is D/2 (16/2 =

8), that is, each subset contains 8 decision variables represented by columns and ten particles

(solutions) represented by rows.


Decision variables 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16

Ind

ivid

ual

s

1

2

3

4

5

6

7

8

9

10

Global decision

variable index

Local decision

variable index

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 1 2 3 4 5 6 7 8 1 2 3 4 5 6 7 8

Ind

ivid

ua

ls

1 1

2 2

3 3

4 4

5 5

6 6

7 7

8 8

9 9

10 10

PSO PSO

Fitness Individual Fitness Individual

Solution vector

STEP

1

STEP

2

STEP

3

STEP

4

Figure 3.6: Co-evolutionary optimisation method


The solution vector, created in step 3, is used for the fitness calculation process. The solution

vector contains two parts selected from the created subsets, as shown in step 3. In this example,

the RF distribution is selected from the first subset array; the FR distribution is selected from

the second subset. Each part represents the best solution in its subset. For example, after an

iteration, the best solution in the first subset is Individual 5 (highlighted by a black colour),

which is used to represent the first part of the solution vector, and Individual 2 from the second

subset is used to represent the second part of the solution. Every particle (individual) in a

subset is evaluated by combining it with all the best individuals in the solution vector. That

is, the solution vector is fed into the objective function for fitness calculation. This is the co-

evolutionary process for the PSO algorithm. For example, to calculate the fitness values of all

particles in the first swarm, each particle from the first subset is sent to be used as the first

part, combined with the second part of the FR subset, and then it is sent to the fitness function

to calculate the fitness value of this particle. The same process is repeated for the RF subset.

The parts – the best individuals in each subset of the solution vector – are updated during the

optimisation process.

The optimisation process (PSO) is called in step 4 to solve each subset separately. Each PSO

operates on each subset of solutions and, during the optimisation process of PSO, the fitness

value of the newly generated solution are calculated by sending it into the solution vector. The

same process is repeated for the second subset.

Figure 3.7 shows the PSO cycle used to solve the two subsets (denoted as Swarm 1 and

Swarm 2). In the first cycle, the PSO process for Swarm 1 is executed, while the representative

(global best) from Swarm 2 is sent to form the second part of the solution vector. During the

first cycle, the PSO sends each particle into the solution vector and obtains the fitness value.

The first cycle will terminate after all particles in Swarm 1 have been evaluated. The search

then executes the second cycle to optimise Swarm 2 and uses the representative (global best)

from Swarm 1 in the solution vector. Once the second cycle terminates, the search repeats the

cyclical process. The process iteratively improves the search for the best solution by updating

the current best particle of each swarm.


PSO

Population

Swarm 1

PSO

Population

Swarm 2

Solution vectorCycle 1

particle

fitness

representative

PSO

Population

Swarm 1

PSO

Population

Swarm 2

Solution vector Cycle 2

particle

fitness

representative

Figure 3.7: PSO cycle process

3.3.4 Initialisation

The potential solutions were randomly initialised within the feasible domain. The particle’s

position was initialised using equation 3.1; it was then transformed within the feasible domain

using equation 3.2.

xij = xlb + rij × (xub − xlb), ∀j = 1, . . . , nx, ∀i = 1, . . . , ns (3.1)

where rij ∼ U(0, 1) and xij is the position of x for j in nx dimensions and i in ns particles. The

random variable, rij , is uniformly distributed between 0 and 1. The lower and upper bounds of

position xij are xlb and xub, respectively.

x′ij =xij∑nx

j=1 xij, ∀j = 1, . . . , nx, ∀i = 1, . . . , ns (3.2)

where x′ij is the transformed position, within the feasible space, of x for j in n dimensions and i

in S particles. For all j in n dimensions, the position is divided by the sum of values in particle

i. This post-processing method was used to initialise positions within the feasible domain.

3.3.5 Objective function

The problem can be defined as a constrained numerical optimisation problem that seeks to

find x, which minimises f(x). This section describes the objective function formulation. The

proposed PSO algorithm inputs the LC advisory distribution, x, into Aimsun, which outputs


the fitness evaluation (see figure 3.8). The problem will be optimised by iteratively trying to

improve a potential solution for the objective function.

Start

Initise PSOparameters

Generaterandom swarm

of particles

Evaluate thefitness of

all particles

Aimsun R©

Input: x

Output: f(x)

Record personalbest fitness ofall particles

Find globalbest particle

Termination criteria met?

Stop

Yes

Update thevelocity ofparticles

Update theposition of

particles

No

Figure 3.8: The flowchart of PSO

In this work, the objective function consisted of two parts: speed and missed turns. The

speed was measured in the conflict area of the weaving segment, where most of the turbulence

typically occurred due to merging and diverging traffic streams. In this study, the auxiliary

lane and lane 3 experienced the most LC turbulence between merging and diverging vehicles;

consequently, speed along these lanes was used as an indicator of traffic flow dynamics, how

smoothly vehicles drove through the segment. The speed was measured by detectors that were

spaced at 10-m intervals. This study used 1-minute aggregation for all detector measurements.


The detector with the minimum speed measurement would represent the point where speed

drop was most significant. Denny and Williams (2005) found that the speed would be the

lowest close to the merge gore areas where the maximum interaction between merging and

diverging vehicles occurred because of the bottleneck formation. Hence, regarding the objective

function, it was pertinent to increase the minimum speed and to reduce speed drop caused by a

LC concentration. The minimum speed, measured at a detector, would be substituted into the

objective function.

Missed turns occurred when a weaving vehicle was unable to perform its required lane

change before the end of the segment; thus, missing its desired turn or exit leg. This tended

to occur when vehicles were assigned a section close to the end of the diverging point, and no

suitable gap was found to change lanes. This is undesirable for drivers and should be avoided.

Hence, in this study, missed turns have been penalised by a factor, M , shown in equation 3.4.

The LC distribution was optimised based on the objective function, summarised in equation

3.3. The free-flow speeds for the freeway and on/off ramps were 100 km/h and 80 km/h,

respectively.

min f(x) =1

S+M (3.3)

where f(x) is the objective function for a given LC distribution, xi, S is the value derived from

the speed detector measurements, and M is the penalty factor for the number of missed turns.

M is a weighted penalty factor that is expressed as:

M = N +m2 (3.4)

where N is a user-defined constant and m is the number of missed turns. The number of missed

turns, m, is defined as the number of vehicles that are unable to find a gap in time to proceed

to their desired exit. The factor has been squared to increasingly penalise this undesirable

outcome.

The proposed PSO was used to improve the LC concentration problem by optimising the

LC advisory distribution.


3.3.6 Constraints

The optimisation problem includes both boundary and summation constraints. These set of

constraints is imposed by conditions that the variable, x, must satisfy to find a feasible solution.

These constraints are presented in equations 3.5 and 3.6.

nx∑j=1

xij = X, ∀i = 1, . . . , ns (3.5)

where X is the value for feasible solutions, as defined by the linear constraint on the LC-

advisory distribution.

xlb ≤ xij ≤ xub, ∀j = 1, . . . , nx, ∀i = 1, . . . , ns (3.6)

where xlb and xub are the lower and upper bound values, respectively.

3.3.7 Velocity

The basic PSO algorithm updated the position of its particles with a velocity equation that was

unconstrained. A constraint handling mechanism was used to guarantee a feasible solution.

The basic velocity equation was implemented, then a constraint-preserving method was

applied to ensure that the particle’s position satisfied the constraints. In this process, where

decision variables have violated the boundary constraint, the violation was discretely distributed

across dimensions which may satisfy the boundary constraint.

Velocity clamping was also implemented to control the exploration of particles within the

boundary constraints. If a particle’s velocity exceeded the specified maximum velocity, the

particle’s velocity was set to the maximum velocity (Engelbrecht, 2007).

3.3.8 Position

Based on the calculated velocity, the updated position remains within the feasible domain. The

positions of all particles are updated using equation 2.2.


3.3.9 Termination criteria

Iterations of the algorithm are executed until a stopping condition is satisfied. In this work, the

criterion was set to a maximum of 50 iterations.

3.4 Summary

This chapter presented the methodology used in the study. The case study and simulation results

are presented in chapter 4.

Chapter 4

Case Study

This chapter covers the microscopic traffic simulation set-up, including the network configu-

ration and simulation settings; the performance indicators used for evaluation; and finally, the

results and discussions.

4.1 Simulation test bed

Traffic simulation has been used to evaluate the application of the C-ITS lane-changing advisory

and the implementation of the optimisation algorithm.

The model was built using a commercially available microscopic traffic simulation software,

AIMSUN (advanced interactive microscopic for urban and non-urban network), which was

developed by Transportation Simulation Systems (TSS) in Spain (Barcelo, 2010). Aimsun con-

tains a microscopic simulator and offers an API with its microsimulation software. This study

used the API, which enables Aimsun to interface with external applications, the development

language Python, and version 8.1.5 of Aimsun.

The simulation period is 15 minutes, with a 10-minute warm-up period. Each test scenario

runs 20 replications to capture the stochastic variation in traffic flow. The average of the 20

simulation runs was used for output analysis.

An empirical study, by (Al-Jameel, 2013), examined the characteristics of driver behaviour

in weaving segments using field data extracted from video recordings of seven motorway weav-

ing sites. This study used the existing network based on the M60 Motorway (Manchester City,

UK). This segment was coded in a previous study by Mai et al. (2016).

39

40 CHAPTER 4. CASE STUDY

(a) M60 Motorway aerial image

(b) M60 Aimsun network

Figure 4.1: M60 Motorway test bed

The network, a short weaving segment with a length of 400 m, has a width of four continu-

ous lanes: three freeway-to-freeway lanes and a one-lane, left-side on-ramp, followed closely by

a one-lane, left-side off-ramp. The two ramps are connected by a continuous freeway auxiliary

lane. The configuration, defined as a one-sided weaving segment, requires no more than two

completed lane changes. The speeds are coded as 100km/h and 80km/h for the freeway and

ramp sections, respectively. The geometry of the weaving segment is shown in figure 4.1

(considering left-hand side traffic direction).

The demand data for the weaving segment were taken from study by Al-Jameel (2013). The

model, which considered only cars in its traffic composition, had the following demand flow

rates:

• FF demand flow: 5300 veh/h

• RF demand flow: 900 veh/h

• FR demand flow: 900 veh/h

• RR demand flow: 100 veh/h

The model calibration and validation processes were undertaken in a previous study by Mai

et al. (2016). In their study, they calibrated the lane-changing model by adjusting the ‘distance

to zone’ parameters, which represented the lane-changing motivation characteristics. Their

model, which uses the observed data from an empirical study by Al-Jameel (2013), calibrates

and validates the high lane-changing concentration problem to represent weaving behaviour

accurately. Hence, their model can be used reasonably for a comprehensive analysis of different

test scenarios. Table 4.1 lists the parameters describing the weaving segment.

4.2. PERFORMANCE INDICATORS 41

Table 4.1: Weaving segment parameters

vFF = freeway-to-freeway flow rate in the weaving segment(veh/h)

vRF = ramp-to-freeway flow rate in the weaving segment (veh/h)vFR = freeway-to-ramp flow rate in the weaving segment (veh/h)vRR = ramp-to-ramp flow rate in the weaving segment (veh/h)vW = weaving demand flow rate in the weaving segment

(veh/h), vW = vRF + vFR

vW = weaving demand flow rate in the weaving segment(veh/h), vNW = vFF + vRR

v = total demand flow rate in the weaving segmnet (veh/h),v = vW + vNW

N = number of lanes within the weaving segment, N = 4

L = length of the weaving segment (m), L = 400

RF-ratio = ramp-to-freeway volume ratio, vRF /vW

4.2 Performance indicators

Performance indicators, or measures of effectiveness, need to be carefully chosen to evaluate

the weaving segment. Average speed is commonly used as an operational indicator; however,

Cassidy and May (1991) found that it does not reliably reflect operational quality in a weaving

segment. Cassidy et al. (1989) observed that speed appears to be insensitive to low and moderate

conditions. Denny and Williams (2005) found that the speed would be the lowest close to the

merge gore areas, where the maximum interaction between merging and diverging vehicles oc-

curred because of the bottleneck formation. The speed would increase once the vehicles moved

through the bottleneck location. Hence, speed will not be used as an operational performance

indicator in this research. Instead, speed will show the traffic flow dynamics, how smoothly

drivers travel through the weaving segment and whether the LC concentration problem has

been alleviated.

Detectors, spaced at 10m intervals, collected speed measurements. This research used 1-

minute aggregation for all detector measurements. The detector speed measurements can be

used to show the speed profile along the weaving segment and to plot the speed contours.

Two performance indicators were used to evaluate the weaving segment and to compare the

optimised case and the base case: average vehicular delay and time savings.

Aimsun recorded the average delay, calculated as the difference between the actual travel


time and the free-flow travel time. The free-flow travel times of the mainline vehicles (FF and

FR) and the on-ramp vehicles (RF and RR) were calculated at speeds of 100 km/h and 80 km/h

for the freeway lanes and ramps, respectively. For mainline vehicles, the actual travel time was

recorded from 500 m upstream of the merge gore to downstream of the weaving segment. For

on-ramp vehicles, the travel time is recorded from 130 m from the merge gore to downstream

of the weaving segment. The unit of average delay time was measured in seconds per vehicle

(s/veh). The time saving (s/veh) was used, as another performance indicator, to indicate the

travel time savings achieved by the advisory control strategy.

4.3 Evaluation of the proposed PSO algorithm

This section gives an example that demonstrates the performance of the proposed PSO.

The proposed PSO has been modified to handle the constraints of the problem; however,

the input parameters are the same as those of the basic PSO. The proposed PSO follows the

methods defined in section 3.3.

In all experiments, the inertia weight, ω, was set to 0.7, while the values of φp and φg were

set to 1.4. When comparing the inertia weights and constriction factors in PSO, Eberhart and

Shi (2000) found that these values gave acceptable results. The velocity clamping (vc) used was

0.2 (higher values were tested; however, this value provided the best results).

The objective function was defined in section 3.3.5. Function evaluations were performed

by passing the potential solution, x, into Aimsun and obtaining a fitness value, f(x). The test

example minimises equation 3.3, subject to the constraints in equation 3.5.

Table 4.2 lists the swarm sizes tested to evaluate the performance proposed PSO.

Table 4.2: Proposed PSO test runs

Run Number of particles

Run A 10Run B 20

Figure 4.2 shows the best fitness values (averaged over five simulations). The results show

how the proposed PSO algorithm converges near a local minima. Run A converges after

approximately 40 iterations, whereas Run B converges after 30 iterations.

4.3. EVALUATION OF THE PROPOSED PSO ALGORITHM 43

Figure 4.2: Proposed PSO results

Table 4.3 shows the best fitness values at the final iteration (over five simulations). The table

also shows the maximum and minimum fitness values at the final iteration, over five simulations.

In this example, the results show that the swarm size has a marginal difference to the final fitness

value. Hence, to save on computational time, a swarm size of ten was used for all simulation

runs.

Table 4.3: Fitness values

Proposed PSO Run A Run B

Average 67.31 66.14Maximum 71.15 73.26Minimum 63.18 59.79Standard Deviation 2.78 5.33

The test example was also used to evaluate the effect of the penalty factor. Initially, the

penalty factor was set to zero, meaning that missed turns were not punished in the objective

function. The results were as expected, showing that the best LC advisory distribution did not

advise vehicles in time to allow them to execute their desired lane change; an average of 25


vehicles missed their exit. When the penalty factor was applied to the objective function, there

were no missed turns for the best LC advisory distribution. The penalty factor is therefore

imperative to the objective function, to avoid vehicles missing their exits. In this study, the

sensitivity for the penalty factor was not investigated.

The results demonstrate that the proposed PSO algorithm can be reasonably used to optimise

the LC advisory distribution.

4.4 Simulation results and discussion

In this section, the performance of the advisory control strategy was evaluated based on the

simulation results. The proposed PSO algorithm found the best LC-advisory distributions. The

PSO code was executed using Spyder (The Scientific PYthon Development EnviRonment) on

an Intel R© CoreTM i7 2.50 GHz processor with 8.0 GB RAM, running on Windows 10, 64-

bit Operating System. The computing times for each PSO experiment was approximately six

hours. There was no focussed attempt to improve the efficiency of the algorithm for this study.

The best LC advisory distribution, obtained from the proposed PSO algorithm, will be

compared with the base case, with no control strategy. To test the strategy, the results are

evaluated between the following two cases:

• Base case: no control

• Optimised case: C-ITS advisory control strategy (optimised LC advisory distribution)

The base case assumes no control strategy. The LC behaviour is governed by Aimsun’s

LC model using the calibrated LC parameters. The base case was used as a benchmark for

comparison.

The advisory control strategy divides the 400-m weaving segment into eight equal 50-m

sections. The RF and FR vehicles are assigned a section, from which they can begin a lane

change. In the optimised case, the best LC advisory distribution, found by the proposed PSO

algorithm, is applied to the C-ITS advisory control strategy.

4.4. SIMULATION RESULTS AND DISCUSSION 45

4.4.1 Performance evaluation

The test bed, described in Section 4.1, was used as an example to evaluate the performance of

the proposed PSO algorithm in optimising the LC advisory distribution. Section 4.1 summarised

the traffic demand used for the test case.

Table 4.4 shows a comparison between the average delay time per vehicle (s/veh) in the

base case and the optimised case. The optimised case shows a substantial delay improvement

of 30% and 34% for the FF and FR movements, respectively. The delay improvement was 8%

and 1% for the RF and RR movement, respectively. On average, for all movements per vehicle,

delay significantly improved by 28%.

Table 4.4: Average delay comparison between base case and optimised case

Movement FF FR RF RR Average

Traffic volume (veh) 5300 900 900 100Expected travel time (s/veh) 52.9 47.1 43.0 37.1Delay in base case (s/veh) 12.8 16.5 9.8 5.2 8.8Delay in optimised case (s/veh) 8.9 10.8 9.0 5.1 6.3Improvement from base case (%) 30 34 8 1 28Significance∗ 0.000 0.000 0.000 0.787

*The delay difference is significant at the 0.05 level

The t-test was performed to examine whether the delays for the base case and the optimised

case were statistically different. The t-test showed that the optimised LC advisory significantly

reduced delay for the FF, FR and RF movements in the weaving segment. The difference in

delay for the RR movement was not significant.

The average speed over distance was used to show the location of speed drop caused by the

LC concentration problem. Figures 4.3(a) and 4.3(b) shows the speed over the auxiliary lane and

lane 3 distances, respectively. As clearly demonstrated in both graphs, the speed profile from

the optimised case shows a considerable reduction in speed drop near the merge gore, which

implies that lane changing was effectively distributed along the weaving segment. The base

case speed profile shows that speed increases after the speed drop, as vehicles move through

the bottleneck location. It is more desirable, with respect to the operational performance, to

have a smoother speed curve. Regarding traffic safety, crashes are more likely to occur during

high deceleration (high-speed drop) and less likely to occur during constant speed (Lee et al.,

2006). A higher speed difference increases the crash risk, as drivers may have a rear-end crash


if distracted or unable to react in time (Wang et al., 2015). Hence, a smoother traffic speed

dynamic, which was achieved by the optimised case, is more desirable.

(a) Speed on auxiliary lane

(b) Speed on lane 3

Figure 4.3: Speed profile on critical weaving lanes

It can be observed from the simulation analyses that the advisory control strategy, which

uses the best LC advisory distribution found by the proposed PSO algorithm, improves the

minimum speed at the bottleneck location. This indicates that the proposed algorithm and

objective function can be used to optimise the LC advisory distribution and, hence, to improve

the operational performance of the weaving segment.


4.4.2 Impact of different OD demands

This section investigates the impact of different OD demands on the LC distributions. The

criteria for OD demand selection, for each scenario, were that the:

• maximum weaving flow of either RF or FR does not exceed 1260 veh/h

• maximum number of passenger cars in the weaving segment is 2200 veh/h/lane.

The tests were conducted using five different OD demands, as shown in table 4.5. The five

OD demands have different RF-ratios, where the FF , RR and total weaving volumes remained

the same as in section 4.4. The level of service (LOS) in each scenario was E, according to

HCM 2010, chapter 12 (TRB, 2010), which indicates that the weaving segment is approaching

congestion – where the demand flow rate exceeds the capacity of the segment. HCM 2010

(TRB, 2010) does not distinguish LOS for different RF-ratios.

Table 4.5: Different demand setting (veh/h)

Test vRF vFR vFF Total weaving vRR RF ratio

A 540 1260 5300 1800 100 0.3B 720 1080 0.4C 900 900 0.5D 1080 720 0.6E 1260 540 0.7

The proposed algorithm was used to optimise the LC advisory distribution for the different

OD demands. PSO, considered a heuristic algorithm, does not guarantee a unique solution for

the optimal LC advisory distribution. However, the optimised LC advisory distribution aims

to change the behaviour of the weaving vehicles to alleviate the LC concentration problem by

better utilising existing infrastructure and thereby improving the operational performance of the

weaving segment.

Figures 4.4 and 4.5 show the performance improvement in lane 3 and the auxiliary lane,

respectively. These figures consist of sub-figures, in which the RF-ratio increases from bottom

to top, and the base case and optimised case are shown on the left and right, respectively. For

each sub-figure, the horizontal and vertical axes represent the distance (m), from the merge gore,

and time (min), respectively. The shading illustrates the average speed measured over time and


distance; the darker shade represents slower speeds and the lighter shade, faster speeds. The

following observations have been made from figures 4.4 and 4.5:

1. Overall, the optimised case, in each scenario, has a lighter shade in the contour plots,

which represents faster speeds along the weaving segment in lane 3 and auxiliary lane,

relative to the respective base case.

2. The bottleneck location in the base case, represented by the dark band concentrated near

the merge gore, is alleviated in the optimised case. In all optimised cases, the speed is

more smoothly distributed across the weaving segment.

3. The gradient of the contours are less steep in the optimised cases than that in the base

cases, where the contours are concentrated near the merge gore.

4. In the base case, the speed decrease near the merge gore, caused by the lane changing

concentration problem, progressively becomes more severe as the RF-ratio increases.

5. The optimised cases perform better in smoothing the speed over the weaving segment.

The contour plots demonstrate that the optimised LC advisory considerably improves

how smoothly drivers travel through the weaving segment.


0.7

0.6

0.5

0.4

0.3

RF-

ratio

Base case Optimised case

Figure 4.4: Contour speeds of lane 3


0.7

0.6

0.5

0.4

0.3

RF-

ratio

Base case Optimised case

Figure 4.5: Contour speeds of auxiliary lane


Figure 4.6 shows a bar chart that compares the average delay, for all vehicles, between

the base case and the optimised case. The line graph, on the same figure, shows the delay

improvement for each scenario. The base case (cross-hatched) indicates that the minimum

average delay was 8.8 s/veh, with an RF-ratio of 0.4. The maximum average delay was 13.7

s/veh, with an RF ratio of 0.7, where the RF movement is greatest at 1260 veh/h. As the

RF-ratio increases from 0.5 to 0.7, the average vehicular delay significantly increases. This

indicates that as the RF demand flow rate increases, in proportion to the total weaving flow, the

LC concentration problem is exacerbated. Since the LC activity tends to be concentrated close

to the merge gore, the heavier RF movement will change lanes into a congested lane 3, adding

to further congestion; whereas, the heavier FR movement, the RF-ratio of 0.3, will change lanes

into the auxiliary lane, where the lane volume is comparatively less. This behaviour, explained

by Lee et al. (2006), shows that FR vehicles are more likely to diverge close to the merge gore

area if the RF ratio is low. Hence, the delay caused by the LC concentration problem is not as

substantial as in the higher RF-ratios.

The average delay results for the optimised case are more stable than those for the base

case, across all RF-ratios. The delay improvement, in the optimised case from the base case,

increases with the RF ratio. The maximum delay improvement was 55.3% when the RF-ratio

was 0.7. The results will be further explained for the application domain analysis in Section

4.4.4.

Figure 4.6: Average delay results


4.4.3 Sensitivity analysis

This section investigates the impact of various traffic patterns on the weaving segment operation.

Further sensitivity analyses were conducted to identify the improvement in the capacity of the

advisory control strategy. The tests considered 27 scenarios: three levels across three variables.

Firstly, three levels for the RF-ratio, namely 0.3, 0.5, and 0.7; three levels for the FF volume

(vFF ), namely, 5300, 4100, and 3250 veh/h; and, thirdly, three levels for the weaving volume

(vW ), namely, 1800, 1200, and 600 veh/h. Table 4.6 defines the levels and variables selected for

the sensitivity tests. Here, the tests will be identified according to the level of each variable. For

example, Test ID 321 has the following traffic pattern properties: RF-ratio = 0.7, vFF = 4110

veh/h, and vW = 1800 veh/h.

Table 4.6: Traffic demand

Level RF −ratio∗ vFF† (veh/h) vW

‡ (veh/h)

1 0.3 5300 18002 0.5 4110 12003 0.7 3250 600

* First, † second and ‡ third variable

Figures 4.7 and 4.8 show the speed over distance on the critical weaving lanes, the auxiliary

lane and lane 3, respectively. The graphs are clustered by weaving volumes (vW ), level 3 (low),

2 (medium) and 1 (high), from top to bottom. The graphs show a comparison between the base

case (left) and optimised case (right). The following observations can be made from figures 4.7

and 4.8:

1. Overall, the optimised LC advisory distribution (optimised case) improves the speed

profile along the critical weaving lanes. The improvement is more pronounced when

the weaving volume is high. Noticeably, the intense speed drop in the base case (high

vW ) is dissipated substantially in the optimised case.

2. Speed drop tends to occur because of a high density of LC at the start of the weaving

length; consequently, it is intensified by greater weaving volumes. Although improve-

ments can be observed for all tests, the advisory control strategy obtain better results

when the weaving volume is high.

The speed profiles are not intended to measure the operational effectiveness. The optimised


cases show that the LC concentration problem has been alleviated successfully; achieving

smoother speed distributions. A throughput analysis did not reveal any improvement.


(a) Base case – speed auxiliary lane low vW (b) Optimised case – speed auxiliary lane low vW

(c) Base case – speed auxiliary lane medium vW (d) Optimised case – speed auxiliary lane medium vW

(e) Base case – speed auxiliary lane high vW (f) Optimised case – speed auxiliary lane high vW

Figure 4.7: Auxiliary lane speed


(a) Base case – speed lane 3 low vW (b) Optimised case – speed lane 3 low vW

(c) Base case – speed lane 3 medium vW (d) Optimised case – speed lane 3 medium vW

(e) Base case – speed lane 3 high vW (f) Optimised case – speed lane 3 high vW

Figure 4.8: Lane 3 speed


Figures 4.9 and 4.10 shows the cumulative LC distributions, for all tests, for the base case

and optimised case, respectively. Figures 4.9(a) and 4.9(b) shows the cumulative LC distribution

for FR and RF vehicles in the base case, respectively. Similarly, Figures 4.10(a) and 4.10(b)

shows the cumulative LC distribution for FR and RF vehicles in the optimised case, respectively.

(a) FR Lane-changing distribution (b) RF Lane-changing distribution

Figure 4.9: Lane-changing distributions (Base case)

(a) FR Lane-changing distribution (b) RF Lane-changing distribution

Figure 4.10: Lane-changing distributions (Optimised case)

The following observations can be made about the cumulative LC distribution of weaving

vehicles over the weaving segment length:

• For all test scenarios, in the base case, a majority (over 80%) of lane changes occur

in the first 100m section of the available 400m weaving length. This causes the LC

concentration problem (described in section 2).


• In the optimised case, the cumulative LC distribution for FR vehicles shows a distinctive

curve, which is more distributed along the weaving length.

4.4.4 Application domain analysis

This section identifies the application domain of the optimised LC-advisory distribution. All

the model parameters are kept the same as in section 4.4.3. The LC-advisory distribution was

optimised for each scenario. The executed lane changes of weaving vehicles will be analysed

for the optimised LC advisory to observe what effect the strategy has on drivers. Before this

analysis, the number of lane changes, per section, is examined for the base case (see in table

4.7).

Table 4.7: Lane-changing distribution (Base case)

RF-

ratio

0.7RF 882 302 50 13 0 0 0 0FR 378 124 27 5 0 0 0 0Total 1260 427 77 18 0 0 0 0

0.6RF 594 400 54 11 0 0 11 0FR 432 223 43 7 0 0 0 0Total 1026 623 97 18 0 0 11 0

0.5RF 378 432 72 9 0 9 0 0FR 495 324 63 9 9 0 0 0Total 873 756 135 18 9 9 0 0

0.4RF 230 403 72 7 0 0 0 0FR 626 356 76 11 0 0 0 0Total 857 760 148 18 0 0 0 0

0.3RF 162 308 59 5 0 0 0 0FR 806 340 76 13 13 0 0 0Total 968 648 135 18 13 0 0 0

1 2 3 4 5 6 7 8Section

From the LC distributions in the base cases, the following observations have been made:

1. The majority of lane changes occur in the first two sections (0-100 m) of the weaving

segment.

2. The dominant weaving demand flow movement dominates the number of lane changes in

the first segment (0-50 m).

3. The last five sections (150-400 m) of the weaving segment are severely underutilised in

all scenarios.

In contrast to the base case, the optimised LC advisory aims to change the LC behaviour of

weaving vehicles to achieve better utilisation and to improve the performance of the weaving


segment. The simulation records the executed number of lane changes for the optimised LC

advisory (see table 4.8). The number of lane changes per section is recorded for RF and FR

vehicles.

Table 4.8: Lane-changing distribution (optimised case)R

F-ra

tio

0.7RF 88 139 340 239 63 113 202 76FR 235 207 72 18 5 2 1 1Total 323 345 412 257 68 116 203 76

0.6RF 108 184 43 119 140 184 227 76FR 301 226 53 34 29 30 31 16Total 409 410 97 153 170 213 257 91

0.5RF 13 68 88 135 230 233 107 26FR 271 216 146 108 81 54 20 4Total 284 285 235 242 311 287 127 30

0.4RF 126 246 119 57 63 69 29 12FR 393 204 108 56 105 84 60 72Total 519 449 227 113 167 153 89 83

0.3RF 59 146 92 65 49 54 54 22FR 542 202 76 113 88 101 88 50Total 601 347 167 178 137 155 142 72

1 2 3 4 5 6 7 8Section

From the LC distributions in the optimised cases, the following observations were made:

1. The number of lane changes for weaving vehicles are distributed across all sections of

the weaving segment. This indicates that the entire length is being better utilised for LC

activity, compared to the base case where it is concentrated in the first two sections.

2. The maximum number of lane changes in a section is considerably lower than that in

the base case. This indicates that the LC concentration problem has been alleviated;

consequently, LC has been distributed across all sections to avoid high LC density in any

given section.

3. Under congested conditions, the volume per lane on the weaving segment is at or close

to capacity. Hence, distributing vehicles across lanes at the weaving segment will create

gaps for LC. Within the first two sections, in most scenarios, the number of lane changes

by FR movements is greater than the RF movement. This indicates that FR vehicles in the

congested freeway lane tend to, as soon as possible, change lanes to the less congested

auxiliary lane; consequently, reducing the volume in lane 3, which creates greater gap

acceptance to facilitate LC for RF vehicles. Priority tends to be given to the FR movement

in the first section as there are more gaps in the auxiliary lane to change lanes, thereby,


decreasing the volume in lane 3, which creates gaps for the RF movement to change lanes

further downstream.

4. In most scenarios, a proportionally high number of lane changes are loaded within the

first two sections (0-100 m), then gradually distributed across the remaining sections; the

lowest number of lane changes occurred within the final section to avoid missed exits due

to overcrowding.

Figure 4.11 shows a comparison of the density across all lanes between the base case, figure

4.11(a), and the optimised case, 4.11(b). Test ID 311, high ramp flow scenario, was used for

this illustration.

The density plot for the base case reveals the impact of the high LC density near the merge,

causing a bottleneck. The bottleneck propagates congestion further upstream on the freeway

mainline. Conversely, the optimised case shows that LC was effectively distributed along

the entire weaving segment length; a uniform density across all lanes can be observed, both

on the upstream and the downstream sections. This demonstrates that the C-ITS advisory

can efficiently smooth out transient disturbances caused by the LC concentration problem;

producing smooth traffic flow dynamics.


(a) Density across all lanes (Base case)

(b) Density across all lanes (Optimised case)

Figure 4.11: Density across all lanes (Test 311)


4.4.5 Discussion

In practice, freeway traffic control measures are implemented to reduce traffic congestion on

the freeway. Ramp metering (RM), a typical traffic control measure in freeway networks, is

designed to relieve or even prevent mainline congestion by regulating the upstream input flow

via traffic lights at freeway on-ramps (Zhao et al., 2016). A review of road traffic control

strategies, by Papageorgiou et al. (2003), explained that RM control strategies make use of

traffic measurements in the vicinity of a ramp to calculate suitable RM values. A common

RM control strategy (ALINEA) controls the ramp flow based on the desired occupancy mea-

surement downstream of the ramp. The strategy aims to prevent congestion on the freeway by

dynamically controlling green or red-phase duration (ramp flow) while stabilising the traffic

flow at a high throughput level.

RM strategies are effective at preventing disruption to mainline traffic flow by regulating

high ramp flows; however, ramp vehicles often suffer considerable delays when on-ramp queues

become excessive. RM can often cause delays for ramp vehicles to maintain flow capacity on

the downstream freeway section. For example, say an on-ramp demand flow is 700 veh/h, at a

metering rate of 600 veh/h/lane, the average delay will be 4.3 minutes per vehicle.

Another problem with RM strategies is once on-ramp queues become excessive, interference

with the arterial road network may occur (Papageorgiou and Kotsialos, 2000). Papageorgiou

et al. (2003) explains that when this occurs, an override of the regulator’s decisions can occur,

allowing more vehicles to enter the freeway and the ramp queue to diminish; often this will

result in congestion on the freeway.

The C-ITS advisory redistributes the LC along the weaving segment, hence, reducing the

LC density concentrated near the merge gore. The advisory can improve traffic flow dynamics

on the mainline without penalising on-ramp vehicle flow. Future research may investigate how

the advisory can be implemented with a RM strategy to increase throughput and reduce ramp

vehicle delay. The C-ITS advisory reduces the density occurring downstream of the ramp,

which may delay the activation of the RM strategy. The C-ITS advisory also facilitates a higher

flow of ramp vehicles; therefore, this may reduce ramp vehicle delays and queue lengths during

RM operation. Future research could explore the potential of combining the C-ITS advisory

and the RM strategies in improving freeway ramp management.


C-ITS applications generate significant volumes of data, which raises questions of whether

such data could be linked to individuals and how C-ITS applications fit within current privacy

regimes in Australia dealing with the collection, use and disposal of personal information

(National Transport Commission, 2012). Driver distraction is another issue for C-ITS and the

use of in-vehicle display units. C-ITS will provide more information to drivers to empower

them to make better driving decisions, however, the challenge is to achieve this without over-

loading the drivers cognitive load (National Transport Commission, 2012). Road authorities and

governments must consider the impact of these issues and their implication on the regulatory

framework.

4.5 Summary

In this chapter, the proposed PSO was evaluated in optimising the LC advisory distribution. The

proposed PSO used a co-evolutionary approach to improve both the RF and the FR advisory

distributions. The LC advisory, which used the resulting distributions, managed the mandatory

lane changes of the weaving vehicles, while the non-weaving vehicles travelled as normal. The

weaving segment performance was then evaluated using the optimised LC advisory distribution.

The traffic simulation analysis revealed that the optimised LC distribution does not substan-

tially affect the operational effectiveness between the test scenarios; however, it does affect the

traffic flow dynamics in the critical weaving area. The research findings are summarised in

chapter 5.

Chapter 5

Conclusions

5.1 Research findings

In this study, a PSO algorithm was proposed for a C-ITS advisory on a freeway weaving

segment. Empirical research has observed that a LC concentration problem occurs in weaving

segments close to capacity. The distribution of lane changes was found to be concentrated

near the entrance, at times as soon as vehicles enter the segment. This behaviour leads to

congestion and reduces the weaving segment capacity. An advisory control strategy was shown

to alleviate the problem by distributing lane changes along the entire segment according to fixed

distributions. Unlike previous methods, this work proposed an optimisation algorithm, based

on PSO, to improve the LC advisory distribution for weaving vehicles. The speed over a short

section of the weaving segment, within the critical weaving area, was used as the objective

function. Traffic simulation was used to evaluate the performance of the weaving segment

using a C-ITS advisory and to compare it with the base case, with no control strategy. These

conclusions were made from the results:

1. The proposed PSO algorithm can be successfully used to improve the performance of

the weaving segment by optimising the LC advisory distribution, given the constraints of

the problem. The PSO algorithm was modified to satisfy the boundary and summation

constraints implicit in the solution representation.

2. The evaluation of the simulation tests revealed that the optimised LC advisory signif-

icantly improved the traffic performance of the weaving segment. The performance

indicators, speed and delay, were improved as a result of the optimised LC advisory,

63

64 CHAPTER 5. CONCLUSIONS

with speed producing a smoother profile than that of the base case.

3. The sensitivity analyses revealed that the optimised LC advisory has greater improvement

with higher RF-ratios. The delay improvement was most significant when the RF-ratio

was 0.7, with the improvement at 55.3%.

4. The optimised LC advisory was shown to effectively distribute the LC of weaving vehi-

cles across the entire length of the weaving segment. Priority tends to be given to the FR

movement in the first section as there are more gaps in the auxiliary lane to change lanes.

This decreases the volume in lane 3, which creates gaps for the RF movement to change

lanes further downstream.

Although field tests would provide more accurate outcomes, the evaluation of traffic simu-

lation shows improved performance for a weaving segment when optimising the LC advisory

distribution. This study concludes that the proposed PSO algorithm can be used to optimise the

LC advisory on a freeway weaving segment, resulting in better LC distributions.

5.2 Recommendations for future work

It is recommended that future research work investigate the following:

• Improving the effectiveness of the proposed PSO algorithm; testing its parameters and

design to improve the quality of the search.

• Investigating the effectiveness of different performance measures (objective functions)

for the weaving segment (for example, maximising traffic safety or throughput capacity).

• Testing, more comprehensively, the assumptions made in the case study, such as pene-

tration and compliance rates, to evaluate the practical implications of the C-ITS advisory

control strategy. For instance, the DSRC connection, assumed to be entirely reliable,

is influenced by many factors, such as measurement discrepancies and communication

delays.

• Investigating the C-ITS advisory with different traffic control strategies, such as ramp

metering, to improve weaving segment traffic performance.

5.2. RECOMMENDATIONS FOR FUTURE WORK 65

• Investigating the impacts of different penetration rates and V2V connectivity will provide

a more thorough analysis of the strategy.

66 CHAPTER 5. CONCLUSIONS

Appendix A

Sensitivity tests – traffic demand

Table A.1: Sensitivity tests – traffic demand

Test ID RF-ratio vFF vRR vFR vRF vW v111 1260 540 1800 7200112 5300 100 840 360 1200 6600113 420 180 600 6000121 1260 540 1800 6010122 0.3 4110 100 840 360 1200 5410123 420 180 600 4810131 1260 540 1800 5150132 3250 100 840 360 1200 4550133 420 180 600 3950211 900 900 1800 7200212 5300 100 600 600 1200 6600213 300 300 600 6000221 900 900 1800 6010222 0.5 4110 100 600 600 1200 5410223 300 300 600 4810231 900 900 1800 5150232 3250 100 600 600 1200 4550233 300 300 600 3950311 540 1260 1800 7200312 5300 100 360 840 1200 6600313 180 420 600 6000321 540 1260 1800 6010322 0.7 4110 100 360 840 1200 5410323 180 420 600 4810331 540 1260 1800 5150332 3250 100 360 840 1200 4550333 180 420 600 3950

67

68 APPENDIX A. SENSITIVITY TESTS – TRAFFIC DEMAND

Appendix B

Lane-changing distribution

Table B.1: Lane-changing advisory distributions

Test ID RF lane-changing advisory distribution FR lane-changing advisory distribution

111 40% 12% 12% 17% 0% 20% 0% 0% 67% 0% 0% 33% 0% 0% 0% 0%112 14% 0% 35% 44% 0% 7% 0% 0% 79% 19% 2% 0% 0% 0% 0% 0%113 1% 0% 26% 0% 73% 0% 0% 0% 100% 0% 0% 0% 0% 0% 0% 0%121 39% 0% 21% 14% 26% 0% 0% 0% 78% 19% 3% 0% 0% 0% 0% 0%122 18% 8% 35% 0% 30% 9% 0% 0% 69% 20% 8% 3% 0% 0% 0% 0%123 10% 0% 55% 0% 0% 35% 0% 0% 100% 0% 0% 0% 0% 0% 0% 0%131 40% 21% 17% 12% 10% 0% 0% 0% 50% 28% 22% 0% 0% 0% 0% 0%132 8% 33% 0% 30% 0% 28% 0% 0% 97% 0% 3% 0% 0% 0% 0% 0%133 0% 0% 60% 25% 14% 0% 0% 1% 99% 0% 0% 1% 0% 0% 0% 0%211 4% 17% 3% 24% 35% 18% 0% 0% 58% 31% 10% 0% 0% 0% 0% 0%212 49% 0% 0% 26% 25% 0% 0% 0% 82% 0% 17% 0% 0% 0% 0% 0%213 0% 28% 31% 30% 5% 5% 1% 0% 84% 16% 0% 0% 0% 0% 0% 0%221 40% 18% 25% 5% 11% 0% 0% 0% 67% 33% 1% 0% 0% 0% 0% 0%222 28% 18% 40% 13% 0% 0% 0% 0% 97% 0% 3% 0% 0% 0% 0% 0%223 0% 17% 43% 0% 7% 32% 0% 0% 100% 0% 0% 0% 0% 0% 0% 0%231 23% 17% 16% 20% 12% 13% 0% 0% 69% 6% 20% 4% 0% 0% 0% 0%232 4% 39% 0% 0% 56% 0% 0% 0% 89% 3% 9% 0% 0% 0% 0% 0%233 4% 38% 15% 0% 43% 0% 0% 0% 100% 0% 0% 0% 0% 0% 0% 0%311 21% 0% 47% 0% 0% 31% 0% 0% 100% 0% 0% 0% 0% 0% 0% 0%312 0% 44% 0% 43% 0% 13% 0% 0% 99% 1% 0% 0% 0% 0% 0% 0%313 14% 10% 30% 21% 14% 10% 0% 0% 100% 0% 0% 0% 0% 0% 0% 0%321 17% 32% 0% 37% 14% 0% 0% 0% 96% 0% 4% 0% 0% 0% 0% 0%322 3% 26% 22% 11% 24% 14% 0% 0% 100% 0% 0% 0% 0% 0% 0% 0%323 31% 0% 5% 6% 29% 29% 0% 0% 76% 24% 0% 0% 0% 0% 0% 0%331 21% 0% 38% 41% 0% 0% 0% 0% 100% 0% 0% 0% 0% 0% 0% 0%332 7% 18% 34% 9% 17% 14% 0% 0% 94% 0% 5% 0% 0% 0% 0% 0%333 20% 0% 45% 0% 3% 0% 32% 0% 82% 6% 13% 0% 0% 0% 0% 0%

Section 1 2 3 4 5 6 7 8 1 2 3 4 5 6 7 8

69

70 APPENDIX B. LANE-CHANGING DISTRIBUTION

Table B.2: Number of lane changes – Base case

Test ID RF number of lane changes FR number of lane changes

111 175 329 62 4 2 2 2 2 845 355 93 17 7 3 2 0112 109 219 61 5 2 0 1 1 615 179 59 20 9 4 2 0113 57 84 37 3 1 0 1 0 351 55 26 12 5 2 0 0121 170 330 74 4 4 2 3 2 827 352 105 27 10 6 3 0122 107 195 67 6 1 1 2 1 609 161 60 22 8 3 2 0123 61 89 42 3 0 0 0 1 341 62 24 11 5 2 1 0131 159 313 87 9 2 2 1 2 843 335 107 32 10 4 2 2132 113 194 70 4 1 1 1 1 623 166 56 19 10 2 1 1133 65 81 41 3 0 0 0 0 336 56 25 10 4 1 0 0211 394 492 83 8 5 5 4 6 520 350 69 11 6 2 2 1212 174 362 94 9 2 3 3 3 394 179 44 15 5 2 1 0213 90 153 69 6 1 1 0 1 225 55 19 8 4 1 0 0221 304 515 119 10 5 3 3 4 497 343 80 19 7 2 1 1222 180 318 122 8 1 2 2 3 395 168 46 15 5 3 1 0223 101 141 76 8 1 1 1 1 227 49 17 7 4 2 0 0231 275 517 152 15 4 4 2 4 471 349 96 18 7 2 1 1232 180 305 128 12 3 1 2 2 403 173 56 14 6 2 1 0233 111 134 69 7 1 1 0 1 227 54 17 7 2 1 0 0311 942 315 48 12 5 4 7 6 403 130 29 8 3 1 1 0312 247 476 148 14 5 3 4 4 194 130 36 8 3 1 0 0313 112 217 108 11 2 2 1 2 129 36 16 3 3 1 0 0321 367 682 239 49 10 6 5 7 219 243 88 17 6 1 0 0322 232 454 172 19 4 4 3 3 204 131 40 11 2 1 0 0323 126 189 101 11 3 1 1 2 134 37 11 6 2 1 0 0331 327 691 289 41 8 6 4 7 173 256 105 15 4 1 1 0332 243 414 205 19 4 3 3 6 199 128 47 6 3 1 1 0333 153 182 105 10 1 2 1 2 125 37 11 5 2 1 0 0

Section 1 2 3 4 5 6 7 8 1 2 3 4 5 6 7 8

71

Table B.3: Number of lane changes – Optimised case

Test ID RF number of lane changes FR number of lane changes

111 62 148 98 70 57 59 56 28 558 215 79 118 95 104 84 58112 15 30 64 124 102 42 15 6 488 172 81 58 47 27 10 3113 2 1 22 19 52 50 32 3 354 44 28 17 5 2 1 0121 62 117 101 91 122 68 19 6 656 292 138 95 80 43 15 7122 20 42 84 55 72 66 29 8 422 143 81 73 67 43 26 9123 6 8 57 38 16 32 23 15 345 54 26 12 5 1 1 0131 64 157 145 96 67 36 8 3 428 251 187 152 143 105 47 19132 11 73 52 83 36 74 32 22 626 132 66 27 15 9 3 2133 0 0 61 61 46 16 5 0 340 48 25 12 4 2 2 0211 12 84 92 139 260 257 113 31 281 225 152 116 96 58 20 5212 82 166 52 74 131 107 30 6 334 130 71 30 32 24 12 6213 2 33 73 96 68 30 10 7 192 50 24 21 14 7 3 1221 100 268 265 153 101 47 19 7 339 274 122 91 73 36 13 2222 49 133 214 147 70 15 3 4 409 131 51 22 12 7 2 0223 1 22 74 61 39 59 46 26 238 37 15 8 5 2 0 0231 62 181 188 174 147 131 64 22 359 188 128 80 69 63 39 15232 10 116 90 48 179 122 56 9 399 115 64 28 21 18 7 4233 5 65 61 37 81 49 23 3 241 39 18 7 2 1 0 0311 94 147 347 254 78 129 214 82 261 206 76 22 9 1 0 1312 3 130 179 212 185 103 59 27 222 82 47 13 6 3 1 0313 19 46 84 91 93 71 36 13 135 27 17 5 2 1 0 0321 59 307 243 287 272 149 34 10 224 214 87 19 20 7 3 1322 10 101 190 151 156 148 96 31 242 82 45 15 5 1 0 0323 43 58 42 23 61 96 79 28 108 38 14 13 11 5 2 0331 82 145 339 455 257 77 10 8 245 200 78 25 5 3 1 0332 19 92 229 170 154 124 75 32 228 79 42 16 8 6 3 2333 47 34 114 68 49 9 66 53 109 27 13 11 9 8 4 1

Section 1 2 3 4 5 6 7 8 1 2 3 4 5 6 7 8

72 APPENDIX B. LANE-CHANGING DISTRIBUTION

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