optimal signal control with multiple objectives in tra c mobility …549872/... · 2012. 9. 5. ·...

Optimal signal control with multipleobjectives in traffic mobility and

environmental impacts

DANNY ROBLES

Master of Science ThesisRoyal Institute of Technology

Stockholm, Sweden 2012

Abstract

The increasing number of motor vehicles in urban areas worldwide requiresa smart traffic management establishing sustainability on the traffic system.Traffic signal control is a powerful tool in this field since it can control flowpatterns in urban areas. Historically, traffic signal optimization was appliedto satisfy the goals in mobility of traffic systems e.g. measured by traveldelay, stops etc., and very little is known if such a strategy would be optimalfor system sustainability in terms of emission and fuel usage. The thesisfocus on finding the trade-offs between mobility and impact measures andcompares these with approximated real signal strategies.

The research objective of the thesis is to create a multi-objective computa-tional framework based on the integration of a microscopic traffic simulationmodel with a micro scale fuel and emission model. The proposed frameworkis able to implement mobility and impact objectives in a multi-objective opti-mization process. The microscopic traffic model VISSIM is used to simulatethe traffic and two different emission models, CMEM and VT-Micro, are usedto estimate the vehicular emissions and fuel consumption. The optimizationis based on NSGA ii, a multi-objective genetic algorithm.

The proposed framework is demonstrated by conducting two case studies, asingle intersection in Wuhan and two coordinated intersections in Stockholm.The investigated objectives used in the optimizations are network delay, av-erage number of stops and average fuel consumption. Moreover, the bestsolution of each objective is subjected to a emission evaluation. Due to timeconsuming optimization processes, an upper limit of iterations is set for bothcases. All simulations are based on 60 minutes of traffic simulations withadditional 15 minutes for warm up.

The study shows that the proposed framework is successful in finding signalcontrol strategies producing better values of the investigated objectives com-pared to the real signal approximations. One could also see apparent trade-offbetween mobility and sustainability depending on the selected objectives.

ii

Sammanfattning

Det okande antalet motorfordon i stadsomraden varlden over kraver smarttrafikstyrning grundat pa hallbara trafiksystem. Trafiksignalstyrning ar ettkraftfullt verktyg inom detta omrade eftersom flodesmonster i tatorter kankontrolleras. Historiskt har optimering av trafiksignaler tillampats for attuppfylla malen pa rorlighet i trafiksystemen, uppmatt genom bland annatrestidsfordrojningar och antalet stopp, och valdigt lite ar kant om en sadanstrategi aven ar optimal for emissionsutslapp och bransleforbrukning. Exam-ensarbetet fokuserar darfor pa att hitta avvagningar mellan trafikrorlighetenoch miljopaverkan, och jamfora dessa med verkliga approximerade trafiksig-nalstrategier.

Syftet med examensarbetet ar att skapa ett berakningsramverk dar det armojligt att optimera flera trafikparametrar samtidigt och ar baserat pa in-tegrationen av mikroskopisk trafiksimulering och mikroskopiska bransle- ochemissionsmodeller. Det foreslagna berakningsramverket kan optimera fleratrafikparametrar samtidigt avseende bade trafikrorlighet och miljopaverkan.Trafiken ar simulerad med det mikroskopiska trafiksimuleringsprogrammetVISSIM. Tva olika emissionsmodeller, CMEM och VT-Micro, anvands foratt berakna bransleforbrukningen och trafikemissionerna. Optimeringen arbaserad pa NSGA II, en genetisk optimeringsalgoritm som kan optimera fleraparametrar samtidigt.

Det foreslagna berakningsramverket demonstreras genom att utfora tva fall-studier, en enkel korsning i Wuhan och tva samordnade korsningar i Stock-holm. De undersokta parametrarna i studien omfattar natverksfordrojning,genomsnittliga antalet stopp och genomsnittliga bransleforbrukningen. Debasta strategierna for varje parameter ar dessutom utsatt for en emission-sutvardering. Pa grund av tidskravande optimeringsprocesser har en ovregrans av iterationer faststallts for bada fallstudier. Alla simuleringar ar baser-ade pa 60 minuters trafiksimulering med ytterligare 15 minuters uppvarmning.

Studien visar att det foreslagna berakningsramverket ar framgangsrik pa atthitta trafiksignalstrategier som producerar battre varden pa de undersoktaparametrarna jamfort med de verkliga signals approximationerna. Det visasaven tydliga skillnader mellan de olika trafiksignalstrategierna beroende pavilken parameter som optimeras.

Danny Robles Optimal signal control with multiple objectives

Acknowledgements

I would like to express my gratitude to those who helped me on this thesisand give a special thanks to Xiaoliang Ma, for his excellent guidance andencouragement during the whole project.

I would also like to thank my family for always supporting me during mystudies. Another special thanks goes to Caroline Nordin for your patienceand understanding for when I am pursuing my curiosity and dreams.

Contents

1 Introduction 11.1 Overview and Motivation . . . . . . . . . . . . . . . . . . . . . 11.2 Objectives and Scope . . . . . . . . . . . . . . . . . . . . . . . 21.3 Thesis Outline . . . . . . . . . . . . . . . . . . . . . . . . . . . 3

2 Literature Review 42.1 Traffic Models . . . . . . . . . . . . . . . . . . . . . . . . . . . 4

2.1.1 Microscopic Models . . . . . . . . . . . . . . . . . . . . 72.2 Emission Models . . . . . . . . . . . . . . . . . . . . . . . . . 14

2.2.1 CMEM . . . . . . . . . . . . . . . . . . . . . . . . . . . 152.2.2 VT-Micro . . . . . . . . . . . . . . . . . . . . . . . . . 17

2.3 Sustainable Traffic Management . . . . . . . . . . . . . . . . . 19

3 Methodology 213.1 Stochastic Optimization . . . . . . . . . . . . . . . . . . . . . 21

3.1.1 Formal Problem Statement . . . . . . . . . . . . . . . . 213.2 Genetic Algorithm . . . . . . . . . . . . . . . . . . . . . . . . 233.3 Multi-Objective Optimization . . . . . . . . . . . . . . . . . . 273.4 NSGA ii . . . . . . . . . . . . . . . . . . . . . . . . . . . . 29

3.4.1 Algorithm . . . . . . . . . . . . . . . . . . . . . . . . . 293.4.2 Crowding Distance Comparison . . . . . . . . . . . . . 31

3.5 Traffic Impact Modelling Framework . . . . . . . . . . . . . . 333.5.1 Model Integration . . . . . . . . . . . . . . . . . . . . . 333.5.2 Optimization Formulation . . . . . . . . . . . . . . . . 36

4 Case Studies 374.1 Isolated Intersection – Wuhan . . . . . . . . . . . . . . . . . . 38

4.1.1 Modelling . . . . . . . . . . . . . . . . . . . . . . . . . 394.1.2 Signal Optimization . . . . . . . . . . . . . . . . . . . 404.1.3 Results . . . . . . . . . . . . . . . . . . . . . . . . . . . 42

i

ii CONTENTS

4.1.4 Discussion . . . . . . . . . . . . . . . . . . . . . . . . . 474.2 Connected Intersections – Hornsgatan . . . . . . . . . . . . . . 49

4.2.1 Modelling . . . . . . . . . . . . . . . . . . . . . . . . . 504.2.2 Signal Optimization . . . . . . . . . . . . . . . . . . . 514.2.3 Results . . . . . . . . . . . . . . . . . . . . . . . . . . . 544.2.4 Discussion . . . . . . . . . . . . . . . . . . . . . . . . . 58

5 Conclusions and Recommendations 60

I Appendices 66

A Additional Results 67

B Signal plan Hornsgatan 75


List of Figures

2.1 Input and output information in traffic simulation software. . 52.2 Level of detail for the model approaches; macroscopic (left),

microscopic (right) and mesoscopic (within the circle) . . . . . 62.3 Model approach depending on geographic area and level of

detail. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 72.4 Communication between the traffic simulator and SSG in VIS-

SIM [23]. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 92.5 VISSIM car-following logic [23]. . . . . . . . . . . . . . . . . . 102.6 General structure of CMEM [28]. . . . . . . . . . . . . . . . . 162.7 Batch form of CMEM [28]. . . . . . . . . . . . . . . . . . . . . 17

3.1 Illustration of global and local minimum. . . . . . . . . . . . . 233.2 Illustration of the stochastic uniform selection process. Each

pointer represent a selection of an individual in the population. 243.3 Scattered Crossover. If the random number is higher than 0.5

for a given position, the child will inherit the attribute fromparent 2, otherwise parent 1 is selected. . . . . . . . . . . . . . 25

3.4 Scattered Crossover. If the random number is higher than 0.5for a given position, the child will inherit the attribute fromparent 2, otherwise parent 1 is selected. . . . . . . . . . . . . . 26

3.5 Illustration of the decision space and the corresponding objec-tive space [12]. . . . . . . . . . . . . . . . . . . . . . . . . . . 29

3.6 Schematic of the NSGA ii process. . . . . . . . . . . . . . . . 313.7 Crowding distance calculation [10]. . . . . . . . . . . . . . . . 323.8 The programming integration . . . . . . . . . . . . . . . . . . 343.9 Framework of the multi-objective signal timing optimization

process. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 35

4.1 Geometric layout of the isolated intersection in Wahun. . . . . 394.2 Convergence of the objectives during evaluation generations

in the Wuhan case. . . . . . . . . . . . . . . . . . . . . . . . . 42

iii

iv LIST OF FIGURES

4.3 Obtained first five fronts of optimizing network delay and num-ber of stops (Wuhan). . . . . . . . . . . . . . . . . . . . . . . 43

4.4 Obtained first five fronts of optimizing number of stops andfuel consumption (Wuhan). . . . . . . . . . . . . . . . . . . . 44

4.5 Obtained first five fronts of optimizing network delay and fuelconsumption (Wuhan). . . . . . . . . . . . . . . . . . . . . . . 46

4.6 Geometric layout of the cross Hornsgatan - Ringvagen (left)and Hornsgatan - Rosenlundsgatan (right). . . . . . . . . . . . 49

4.7 Signal control description of case Hornsgatan. . . . . . . . . . 524.8 Convergence of the objectives during evaluation generations

in the Hornsgatan case. . . . . . . . . . . . . . . . . . . . . . . 544.9 Obtained first front of optimizing network delay and number

of stops (Hornsgatan). . . . . . . . . . . . . . . . . . . . . . . 554.10 Obtained first front of optimizing number of stops and fuel

consumption (Hornsgatan). . . . . . . . . . . . . . . . . . . . 564.11 Obtained first front of optimizing network delay and fuel con-

sumption (Hornsgatan). . . . . . . . . . . . . . . . . . . . . . 58

B.1 The city signal plan for Hornsgatan-Ringvagen. . . . . . . . . 75B.2 The city signal plan for Hornsgatan-Rosenlundsgatan. . . . . . 76


List of Tables

2.1 Comparison of micro-simulation software [9]. . . . . . . . . . 13

4.1 Approximated signal timing from manual recordings at theisolated intersection in Wuhan (times are in seconds). . . . . . 40

4.2 Comparison of environmental impacts of approximated realcase and extremes from delay and stops optimization (Wuhan). 43

4.3 Comparison of environmental impacts of approximated realcase and extremes from stops and fuel consumption optimiza-tion (Wuhan). . . . . . . . . . . . . . . . . . . . . . . . . . . . 45

4.4 Comparison of environmental impacts of approximated realcase and extremes from delay and fuel consumption optimiza-tion (Wuhan). . . . . . . . . . . . . . . . . . . . . . . . . . . . 46

4.5 Comparison of environmental impacts of approximated realcase and extremes from optimizing all objectives (Wuhan). . . 47

4.6 Traffic flow in the Hornsgatan and Ringvagen intersection. . . 504.7 Traffic flow in the Hornsgatan-Rosenlundsgatan intersection. . 504.8 Approximated signal timing of Hornsgatan-Ringvagen with

turning movements (times are in seconds). . . . . . . . . . . . 514.9 Approximated signal timing of Hornsgatan-Rosenlundsgatan

with turning movements (times are in seconds). . . . . . . . . 514.10 Description of control parameters used in Hornsgatan opti-

mization. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 524.11 Comparison of environmental impacts of approximated real

case and extremes from delay and stops optimization (Horns-gatan). . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 55

4.12 Comparison of environmental impacts of approximated realcase and extremes from stops and fuel consumption optimiza-tion (Hornsgatan). . . . . . . . . . . . . . . . . . . . . . . . . 57

v

vi LIST OF TABLES

4.13 Comparison of environmental impacts of approximated realcase and best found point from delay and fuel consumptionoptimization (Hornsgatan). . . . . . . . . . . . . . . . . . . . . 57

A.1 Traffic signal timing and resulting objectives from the opti-mization of network delay and number of stops (Wuhan). . . . 68

A.2 Traffic signal timing and resulting objectives from the opti-mization of delay and fuel consumption (Wuhan). . . . . . . . 69

A.3 Traffic signal timing and resulting objectives from the opti-mization of stops and fuel consumption (Wuhan). . . . . . . . 70

A.4 Traffic signal timing and resulting objectives from the opti-mization of delay, stops and fuel consumption (Wuhan). . . . . 71

A.5 Traffic signal timing and resulting objectives from the opti-mization of network delay and number of stops (Hornsgatan). 72

A.6 Traffic signal timing and resulting objectives from the opti-mization of number of stops and fuel consumption (Hornsgatan). 73

A.7 Traffic signal timing and resulting objectives from the opti-mization of network delay and fuel consumption (Hornsgatan). 74


Acronyms

CMEM Comprehensive Modal Emission Model.

CO Carbon Monoxide.

CO2 Carbon Dioxide.

COM Component Object Model.

CPF Catalyst Pass Fraction.

EPA Environmental Protection Agency.

GA Genetic Algorithm.

GUI Graphical User Interface.

HC Hydrocarbon.

HGV Heavy Goods Vehicle.

ISA Intelligent Speed Adaptation.

ITS Intelligent Transportation System.

LDV Light Duty Vehicle.

LGV Light Goods Vehicle.

MO Multi-Objective.

NOx Nitrogen Oxides.

NSGA Non-dominated Sorting Genetic Algorithm.

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viii Acronyms

ORNL Oak Ridge National Laboratory.

SSG signal state generator.

TRB Transport Research Board.

VBA Visual Basic for Applications.

VISSIM A German acronym for “Traffic in Towns - Simulation”.

VT-Micro model Virginia Tech Microscopic energy and emissions model.


Chapter 1

Introduction

1.1 Overview and Motivation

In a growing traffic environment it is apparent that the traffic congestionproblem is becoming worse in major cities. Traffic congestion in urban areasis an important topic since it impacts many significant parts of our infras-tructure. Excessive crowding may result in high delay times for importanttransportations which, in a wider sense, can affect the economic growth.For businesses it decreases productivity and labour costs. Also from thevehicles point of view, congestion leads to higher speed fluctuations and fre-quent stops which increases the fuel consumption and consequently resultin higher emissions. An increase in fuel consumption and emissions impactsour environment by the greenhouse effect, the social health by pollution andour economy by increased fuel prices. For the conference on introducingsustainability into transportation planning, several committees in the UStransportation research board (TRB) have identified unsustainable impactsof traffic system, as a first step towards a sustainable transportation system[2]. Some of the unsustainable impacts discussed are non-renewable fuel de-pletion and energy insecurity, greenhouse gas emissions, fatalities and injury,local air quality, and congestion.

To achieve a sustainable traffic system, focus should be not only on mobility,but also energy and environment. One way of dealing with a problem ofthis kind is to optimize traffic control, especially signal control in the urbancontext. Traffic signal timing is the technique which traffic engineers use todetermine who has the right of way at an intersection and is one of the most

1

2 Introduction

critical component in traffic optimization, since it can control flow patternsin congested urban areas. The current practice on urban traffic signal con-trol systems mostly implement signal plans that optimize mobility measures,such as vehicular delay or number of stops. It is however not clear whetherminimizing vehicular delay and stops will achieve a more sustainable trafficsystem. This indicates that the optimal signal timing strategies that mini-mizes vehicular delay or stops may not achieve least fuel consumption andemission or vice versa. The important issue is to find the trade-offs betweendifferent criteria.

By optimizing signal timings the fuel consumption and emission can be re-duced. From being a predominantly deterministic tool based on analyticaltheory of traffic flow, signal optimization tools have evolved to current popu-lar methods that optimize signal timing by utilizing the stochastic nature oftraffic flow modelled through microscopic simulations. Most of the researchwhere vehicle fuel consumption and emission are controlled by signal timingshave been done using macroscopic traffic models. These models estimate thefuel consumption and emission from the average speed in a link. Nowadaysmicroscopic simulation models can be used to obtain more accurate results.The introduction of microscopic simulations in traffic signal optimization is acomplicated task since it involves a microscopic and stochastic system. Thismeans that a stochastic optimization method is required to handle the sim-ulation.

The thesis will present a framework developed to optimize multi-objectivetraffic criteria focusing on both mobility and impacts. The microscopic traf-fic simulation model VISSIM is used to create the network and conduct sim-ulations. Emissions are calculated from either the ancillary software CMEMor the VT-Micro model. A fast and elitist multi-objective genetic algorithmis used to perform system optimizations.

1.2 Objectives and Scope

The main objectives of the study are the following:

• Extend the current practice of optimal signal control into the multi-objective context and review the possible approaches for multi-objectiveoptimization.


3 Introduction

• Create a computational framework based on the integration of a mi-croscopic traffic simulation model with micro-scale emission models, toimplement objectives in MO optimization.

• Evaluate and compare different signal control strategies by conductingcase studies.

1.3 Thesis Outline

The thesis is made out of five chapters, starting with an introduction tothe study. Chapter 2 provides an overview of the essential traffic impactmodelling components used in the thesis and some previous studies and lit-erature published on the topic. Chapter 3 presents the proposed frameworkwith explanations on the methods incorporated. In Chapter 4, the proposedframework is demonstrated by two case studies. Here, the modelling, opti-mization formulation and results are presented. Each case is concluded witha discussion about the obtained results. Chapter 5 concludes the thesis andgives recommendations for future studies. All results of the optimizationprocesses are tabulated in Appendix A.


Chapter 2

Literature Review

This chapter, by literature study, presents the essential components to quan-tify environmental impacts of traffic flow and aims to give a general idea ofhow each component works.

2.1 Traffic Models

The increasing popularity of simulation models is due to the efficiency inanalysing a wide variety of dynamic problems for large systems, which areseldom achievable by other means. Simulation models often handle complexprocesses characterized by interaction of many system components or enti-ties. Mathematical and logical representation of the behaviour of one entityand the interaction of a limited number of entities can be obtained with ac-ceptable confidence. But with more entities the complexity increases and ananalytical representation is in general not adequate to use.

Traffic simulation models, similar to other simulation models, are designedto mimic the behaviour of the real traffic system. A detailed descriptionof the system performance can be obtained by using a properly designedsimulation model where separate entities are integrated to simultaneouslyinteract. The model is a mathematical or physical abstraction that describesthe actual system intended to promote understanding. A simulation refersto a computerized version of the model which is run over time to study thebehaviour of the defined interactions. In [13], implementation of traffic sim-ulation models is discussed where areas such as testing new designs, training

4

5 Literature Review

Figure 2.1: Input and output information in traffic simulation software.

personal and safety analysis are included.

There are alternative approaches available that lies in the classification oftraffic simulation models. The most common approach is to categorize ac-cording to their levels of details such as microscopic, mesoscopic and macro-scopic models. The use of an approach depends on the specific applications.The input and output of traffic simulations are illustrated in Figure 2.1

Macroscopic model tends to model traffic as a continuous flow, often us-ing formulations based on hydrodynamic flow theories. The entities andtheir activities and interactions are described at a low level of detail. Traf-fic streams are, for example, represented in some aggregate manner such asa statistical histogram or by scalar values of flow rate, density and speed [16].

Microscopic model describes the system entities and their interaction ata high level of detail. These models have the capability to model each indi-vidual vehicle within a network. They are the only modelling tools availablewith the ability to examine certain complex traffic problems, such as com-


6 Literature Review

Figure 2.2: Level of detail for the model approaches; macroscopic (left),microscopic (right) and mesoscopic (within the circle) .

plex junctions [27]. This is the simulation model used in the thesis. A morethorough description of microscopic simulation is given in section 2.1.1.

Mesoscopic model combines the properties of both microscopic and macro-scopic simulation models. Simulations of individual vehicles are done on anaggregated level, usually by speed-density relationships and queuing theoryapproaches. The models generally represent most entities at a high level ofdetail but describe their activities and interactions at a low level of detail [8].

The level of detail of each modelling approach is illustrated in Figure 2.2 1.In Figure 2.3 a simple guideline of when a simulation model is appropriateis given. For a more thorough investigation of when microscopic simula-tion is necessary, the reader is refereed to The use and application of micro-simulation traffic models [27].

1http://sumo.sourceforge.net/doc/current/docs/userdoc/Theory/Traffic Simulations.html


7 Literature Review

Figure 2.3: Model approach depending on geographic area and level of detail.

2.1.1 Microscopic Models

Basic principle

As mentioned in section 2.1, a micro-simulation model is a tool to describetraffic situations in the real world. It is able to represent the traffic systeminvolving the road, drivers and vehicles in a microscopic view where eachvehicle is simulated based on the driver behaviour. In recent years, with theimprovement of computing power, more practical use has been enabled bymicroscopic traffic models. These can be used to measure several effects ap-plied to the network, as ramp metering, route diversity, variable speed limits,etc.

Microscopic traffic models was developed based on the driver behaviour mod-els. The most important among these models is the car following model, i.e.driver’s acceleration and deceleration behaviour due to interactions of nearbyvehicles [4]. A car-following model typically characterizes the behaviour of afollowing vehicle (vehicle n) that follows a lead vehicle (vehicle n − 1) [26].An essential property of all microscopic simulation models is the predictionof the operation of individual vehicles in real time, over a series of short timesteps, and the usage of driver behaviour models such as the car-following,gap acceptance and lane-changing models.

For the thesis, microscopic simulation software VISSIM is selected as thetraffic modelling tool where all traffic will be simulated.


8 Literature Review

VISSIM

VISSIM2 is a commercial microscopic simulator developed by PTV AG Karl-suhe, Germany, with add-ons being provided by various research institutions.It is a multi-modal flow simulator intended for the technical staff responsiblefor signal control, public transport operators, city planners and researchers toevaluate the influence of new traffic measures and vehicle technologies. Theprimary area of application is the detailed modelling of traffic flows on urbannetworks. VISSIM can analyse private and public transport operations dur-ing constraints such as vehicle composition, lane configurations, traffic signal,etc. VISSIM is however not suitable for corridor capacity improvements atthe regional level, or for evaluation of network wide effects of traveller infor-mation systems [6].VISSIM can be applied to a variety of transportation problems such as [23]:

• Development, evaluation and fine-tuning of signal priority logic

• Evaluation and optimization of traffic operations in a combined networkof coordinated and actuated traffic signals

• Analysis of slow speed weaving and merging areas

• Comparison of design alternatives including signalized and stop signcontrolled intersections, roundabouts and grade separated interchanges.

The simulation model consists of two primary components, the simulator andthe signal state generator (SSG). The traffic simulator includes the micro-simulation flow model with the corresponding car-following logic and lanechange logic and is where the user graphically builds the network. The userbegins by importing either an aerial photo or schematic drawing of the studyarea into the simulator. The user then begins building the network and ap-plies attributes (e.g. lane width, speed zones, priority rules etc.). The SSGis a signal control software sampling detector information from the trafficsimulator on a discrete time step basis. The SSG permits the user to anal-yse impacts from signal operations including fixed time, actuated, adaptive,transit signal and ramp metering. The signal status is then determined forthe following time step and returns this information to the traffic simulator.Below is an illustration of the communication between traffic simulator andSSG.

The modelling of car-following and traffic stream behaviour requires a math-ematical representation that captures the most important features of the

2http://www.vissim.de/index.php?id=1801 (2012-03-09)


9 Literature Review

Figure 2.4: Communication between the traffic simulator and SSG in VISSIM[23].

actual behaviour and is thus an important attribute in traffic simulationmodels. The car-following model incorporated in VISSIM belongs to a fam-ily of models known as psycho-physical or action-point, which is a version oftwo models developed by Wiedemann (Wiedemann74 and 99 models) [26].The basic concept of this model is that it uses thresholds or action-pointswhere the individual driver changes his/her driving behaviour. A driver of afaster moving vehicle will start to decelerate when he reaches his individualperception threshold to a slower moving vehicle. Since the individual drivercannot exactly determine the speed of the leading vehicle, his speed will fallbelow the vehicle in front until he slightly starts to accelerate again afterreaching another perception threshold. An iterative process is thus result-ing of acceleration and deceleration. The car-following logic is displayed inFigure 2.5.

The threshold expressed in an abbreviated form is explained as [11]:

AX Desired space between the front of two successive vehicles in a standingqueue.

BX A safety distance.

ABX Desired minimum following distance which is a function of AX, BXand the velocity.

SDV Action point where the driver consciously detects a slowing leading


10 Literature Review

Figure 2.5: VISSIM car-following logic [23].

vehicle. SDV increases with higher speed differences ∆v.

CLDV An additional threshold from the original work of Wiedemann mod-elling the additional deceleration by usage of the brake with largervariation than SDV.

OPDV Action point where the following vehicle observes that he is drivingslower than the leading vehicle and starts to accelerate.

SDX Perception threshold modelling the maximum following distance.

Individual driver behaviour is replicated to represent the stochastic distri-bution of speed and spacing threshold. Calibration has been done throughmultiple field measurements at the technical University of Karlsruhe [23].To ensure that changes in driver behaviour and vehicle improvements are ac-counted for, periodical field measurements are conducted with their resultingmodel parameter updates.

The traffic flow model of VISSM is discrete, stochastic and micro-scale withdriver vehicle units being specified as single entities. The traffic is simulated



by moving driver-vehicle-units through a network where each specific vehicleis assigned a driver with specific behaviour characteristics. The driver be-haviour corresponds to the technical capabilities of his vehicle. The defaultvehicle types in VISSIM are cars, LGVs, HGVs, Buses, trams, bicycle andpedestrians. It is possible to modify the existing vehicle types and createnew ones.

The dynamic data, containing all information about the simulated traffic,include:

• The desires speed composition

• The desired and maximum acceleration and deceleration

• The traffic composition

• The traffic volumes entering each link

• Routing decisions

The network is created by merging links, which are categorized by their type,the number of lanes in each direction and the width of the lanes with Connec-tors to replicate turning movements. Also other roadway infrastructure suchas reduced speed areas, traffic signal heads and stop lines can be used. Datasuch as network definitions of road and tracks, technical vehicle and driverbehaviour specifications, car volume and paths, transit routes and sched-ule are generally entered graphically through dialogue boxes. VISSIM doeshowever offer an additional module which provided COM (component objectmodel) functionality for use with external programming environment [22].The supported programming environments are Visual basics for application(VBA) and Python. With the COM interface it is possible to automate cer-tain tasks in VISSIM by executing commands from an external program.

A large range of output files are available in VISSIM where the user canspecify outputs on specific time interval, vehicles and links. This means thatoutputs as average delay of all vehicles in the network due to network in-teractions can be obtained. Since VISSIM has a stochastic behaviour it canproduce different results for every simulation run by utilizing one set of data.This stochastic behaviour is due to the random number generator initializedby the random seed. Simulation run with identical input files and randomseeds generate identical results. Using different random seeds changes theprofile of the arriving traffic and therefore results may also change. By run-ning multiple simulations with different random seeds, the output can be



objected to statistical analysis to obtain meaningful results.

VISSIM is not only able to model congested intersections at a microscopiclevel but it is also able to render 3-dimensional visual images of real trafficoperations. This feature is practical when presenting the result to a non-specialist or more important, the decision maker.

Other Models

There are currently numerous microscopic simulation software packages avail-able for research and planning worldwide. The different simulation modelshave been developed in the past at varying levels of complexity and networksize. The available packages vary in their ability to deal with different traf-fic situations and behaviour. Some are developed to deal with motorwaycorridors and are not suited to represent urban traffic behaviour found incentres where there is a high level of interactions between vehicles. Differentcountries and regions adopt programmes according to availability, capabilityand preferences. Table 2.1 compares basic features of VISSIM and two otherwidely used microscopic simulation software.

A comparison of VISSIM and PARAMICS shows that the packages are gen-erally very similar, but that PARAMICS is more suited for larger networksand motorways while VISSIM is better suited for detailed urban drivingconditions [6]. In [5] a detailed technical comparison is done between themicro-simulation software VISSIM and CORSIM. Here it is seen that eventhough there are documented differences between the two models at the pro-gramming level, related to vehicle and driver behaviour, the biggest differenceobserved is the variability of the models. This variability can be addressedby multiple runs.



Model Compari-son

CORSIM VISSIM PARAMICS

User interface GUI and text editor GUI and text editor, GUI and text editor

Network limitation Unlimited links andvehicles, 900 nodes,7000 detectors, 1000actuated signals,1000 pedestrianphases, 9999 feetlink length

Memory on com-puter limits thenetwork size

Memory on com-puter limits thenetwork size

Traffic control Yield-,stop- and pre-timed actuated sig-nal, ramp meteringcontrol roundabout

Stop sign, priorityrules, pre-timedand actuated signal,roundabout

Priority junction,stop sign, pre-timedand actuated signal,roundabout

Multi-model Car, trucks, pedes-trian and userfriendly modification

Car, trucks, bus, rail,tram, bike, pedestri-ana and user friendlymodification

Car, trucks, bus,pedestrians and userfriendly modification

Traffic assignment Static traffic assign-ment with equilib-rium and optimiza-tion

Static traffic assign-ment and dynamicassignment

Static assignmentand dynamic assign-ment

Measure of perfor-mance

Delay time, trafficvolume, travel time,control delay byturning movements,stopped delay, queuetime, queue length,vehicle speed, vehiclefuel consumption,vehicle emission bylink

Traffic volume, vehi-cle speed and meanspeed, travel time,total delay, stoppeddelay, average queuelength, maximumqueue length, ve-hicle stops vehicleemission

point/link flow andspeed, headway,occupancy, accel-eration, density,link/bus total delay,turn/queue/linkcounts

Graphic output 2D animation 2D and 3D anima-tion

2D and 3D anima-tion

Multi-Run Corsim driver inter-face window, com-mand line, scripts

Multi interface, com-mand line

command line

Table 2.1: Comparison of micro-simulation software [9].



2.2 Emission Models

One fundamental research question regarding environmental impact analysisof road transportation is how the level of vehicular exhaust emission andfuel consumption is modelled correctly. Existing vehicle emission modelscan generally be classified into macroscopic models and microscopic models.Macroscopic models are aggregated models based on assumed and standard-ized average driving cycles tested on dynamometers, where a driving cycleconsists of a unique profile of starts, stops, cruises at constant speed, accel-eration and deceleration [1]. This makes it technically difficult to evaluatespecific traffic improvements strategies in detail unless the strategy changesthe average traffic behaviour significantly. Therefore aggregate models aremostly used for planning and evaluation of static approaches estimating totalor average traffic emission and fuel consumption.

Microscopic emission models have become a research focus due to their ca-pability of evaluating traffic impacts prior to field implementations. Thesemodels estimate vehicle pollutants at a second by second level of resolutionusing either engine or vehicle speed/acceleration data. An important aspectof microscopic emission models is that they can be used together with mi-croscopic traffic models for management of emission and fuel consumptionthrough dynamic traffic control and operations, and is why it is used for thethesis.

Microscopic emission models estimate vehicle fuel consumption and emissionby retrieving information about instantaneous states of each individual ve-hicle on roads, i.e. vehicle velocity, acceleration, engine performance indices,etc. Mathematically, a microscopic emission model can be represented by

Ei,j(t) = f(Cj, a, v, ..., t, ψi,j) (2.1)

where the subscript i represent the gas type and j represent the vehiclecategory Cj. ψi,j represent parameters for the model. Here a and v are theacceleration and velocity.

Two approaches in microscopic emission modelling is power demand-basedemission modelling and regression modelling. For the thesis, both approachesare investigated, where CMEM is the power-demand model and VT-Microis the regression model. The models are presented in the following sections.



2.2.1 CMEM

CMEM3 (Comprehensive Modal Emission Model) is a microscopic emissionmodel developed at the University of California, Riverside. The model is aphysical, power-demand model based on a parameterized analytical repre-sentation of emission production. The process to calculate emission is bro-ken down into different modules or components that correspond to physicalphenomena associated with vehicle operation and emission production. Ananalytical representation of each component consisting of various parametersthat characterize the process is then modelled. These parameters representthe variation of vehicles such as technology, fuel delivery system, emissioncontrol technology, etc. The development of CMEM involved extensive datacollection for both engine-out and tailpipe emission of over 300 automobilesand light trucks in 26 vehicle categories. These data where measured at asecond by second level of resolution. The term comprehensive in CMEMcomes from the fact that it is able to predict emissions for a wide variety ofLDVs in various states of condition, e.g. properly functioning, deterioratedand malfunctioning [28].

The main purpose of CMEM is to predict vehicle tailpipe emission as a func-tion of vehicles operating modes, such as acceleration, deceleration, idle andcruise. The tailpipe emission is modelled as the product of three components,namely fuel rate (FR), engine-out emission indices (gemission/gfuel) and timedependent catalyst pass fraction (CPF):

Etailpipe = FR ∗ (gemission/gfuel) ∗ CPF (2.2)

The fuel rate consumption is given in grams per second, engine-out emissionindices is grams of engine-out emission per gram of fuel consumed and thecatalyst pass fraction is defined as the ratio of tailpipe to engine-out emis-sions.

The complete model consist of six modules: (1) engine power demand, (2)engine speed, (3) fuel/air ratio, (4) fuel-state, (5) engine-out emissions and(6) catalyst pass fraction. The model requires vehicle and operation variablessuch as speed, acceleration and road grade, and model calibrated parameterssuch as cold start coefficient, engine friction factor as inputs. Moreover, thereare also four operating condition in the model: (a) variable soak time, (b)

3http://www.cert.ucr.edu/cmem/ (2012-03-09)



stoichiometric operation, (c) enrichment and (d) enleanment. The output istailpipe emission and fuel consumption. In Figure 2.6 one can see the generalstructure of the model.

Figure 2.6: General structure of CMEM [28].

The development of CMEM started in the programming environment Mat-lab4. In order to use the model outside the development environment, exe-cutable code was created in JAVA from the source code. A command lineuser interface was developed from the source code to run on both PC envi-ronment and the UNIX environment. Today, CMEM also offers a GUI tomake it easier to use. The executable code takes on two forms: Core modeland Batch model. The core model allows the user to obtain emissions from asingle specified vehicle category and a given vehicle activity file. The batchmodel allows the user to obtain emission data from multiple vehicles of dif-ferent vehicle types with different trajectories. This form suits best whenexamining a network of vehicles and is thus the one used for the thesis.

The batch model requires three input files: A parameter control file, a soak-time file and a vehicle activity file. The output files are a second-by-second,time ordered vehicle emission file and a vehicle integrated emission file. Thecontrol input file specifies the vehicle categories and the soak time to each

4http://www.mathworks.se/ (2012-03-09)



vehicle. The vehicle activity file consists of the vehicle trajectories corre-sponding to each vehicle. The soak time file specifies how long each vehiclehas been stopped prior to the model application. In Figure 2.7 an illustrationof the batch process is given.

Figure 2.7: Batch form of CMEM [28].

2.2.2 VT-Micro

The Virginia Tech microscopic energy and emission model (VT-Micro model)was developed by using chassis dynamometer data, collected at the OAKRidge National Laboratory (ORNL) and the Environmental Protection Agency(EPA) [3]. These data included fuel consumption and emission rate measure-ments (CO, HC, NOx, CO2) as a function of the vehicle’s instantaneous speedand acceleration levels.

The model was developed as a regression model from experimentation withnumerous polynomial combinations of speed and acceleration levels where



linear, quadratic, cubic and quartic terms were tested. The final regressionmodel included a combination of linear, quadratic and cubic speed and ac-celeration terms as shown in the following equation

Ee =3∑i=0

3∑j=0

(Kei,j ∗ vi ∗ ai) (2.3)

where Ee is the instantaneous emission or fuel consumption rate, Kei,j is the

regression model coefficient for Ee at speed power vi and acceleration poweraj.

The ORNL data consisted of nine normal emitting vehicles including sixlight duty vehicles (LDV) and three light duty trucks. The collected datacontained between 1300 and 1600 individual measurements for each vehicleand emission combination depending on the driving operation envelope [24].Typical acceleration and vehicle speed values ranged from -1.5 to 3.7 m/s2 atincrement of 0.3 m/s2 and 0 to 33.5 m/s at increment of 0.3 m/s respectively.

The model needed to be modified since it, in a few instances, producednegative dependent variable values. To address this problem, a logarithmtransformation is applied resulting in the equation [24]

Ee = e

3∑i=0

3∑j=0

(Kei,j∗vi∗ai)

(2.4)

Since vehicles exert power in positive acceleration while vehicles do not exertpower in negative acceleration, the model needs to be separated for negativeand positive accelerations. Consequently, separate regression models weredeveloped for positive and negative acceleration:

Ee =

e

3∑i=0

3∑j=0

(Lei,j∗vi∗ai)

for a ≥ 0

e

3∑i=0

3∑j=0

(Mei,j∗vi∗ai)

for a < 0

(2.5)

Here L and M are the regression coefficient for Ee at speed power ’i’ andacceleration power ’j’. It is these sample model coefficient that need to becalibrated for estimating fuel consumption and emission for a composite ve-hicle.



2.3 Sustainable Traffic Management

Sustainable traffic management can build a sustainable traffic system by con-trolling the traffic. To achieve this, new innovations or smarter managementof current traffic control parameters needs to be considered. Also, testing ofnew indicators, methods and instruments for the environmental analysis andmonitoring of the impacts of the traffic system is needed. A convenient wayto perform these testing is by using computer simulations.

There have been several studies where various traffic simulation tools havebeen used with various methods to estimate fuel consumption and vehicleemission. Many of them have shown that by optimizing traffic signal the fuelconsumption and/or vehicle emission can be decreased, but these studies arebased on macroscopic or mesoscopic models. Recently, several microscopicsimulation software tools have been used when dealing with time-step eval-uation of vehicle emissions. In [17] VISSIM and CMEM where successfullyintegrated where the relationship between emission and the aggressiveness ofdriving where quantified. Also in [31] VISSIM is integrated with CMEM toanalyse how traffic-flow improvements can potentially affect pollutant emis-sion and fuel consumption in both the short-term and the long-term. Othercontrol measures have also been controlled to reduce fuel consumption andemissions. In [19] a new technology of the intelligent transportation system(ITS), namely the intelligent speed adaptation (ISA), has been integratedwith microscopic traffic and emission models. The integrated model is ap-plied to test different technological design and evaluate their emissions.

Historically, macroscopic optimization programs have been used to optimizetraffic signal plans. Today there are complete traffic optimization modelsavailable, such as TRANSYT 5 and Synchro 6, intended to optimize trafficmobility measures. In [21] a network optimization regarding traffic mobilityis performed using Synchro as optimization tool where the total delay timeis reduced. Nowadays, when more microscopic evaluation is performed, astochastic optimization method is needed. The Genetic algorithm (GA) isa stochastic optimization approach that has been recognized as a successfuloptimization tool. There have been several studies where microscopic trafficsimulation tools have been used together with GA to find better signal timingplans. In [32] a GA optimization was tested on two VISSIM networks and

5https://www.trlsoftware.co.uk/products/junction signal design/transyt6http://www.trafficgroup.com/services/synChro simtraffic 2D simulation.html



compared with a SYNCHRO optimization. The result showed that timingplans optimized by the GA outperformed the best SYNCHRO optimizationin both reducing delay and stops.

To optimize several objectives simultaneously one faces a multi-objectiveoptimization problem. One way to tackle this problem is to convert theobjectives into a single-objective problem and apply single-objective opti-mization methods. These methods use weighted sum or goal programmingtechniques to find optimal solutions. From these methods, only one singlePareto-optimal solution is found in each simulation run. Another possibil-ity to solve multi-objective optimization problems is to use a multi-objectiveoptimization technique that optimizes the objectives simultaneously. In [7] amulti-objective GA is used for the optimization of a traffic-actuated controllerbased on VISSIM simulations. The result showed that parameters found bytheir multi-objective optimization algorithm can be superior to those definedby a traffic engineer with respect to several objectives including vehicle traveltimes and number of stops.

There have recently been several studies on optimizing traffic signal timing toreduce fuel consumption and vehicular emissions where single-objective opti-mization has been conducted. In [33] an integration of VISSIM and CMEMis optimized with a program called VISGAOST, which is a GA optimizationprogram for signal timings of traffic controllers based on their performance inVISSIM. Here, the potential of optimizing an integrated microscopic trafficand emission model to reduce vehicular emission is shown. VISSIMs ownmethod of estimating fuel consumption is said to significantly overestimatetotal fuel consumption when it is compared with CMEM fuel consumption.This may be because the VISSIM formula to calculate fuel consumptionis highly influenced by the number of stops. Another study of optimizingmicroscopic traffic and emission models to improve fuel consumption and ve-hicular emissions is conducted in [20], but with CORSIM as the microscopictraffic simulation model and VT-micro as the emission model. Here, a GAbased optimization algorithm is used to find traffic signal timing strategiesthat improve mobility and sustainability. This study successfully performedtwo strategies where one optimized sustainability and the other optimizedmobility. A important conclusion drawn from the report is that there areapparent trade-offs between mobility and sustainability depending on the se-lection of objective functions, and that future research should investigate amulti-objective approach to account for these traffic measures.


Chapter 3

Methodology

3.1 Stochastic Optimization

During the last decades stochastic optimization algorithms have been grow-ing rapidly in popularity, with a couple of methods now becoming “industrystandard” approaches for solving difficult optimization problems. Methodsincluded in the stochastic optimization framework are used in areas suchas transportation engineering as well as aerospace engineering, business andmedicine.

Stochastic algorithms have become attractive since they provide means ofcoping with inherent system noise and systems that are highly non-linearand non-convex. It is often used when classical (analytical or numerical)methods fail. When encountering a complex problem where the parametersaffecting the objective function makes it highly non-linear and large, usuallyonly local minima can be obtained by classical methods. Classical determin-istic optimization assumes that perfect information is available about theobjective function (and derivatives if relevant) and uses this information todetermine the search direction in a deterministic manner in each time step.However, in many practical problems, such information is not available.

3.1.1 Formal Problem Statement

Let Ω be the domain of allowable values for a vector θ. As for other opti-mization algorithms the fundamental problem is to find a vector Θ ε Ω that

21

22 Methodology

minimizes a scalar value objective function O(Θ). Of course a maximizationproblem can be trivially converted to a minimization problem by changingthe sign of the criterion. The minimization of an objective function can berepresented as finding the set:

Ω? ≡ argminΘεΩ

O(Θ) = Θ?ε Ω : O(Θ?) ≤ O(Θ) ∀ ΘεΩ (3.1)

where Θ is the p-dimensional vector of parameters being adjusted and Ω isa subset of Rp (Rp is the Euclidean space of dimension p). This statementshould be understood as Ω? is the set of values that minimizes the objectivefunction O(Θ) subject to Θ? satisfying the constraints represented in Ω. Thesolution set Ω? can be a unique point, as well as a countable number of pointsor a set containing an uncountable number of points.

Stochastic optimization methods are applicable when there is random noisein the measurement and/or there is a random choice made in the searchdirection as the algorithm iterates towards a solution. Here the focus willbe on the second property mentioned above. Relative to this property, itis beneficial to introduce randomness to the search process as a means toachieve a faster speed convergence and making the algorithm less sensitiveto modelling errors. Even though the injected randomness may seem coun-terproductive it is well known to have beneficial effects in some settings [29].When seeking for an optimal point, the injected randomness allows sponta-neous movements to unexplored areas of the search space where there mightbe an unexpected good value of the objective function. This way, the methodcan jump around until it cannot find better solutions.

In Figure 3.1 a curve O(Θ) with many local minimum in the range Θ ε[0, 50]can be seen. A simple function with one variable is chosen to illustrate thebeneficial of randomness to the search process to ease the understanding. InFigure 3.1 it can be seen that if the random search is located at the rangeΘ ε[27, 40], the local minimum at Θ=29 or Θ=36 will be the closest to befound. If the search direction is injected with randomness, the search spacecan be moved to Θ ε[0, 10] where the real global optimum is.


23 Methodology

Figure 3.1: Illustration of global and local minimum.

3.2 Genetic Algorithm

Genetic algorithm (GA) is a stochastic optimization technique that belongsto one category of the evolutionary algorithms. It is a method used to gener-ate solutions to optimization and search problems. By using a GA, optimalor near optimal solutions can be found. The algorithm is inspired by Dar-win’s theory about the survival of the fittest.

GA starts with a set of solutions (chromosomes) called a population. Solu-tions within the population are crossed to form new chromosomes (offspring).The chosen chromosomes in a population to be crossed (parents) are selectedaccording to their fitness. The higher the individual fitness is, the higherthe chance to be selected to reproduce. Some steps of the algorithm used inthe thesis will be presented below. To learn more about GA the reader isreferred to [29].

Encoding There is accumulating evidence that real-number coding oftenoffers performance equal or superior to that available with binary-based cod-ing [29] and the encoding is therefore chosen to be real coded. This meansthat no encoding is actually done since the chromosomes in each populationconsist of its real number.


24 Methodology

Figure 3.2: Illustration of the stochastic uniform selection process. Eachpointer represent a selection of an individual in the population.

Selection The selection process handles the method of how individualsare selected to become parents. The selection process used in the thesis iscalled stochastic uniform and work as follow: A line is outlined where eachindividual corresponds to a section of length proportional to its scaled value.The algorithm steps through the line in steps of equal size. At each stepthe algorithm lands on, a parent is allocated. The first step is a randomuniform number lower or equal to the step size. The entire line is covered innparent steps, where nparent is the number of parents in the genetic algorithm.It should be noted that an individual can be selected more than once as aparent, in which case it contributes its genes to more than one child.

Crossover The crossover operations implemented in the GA generate newoffspring’s to the new (next) population. The operation creates offspring ofthe pairs of parents from the selection step. The crossover process used iscalled scattered crossover and creates uniformly distributed random numbersto decide which of the parents attribute to inherit in the child. This meansthat for each position in the gene, a random number decides if the attributecomes from parent 1 or parent 2. In Figure 3.3 an illustration is given, whereif the random value for a given position is higher than 0.5 parent 2 is selected,otherwise parent 1 is selected.


25 Methodology

Figure 3.3: Scattered Crossover. If the random number is higher than 0.5 fora given position, the child will inherit the attribute from parent 2, otherwiseparent 1 is selected.

Mutation The GA has a mutation operator, since the initial populationmay not contain encoded information rich enough to find the solution throughcrossover operations alone. The purpose of a mutation operator is to makesmall random changes to a chromosome. The used mutation operator addsa uniformly random number, between the constrained range, to each entryof the parent vector.


26 Methodology

Basic outline of the Genetic Algorithm

Below is the basic outline of how a genetic algorithm is composed.

Figure 3.4: Scattered Crossover. If the random number is higher than 0.5 fora given position, the child will inherit the attribute from parent 2, otherwiseparent 1 is selected.


27 Methodology

3.3 Multi-Objective Optimization

Multi-objective optimization (MOO), also known as multi-criteria or multi-attribute optimization, is an optimization class that handles more than oneobjective to optimize [34]. Since many real-world optimization problems arenaturally posed with multiple objectives, MOO methods are needed. A wayto tackle this is to artificially convert the problem to a single objective andperform single objective optimization to solve it. A classical approach is thelinear weighted sum method, where the objective can be combined into asingle objective as [30]

Optimize : f(x) =l∑

k=1

ωkOk(x) (3.2)

where the weights ωk correspond to objective function Ok and has the prop-erty

l∑k=1

ωk = 1, ωk ≥ 0, k = 1, ..., l (3.3)

It does however exist a number of fundamental differences between the work-ing principles of single- and multi-objective optimization, and MOO problemsshould thus be solved by a multi-objective optimization technique.

Single-objective optimization problems are usually characterized by searchingfor a single solution which optimizes the whole objective function. Extendingthe idea to multi-objective optimization, one may wrongly assume that inMOO problems optimal solutions corresponding to each objective function issought. This is however not the case since MOO problems give rise to a set oftrade-off optimal solutions, known as Pareto-optimal solutions, and the taskis to find as many of them as possible. The following properties distinguishmulti-objective optimization problems from single-objective problems [12]:

• Cardinality of the optimal set is usually more than one.

• Two distinct goals of optimization, instead of one.

• Possesses two different search spaces.

The meaning of these properties are discussed below.


28 Methodology

The first property comes from the fact that a multi-objective optimizationproblem with conflicting objectives, results in a set of Pareto-points (Pareto-optimal solutions) unlike the usual notation of one optimal point associatedwith single-objective optimization. A multi-objective optimization (mini-mization) problem can be written as:

f = minΦ

(O1(Φ), O2(Φ), O3(Φ), ..., On(Φ)) (3.4)

where O1(Φ), O2(Φ), O3(Φ), ..., On(Φ) are the different objectives to mini-mize and Φ is a vector of optimization or decision variables.

To be considered as Pareto-optimal, one objective cannot be improved furtherwithout degrading the other objectives. Mathematically this can be describedby the following [12]: a feasible vector of decision variables Φ? is Pareto-optimal to the solution of Equation 3.4 if there does not exist any other Φsuch that

Ok(Φ) ≤ Ok(Φ?) ∀ k, and Ok(Φ) < Ok(Φ

?) for at least one k (3.5)

Here Ok is the value of objectives k.

The second property, that MOO problems have two distinct goal of optimiza-tion, comes from the following independent goals:

1. Convergence of Pareto-optimal solution

2. Maintaining a set of maximally spread Pareto-points

To achieve each of these goals, the MOO algorithm must have specific prop-erties handling them, as one can se in Section 3.4.

The third property is about the addition to the usual decision variable space,common for all optimization problems. For MOO, the objective functionconstitute a multi-dimensional space, called objective space (Z). This meansthat for each solution Φ in the decision space, there exists a point in theobjective space. Figure 3.5 illustrate the decision and objective space with amapping between them, i.e. it shows that for each point in the three dimen-sional decision space there is a corresponding point in the two dimensionalobjective space.


29 Methodology

Figure 3.5: Illustration of the decision space and the corresponding objectivespace [12].

3.4 NSGA ii

The non-dominated sorting genetic algorithm (NSGA) ii is a fast and elitistmulti-objective genetic algorithm capable of finding multiple Pareto-optimalsolutions in one single run. The algorithm has the three following features[10]:

• An elitist principle.

• An explicit diversity preserving mechanism.

• Non-dominated solutions are emphasized.

The meaning of these features will be given below in the presentation of howthe algorithm is composed.

3.4.1 Algorithm

Since the NSGA ii is a GA designed for multiple objectives, it handles regularfeatures of genetic algorithms such as populations, mutations, selection, etc.as described in Section 3.2. The first step of the algorithm is to create apopulation Pi, consisting of a set of solutions to the objectives, i.e. each


30 Methodology

population individual contains the dependent variable to the objectives. Thepopulation is then sorted based on non-domination of the objectives in eachfront. The definition of non-domination (for minimization problem) is [12]:

A solution Φ1 is said to dominate the other solution Φ2 when there are Nobjective functions, if both conditions 1 and 2 are true:

1. The solution Φ1 is no worse than Φ2 in all objectives, that isOj(Φ1) ≤ Oj(Φ2) for all j = 1, 2, ..., N

2. The solution Φ1 is strictly better than Φ2 in at least one objective,Oj(Φ1) < Oj(Φ2) for at least one jε[1, 2, ..., N ]

Among a set of solutions M , the non-dominated set of solutions M ′ are thosethat are not dominated by any other member of the set M . If M is the entiresearch space, the resulting non-dominated setM ′ is the so called Pareto-front.

The solutions in the population Pi are divided into different fronts, wherethe first front is a non-dominated set of the current population, the secondfront is only dominated by the individuals of the first front, and the rest ofthe fronts follow this logic. All individuals situated in each front are assignedrank values based on which front they belong to. The ranking starts at onefor the first front and increases by one for each subsequent front. When thehierarchy of the initial population is determined, the population is enteredin a loop and renamed to Pt, where t is the current iteration number.

The loop initiates with the GA features selection, crossover and mutation togenerate an offspring population Qt of size N (same size as the initial pop-ulation). Thereafter, the two populations are combined together to form anew population of size 2N called Rt. Again, the sorting process described forthe initial population is used to classify the entire population Rt. Since allprevious solutions are included in this new combined population Rt, elitismis ensured. The concept of elitism means that if a solution in the parent pop-ulation is better than all solutions in the offspring population, the solutionshall survive and be part of the new population Pt+1.

Solutions belonging to the first front, here called f1, are the best solutionsin the combined population and are thus emphasized more than any othersolution in Rt to be inserted into the new population Pt+1. Since the newpopulation is of size N, not all fronts of Rt will be accommodated into Pt+1.If the first front f1 is smaller than N, all solutions belonging to this front are


31 Methodology

selected to be copied into the new population. The remaining members of thenew population are chosen from the subsequent non-dominated fronts in theorder of their ranking, i.e. solutions from front f2 are chosen next followedby solutions from front f3, etc. This insertion of fronts is continued untilno more fronts can be housed. Assuming that fl is the last non-dominatedfront beyond which no other front can be accommodated, there may existmore solutions in fl than the remaining slots available in the new population.If including fl exceeds the limitation of N solutions in the new population,a crowding distance comparison is performed to make the diversity of theselected solutions as high as possible.

The crowding distance is a measure of how close the individuals of the samerank are to each other. The crowding distance comparison is described laterin this section. Since large average crowding distance will result in a betterdiversity in the new population, the individuals with highest values are se-lected to fill the remaining slots. In Figure 3.6 an illustration of the NSGAii process is given.

Figure 3.6: Schematic of the NSGA ii process.

3.4.2 Crowding Distance Comparison

The crowding distance comparison is a mean to maintain a good spread ofsolutions in the optimization process. Note that only solutions with the samerank are compared. A local crowding distance di is given to each solution iwhich is a measure of the search space around solution i that is not occupiedby any other solution in the population. The crowding distance can be com-puted in various ways, but in this thesis a crowding distance metric is used.


32 Methodology

To estimate the density of solutions surrounding a particular solution i in thepopulation, the average distance of two solutions on either side of solution ialong each of the objectives is calculated. This crowding distance quantitydi serves as an estimate of the perimeter of the cuboid formed by using thenearest solutions as the vertices. The procedure initiates by sorting the setof solution for each objective in ascending order of magnitude. Thereafter,the boundary solutions for each objective (the first and last in the sorting)are assigned an infinite distance value. All other intermediate values areassigned a value equal to the absolute normalized difference between thefunction values of two neighbouring solutions, as

d(i)mdistance =I(i+ 1)m − I(i− 1)m

fmaxm − fminm

(3.6)

Here I(i)m denotes the solution index of the ith component of the set I andthe parametersfmaxm and fminm are the maximum and minimum value of themth objective function. The values d(i)mdistance are the crowding distance forthe individual i of the objective m.

This calculation is continued with all other objectives and the overall crowd-ing distance is calculated as the sum of individual distance values correspond-ing to each objective. An illustration of the crowding distance calculation ofan individual i of objective m is given in Figure 3.7

Figure 3.7: Crowding distance calculation [10].


33 Methodology

3.5 Traffic Impact Modelling Framework

3.5.1 Model Integration

The proposed framework is an extension of a previous single objective op-timization method established by [15], where VISSIM is integrated withCMEM to calculate the mobility and impacts. In this thesis, the methodis extended to handle multiple objectives able to identify conflicting mobilityand impact measures. The proposed framework is described below with theused methods and software.

The traffic network is constructed and simulated in VISSIM. The instanta-neous states of each vehicle on the roads are outputted from VISSIM, wherea selection of vehicle types are inserted into the emission model. VISSIMalso calculates and outputs traffic performance indices to be used in the op-timization process. The vehicle instantaneous states, needed by the emissionmodel as inputs, are used to calculate the vehicular fuel consumption andemissions from each individual vehicle. After both VISSIM and emissionmodel execution, information about the network mobility and impacts areobtained and an evaluation can be done.

As mentioned in Section 2.1.1, traffic performance indices such as averagedelay, average stops etc. can be obtained from VISSIM, and can thus beobjectives in the optimization process. The same applies to the output fromthe emission model, such as vehicular fuel consumption, emission of HC, CO,etc. The selection of objectives depends on the purpose of the optimization.To implement multiple traffic simulation runs with enhanced computing per-formance, the COM (Component Object Model) server interface of VISSIMtraffic simulator is called using python1, an object-oriented programming lan-guage.

The stochastic optimizer is implemented in Matlab, a high level mathemat-ical computing language. The optimization is based on NSGA ii, a fastand elitist multi-objective genetic algorithm, see Section 3.4. Figure 3.8 il-lustrates the integrated framework for VISSIM traffic simulation, emissioncomputation and stochastic optimization. Here one can see that Matlab isused to call Python scripts that create COM objects controlling VISSIM

1http://python.org/ (2012-03.09)


34 Methodology

Figure 3.8: The programming integration

simulations. Matlab also runs the emission model, which receives VISSIMoutputs and returns its own output to Matlab. As it can be seen, differentVISSIM outputs are provided to the emission model and Matlab.

The optimization process initiates with the creation of a population, consist-ing of the control parameters for the signal plans in the VISSIM network.The VISSIM network is then simulated using these control parameters. Thenumber of simulation runs needed in each optimization process depends onthe population size and the number of random seeds used. The simulationruns have a direct impact on the computational cost and solution accuracyachieved. The amount of simulation runs for each population is calculatedby multiplying the total number of random seeds and the population size.

The Python script mentioned above is thus called from Matlab to executeVISSIM simulations. The information from the simulations is then retrievedand divided into emission model inputs and optimization objectives. Theemission model use its input files to compute the fuel consumption and emis-sions, which then also are added as optimization objectives. Since the I/Ooperations during the optimization handle large data files (a vehicle instanta-neous file has up to million lines) parallel computing has been used to increase


35 Methodology

the computational speed. The GA optimizer then uses its search heuristicto find better control parameters to improve the traffic network according tothe chosen objectives. A new population is created and the process startsagain. The computational framework is given in Figure 3.9

Figure 3.9: Framework of the multi-objective signal timing optimization pro-cess.


36 Methodology

3.5.2 Optimization Formulation

An optimization formulation for the proposed target area regarding mobilityand impacts is given. To ease the understanding a formulation where theoptimization has two objectives, namely the network average time delay andfuel consumption, is outlined. Here the control parameters consist of thecycle length, C, and the green time interval, gi. Of course the objectivescan easily be modified to include more and other objectives, and the controlparameters can easily be changed as well depending on the control logicapplied for the system. The optimization formulation is given below:

find S = C, gi

minS

(E(d(S, r)), E(f(S, r))) (3.7)

subject toCmin ≤ C ≤ Cmax

Θ1,min ≤ g1/C ≤ Θ1,max



.

.

.

Θn,min ≤ gn/C ≤ Θn,max

n∑i=1

gi + LTi = C

Here the objectives E(d(S, r)) and E(f(S, r)) are the expected time delayand expected fuel consumption respectively associated with a timing plan Sand a set of random seeds r. The formulation limits the cycle length andgreen split by an upper and lower limit. S is the signal settings controllingthe vehicles and LTi is the lost time of phase movement i.


Chapter 4

Case Studies

In order to best demonstrate the impact of the developed framework, twocase studies have been conducted to apply and evaluate the computationalframework and signal optimization approaches. Whereas the first case stud-ies signal plan at a big but isolated intersection, and the second case considerstwo neighbouring intersection that need coordination. A more thorough de-scription is given in each respective section. Traffic performance measuresand traffic impact measures used as objectives in the optimization processare explained below.

Network delay The total delay time due to driving in a lower speed thanthe desired speed, and summed over all vehicles in the network.

Average stops per vehicle The average number of stops a vehicle per-forms in the traffic network.

Average fuel consumption The average fuel consumption per vehicle inthe network.

The case studies are investigated in separate sections where each sectioninitiates with a presentation of the case and the modelling. Then, the opti-mization formulation is introduced followed by the main results. Each casestudy section ends with a discussion about the case study results. The restof the results, including signals strategies from other inferior found fronts,are presented in Appendix A. The main results contain the outcome of theoptimization objectives ( the Pareto-front1) and the emission levels of the

1It may not be the real Pareto-front since the optimization provides near optimalsolutions

37

38 Case Studies

best found solutions of each objectives. Since the computational effort toperform these search processes in a microscopic scale is time consuming, themain results also include the computational time for the processes.

The optimizations are based on evaluation of traffic and emission perfor-mances accumulated during 60 minutes of simulation with additional 15 min-utes for warm up. The simulation warm up is needed to achieve steady-statetraffic condition in the network. Since microscopic simulation models oftenshow variability in their performance measures, it is crucial to account forsuch variability during the optimization. As mentioned in Section 3.5, thearithmetic mean is chosen as the representative value to accommodate suchvariability. This study uses the calculated mean value based on 5 random-seeded VISSIM simulation runs as objective function values.

4.1 Isolated Intersection – Wuhan

The first case study analyses an isolated intersection in Wuhan, China. Theintersection has four arms where each of them has five lanes in each direction,three straight through, one right-turn lane and one left-turn lane. The left-turning lane from the west direction has the additional turning ability of a u-turn, which will place the vehicle towards the west direction. The main roadof this intersection is the Youyi road. A geometric layout of the signalizedintersection is given in the Figure 4.1.


39 Case Studies

Figure 4.1: Geometric layout of the isolated intersection in Wahun.

4.1.1 Modelling

The traffic network is modelled in VISSIM where a previous calibration hasbeen done by [15]. The calibration used on-spot data collected by camerasand manual recording during 15:00-17:00 on may 20th, 2010. The signaltimings were recorded manually since detailed control logic was not available.The calibration process can be summarized by the following steps:

1. Set up VISSIM network with demand levels and turning movementsaccording to real measurements

2. The average flow speed measurements at the stretches are selected asstatistical measures for the calibration.

3. Six longitudinal and six lateral parameters are chosen as behaviouralparameters according to analysis of car-following and lane changingmodels. The ranges of these parameters are based on default settings.

4. A GA is used to optimize the parameter estimation. Ten replicationof VISSIM simulation with different random seeds where simulated to


40 Case Studies

estimate the average traffic characteristics at the stations.

5. Model validation where based on traffic counts obtained at the samelocations as speed observations.

The validation process is based on 20 simulation runs, each of them consist-ing of two hour simulation with a warming up period in the beginning.

The emission and fuel consumption is calculated by the VT-Micro model,which has been calibrated in [14]. Here, multiple linear regression procedureswhere applied to obtain the model coefficient described in section 2.2.2. Themodel is calibrated by PEMS measurements in Chine.

For the case study, only emissions from the LDV4 vehicle category are investi-gated. The delay and stops are however investigated for all vehicle categories.

4.1.2 Signal Optimization

The signal optimization is based on the original signal approximated by [15]given in Table 4.1 below.

Phase order Description Cycle time Green time1 Left-turn traffic on east and

west arm145 18

2 Direct traffic on both eastand west arm

145 78

3 Direct and left-turn trafficon north arm

145 15

4 Direct and left-turn trafficon south arm

145 15

Yellow time is 3 seconds and transition time between phases is 2 seconds

Table 4.1: Approximated signal timing from manual recordings at the iso-lated intersection in Wuhan (times are in seconds).

The green times of each phase are chosen as control parameters for the op-timization, resulting in four control parameters. These parameters limit thecycle and green times to given ranges. An optimization formulation with allpreviously described objectives is given below.


41 Case Studies

minS

(E(d(S, r)), E(s(S, r)), E(f(S, r))) (4.1)

subject to99 ≤ C ≤ 194

10/194 ≤ g1/C ≤ 25/99

50/194 ≤ g2/C ≤ 100/99

10/194 ≤ g3/C ≤ 25/99

10/194 ≤ g4/C ≤ 25/99

4∑i=1

gi + 19 = C

Here, E(d, r), E(s, r) and E(f, r) are the expected value of the delay, stopsand fuel consumption respectively. As one can see, the green split and cyclelength depends on g1, g2, g3 and g4 which are the green times of each phaseaccording to the numbering in Table 4.1.

The investigation will explore search processes where one objective is com-peting with another objective, thus revealing the trade-off between thesemeasures. Since the search process is very time consuming, a compromisebetween the search time and result needs to set, limiting the search time bya fix number of generations. In figure 4.2, the convergence of a search pro-cess with a population size of 20 is presented. Here, one can see that after 20generations the difference in the objectives does not change much thus givingan indication that 20 generations is sufficient to obtain reasonable results.Therefore, the presented results are conducted with:

• population size of 20.

• generation size of 20.


42 Case Studies

Figure 4.2: Convergence of the objectives during evaluation generations inthe Wuhan case.

4.1.3 Results

This section provides the main results of the investigation where, as men-tioned previously, all objectives are compared to each other. As a final com-parison, a three-objective optimization process has been conducted with allobjectives. Keep in mind that since each combination of objectives presentedbelow are subjected to a separate stochastic optimization process, with sep-arate initial solutions, the final solution of equal objectives does not need tobe the same. The result of each optimization approach is compared with thefixed approximation of the real signal timing.

Average delay vs Average stops

Here, the first optimization approach regarding average network delay andaverage stops per vehicle is presented. In Figure 4.3 the computed first fivefronts are shown, where front 1 is the best found. One can clearly see how thefronts are moving to achieve better values and finalize in a front consistingof 7 points. This front clearly demonstrates a trade-off between these objec-tives, where a lower delay results in higher number of stops and vice versa.As one can see, the extremes are located at the edges of the first front wherethe point representing the minimum of average network delay is furthest tothe left. Between these extremes we find solutions where different trade-offbetween both objectives exist. The search took about 4 hours to perform


43 Case Studies

and is much faster than the other optimization strategies since the emissionmodel is not needed.

Figure 4.3: Obtained first five fronts of optimizing network delay and numberof stops (Wuhan).

The impacts of the two extreme solutions of the best front in Figure 4.3 to-gether with its traffic performance measures and the resulting signal timingplan are presented in Table 4.2. Here, the simulation result from the approx-imated real traffic signal is also provided to compare the solution strategies.

Signalcase

Signal plan Traffic measures Emission and fuel consumption

delay[h]

stops speed[km/h]

HC[g/km]

CO[g/km]

Fuel[g/km]

CO2

[g/km]

Real case[18, 78, 15, avg. 24.61 0.434 34.13 0.38 10.11 76.05 265.5615, 145] std. 0.59 0.007 0.19 0.014 0.12 0.88 3.94

minstops

[10, 89, 12, avg. 22.75 0.397 34.74 0.352 9.66 74.32 257.6012, 142] std. 0.42 0.003 0.22 0.008 0.255 0.8 3.96

mindelay

[10, 53, 10, avg. 18.94 0.435 36.07 0.389 10.41 76.03 267.1211, 103] std. 0.63 0.012 0.25 0.01 0.28 0.94 4.16

Table 4.2: Comparison of environmental impacts of approximated real caseand extremes from delay and stops optimization (Wuhan).

The table shows that the search is successful in finding traffic signals pro-ducing better results than the real signal, with respect to the optimized


44 Case Studies

objectives. One can also see that when delay is minimized, most of the traf-fic impact indices are not significantly different from the real case. But whenaverage number of stops is minimized, one can see significant improvementof the impact measures.

Average stops vs Average fuel consumption

The results from the investigation regarding the objectives average stops pervehicle and average fuel consumption per vehicle are given below. The searchprocess took about 19.4 hours and resulted in a Pareto-front consisting of 2points. The five best fronts are presented in Figure 4.4 where one can seehow the fronts are moving towards the best front.

Figure 4.4: Obtained first five fronts of optimizing number of stops and fuelconsumption (Wuhan).

In Figure 4.4 one can see that even though the difference between the objec-tives is not that big, there is a trade-off between them. The small differenceindicates that the objectives are conflicting in a narrow space. In Table 4.3the strategies are compared with the real approximated signal.

Table 4.3 shows that the optimized values are significantly reduced with re-spect to the objectives. As one can see, number of stops are reduced with al-most 10 percent and fuel consumption with about 3 percent. Moreover, foundsignal strategies produce significantly better result of the impact measures


45 Case Studies

Signalcase


delay[h]

stops speed[km/h]

HC[g/km]

CO[g/km]

Fuel[g/km]

CO2

[g/km]

Real case[18, 78, 15, avg. 24.61 0.434 34.13 0.38 10.11 76.05 265.5615, 145] std. 0.59 0.007 0.19 0.014 0.12 0.88 3.94

minstops

[11, 94, 10, avg. 23.15 0.392 34.64 0.345 9.49 73.95 255.7513, 147] std. 0.68 0.008 0.22 0.008 0.08 0.66 2.83

minfuel

[11, 94, 11, avg. 24.94 .0.399 34.03 0.338 9.29 73.61 253.3610, 145] std. 1.25 0.013 0.38 0.01 0.13 0.62 2.61

Table 4.3: Comparison of environmental impacts of approximated real caseand extremes from stops and fuel consumption optimization (Wuhan).

compared to the real case. However when minimizing the fuel consumption,the delay is higher than the real case. Note that the standard deviation forthis measure is high, indicating widely spread values. By comparing the twoextremes one can see that even though the difference is not much, minimizingfuel consumption results in lower emission values than minimizing stops.

Average delay vs Average Fuel consumption

The results from the search of minimizing average network delay and aver-age fuel consumption per vehicle is presented below. The search took about19.1 hours to perform where a first front consisting of 6 points is found, seeFigure 4.5. As one can see from the figure, the first front consist of morepoints than the other fronts, indicating a good spread at the final front. Theresult implies that the objectives are conflicting.

A comparison of the extreme signal strategies with the approximated realsignal is given in Table 4.4. Here one can see that optimizing fuel consump-tion also result in better emission values. The best delay strategy decreasesthe network delay with about 22 percent compared with the real case, butproduce similar emission results.


46 Case Studies

Figure 4.5: Obtained first five fronts of optimizing network delay and fuelconsumption (Wuhan).

Signalcase


delay[h]

stops speed[km/h]

HC[g/km]

CO[g/km]

Fuel[g/km]

CO2

[g/km]

Real case[18, 78, 15, avg. 24.61 0.434 34.13 0.38 10.11 76.05 265.5615, 145] std. 0.59 0.007 0.19 0.014 0.12 0.88 3.94

mindelay

[11, 52, 10, avg. 19.15 .439 36.00 0.393 10.51 76.26 268.1811, 103] std. 0.68 0.013 0.26 0.011 0.327 0.956 4.212

minfuel

[12, 90, 10, avg. 23.32 .0.397 34.56 0.345 9.566 74.09 256.2411, 145] std. 1.09 0.006 0.42 0.01 0.12 0.72 3.87

Table 4.4: Comparison of environmental impacts of approximated real caseand extremes from delay and fuel consumption optimization (Wuhan).

Optimization of all objectives

When performing an optimization of more than two objectives, the result maybecome harder to grasp. Bear in mind that performing a three-objective opti-mization will have three different competing objectives, and will thus not givesuch an intuitive Pareto-frontier as with two objectives. Therefore, the resulthere will only present the best value of each objective found in the searchprocess. The search lasted about 19.2 hours and found a first front consistingof 5 points. Note that in Appendix A, the remaining strategies are presented.

The result has similar patterns as the two-objective optimizations presented


47 Case Studies

previously, where the most conflicting objectives are delay-stops and delay-fuel consumption. In Table 4.5 the points representing the best solution foreach objective are presented, where a comparison with the real signal canbe seen. Here one can see that this search provides less improvements inthe objectives, indicating that introducing more conflicting objectives givesinferior results. However, the overall result in improved.

Signalcase


delay[h]

stops speed[km/h]

HC[g/km]

CO[g/km]

Fuel[g/km]

CO2

[g/km]

Real case[18, 78, 15, avg. 24.61 0.434 34.13 0.38 10.11 76.05 265.5615, 145] std. 0.59 0.007 0.19 0.014 0.12 0.88 3.94

mindelay

[13, 57, 11, avg. 20.73 0.439 35.45 0.386 10.34 76.20 267.8213, 113] std. 0.32 0.005 0.15 0.011 0.165 0.85 3.65

minstops

[11, 98, 10, avg. 23.63 0.395 34.46 0.352 9.71 74.83 259.1214, 152] std. 0.59 0.007 0.23 0.011 0.246 0.71 3.54

minfuel

[12, 85, 13, avg. 24.23 .417 34.24 0.358 9.73 74.49 258.1210, 139] std. 1.05 0.008 0.32 0.015 0.063 0.28 1.37

Table 4.5: Comparison of environmental impacts of approximated real caseand extremes from optimizing all objectives (Wuhan).

4.1.4 Discussion

The evolutionary computing based stochastic search algorithm is success-ful in finding conflicting solutions between different objectives, thus givinga decision maker the opportunity to choose a strategy best suited for hisapplication. The search is also successful in finding strategies producing bet-ter results in the objectives, where the three-objective optimization foundstrategies superior in all considered measures.

Since the search process is time consuming, the upper limit of 20 generationsneeded to be set. Despite of this limitation, the process finds a good spreadof most conflicting objectives in the first front. It is notable that with ahigher generation number, more or better fronts may be found. As one cansee, the computational time varies much whether the emission model is usedor not. An increment of one generation without the emission model increasesthe computational time with about 12 minutes. With the emission model anincrement of one generation increase the computational time with about 58minutes.


48 Case Studies

As one can see from the results, the strategies obtained when minimizing thedifferent objectives are unequal and follow a similar pattern for each searchprocess. The strategies resulting in smallest network delay has a shorter cy-cle length, mostly due to the reduction of green time on the main road. Thiscan be due to when minimizing delay, the waiting time for the vehicles onthe minor roads affects the total delay more any other objective.

From the strategies resulting in smallest average number of stops, a longcycle time is obtained with a high green time on the main road. This canbe explained by the fact that this road has more traffic, and a red light willconsequently cause many vehicles to stop. Since a stop is counted when thevehicle velocity is zero, a red light will force a vehicle to stop once. Thestrategy of having long green time on road, thus short red time, will lead tofewer stops in simulation.

When fuel consumption is to be minimized, the strategy is similar to theleast stops strategy. This can be due to that it costs much energy to accel-erate a vehicle from stationary position to a given velocity. Also, fewer stopsshould result in less acceleration fluctuations and thus less fuel consumption.There does however exist differences between these objectives, implying amore complex behaviour of the fuel consumption against traffic dynamics.

The best strategy to reduce vehicle emissions is found when minimizing fuelconsumption. The reduction of CO2 is expected since the carbon dioxideis produced from the engine combustion. The emission of CO and HC arehowever more complex and are produced from incomplete combustion. Butsince all these emissions are deduced from the fuel combustion, it seems thatreducing fuel will also reduce emission giving the conclusion that saving fuelconsumption at the intersection has an obvious impact in emission reduction.


49 Case Studies

4.2 Connected Intersections – Hornsgatan

The second case study treats with two connected signalized intersections inStockholm, namely Hornsgatan-Ringvagen and Hornsgatan-Rosenlundsgatan.The main street here is Hornsgatan, a street connecting the entrances to thesouth of Stockholm between Liljeholmsbron-Hornstull and Slussen. It is ahighly congested street creating serious problems considering safety and en-vironment. As a consequence, in January 2010, the city of Stockholm bannedstudded tires on most of Hornsgatan to manage EU air quality directives.

The Hornsgatan-Ringvagen intersection, also referred as intersection 1, is acongested crossing with four arms. The north arriving direction has threelanes, one for left turn, one for driving through the intersection, and one forright and straight through. The south arriving direction also has three lanes,but here two lanes are for left turns and one is for right turn and throughthe intersection. The west arriving direction has a two lane approach whereone lane is for passing through and the other is for right turns. The eastarm, receiving arriving traffic from the Hornsgatan-Ronsenlundsgatan inter-section, also has two lanes. Here one lane is for passing through and right,and the other lane is only for straight through. About 270 meters east ofthe first intersection described above is the second intersection, Hornsgatan-Rosenlundsgatan, a three arm signalized intersection. The west arm, con-sisting of traffic from the first intersection, has two lanes, one for straightthrough the intersection and one for right turns. The east arm also has twolanes, one for straight through and one for left turns. The south arrivingdirection only has one lane, able to turn both right and left. The geometriclayout of the intersections are displayed in Figure 4.6.

Figure 4.6: Geometric layout of the cross Hornsgatan - Ringvagen (left) andHornsgatan - Rosenlundsgatan (right).


50 Case Studies

4.2.1 Modelling

The traffic network is modelled and simulated with VISSIM using data re-trieved from field measurements done by students in the course Traffic engi-neering at KTH. The traffic flow composition and distribution was calculatedby student using manual counting equipment and video cameras accordingto the instruction given in [18].

The traffic flow data for the intersections are given in Table 4.6 and Table4.7 below. The vehicle trajectories are inserted into VISSIM using its vehicleinputs and routes features.

Approach Driving direction Flow (vehicle/Hour)

NorthRight 40

Through 100Left 120

South

Right 70Through 60Left (1) 230Left (2) 160

WestThrough 380

Right 380

EastRight 130

Through (1) 280Through (2) 310

Table 4.6: Traffic flow in the Hornsgatan and Ringvagen intersection.

Approach Driving direction Flow (vehicle/Hour)

SouthRight 100Left 100

WestRight 120

Through 450

EastThrough 620

Left 120

Table 4.7: Traffic flow in the Hornsgatan-Rosenlundsgatan intersection.

To estimate vehicle fuel consumption and emission, the emission model CMEMdescribed in Section 2.2.1 is used. The calculations are performed with de-


51 Case Studies

Phase order Turning movements Cycle time Green timeP1 → 89 32P1 ← 89 32P2 ↑ 89 18P3 ↓ 89 15P4 89 32

Yellow time is 3 seconds

Table 4.8: Approximated signal timing of Hornsgatan-Ringvagen with turn-ing movements (times are in seconds).

Phase order Turning movements Cycle time Green timeP1 → 89 66P1 ← 89 66P2 89 14

Yellow time is 3 seconds

Table 4.9: Approximated signal timing of Hornsgatan-Rosenlundsgatan withturning movements (times are in seconds).

fault settings given in [28]. The vehicle composition in the network is VISSIMdefault settings, i.e. 98 percent cars and 2 percent HGV (truck).

4.2.2 Signal Optimization

The signal timing optimization are based on fixed-time approximations ofthe signal timing scheme from the City of Stockholm 2006, during averagetraffic flow conditions. The signal timing schemes are given in Appendix B.In Table 4.8 and Table 4.9, the approximated real signal plan and turningmovements used in the optimization are presented. The offset is approxi-mated to 19 seconds, calculated from the start of the green signal for theeast direction in the Hornsgatan-Ringvagen intersection to the start of thesame direction in the Hornsgatan-Rosenlundsgatan intersection.


52 Case Studies

Control parameter Control description

1Length of phase 1 of intersection 1

Determine when phase 2 starts of intersection 1


Determine start of phase 3 and end of phase 4 of intersection 1


Determine the end of the cycle length

Determine the end of phase 1 of intersection 2

4 Length of phase 4 of intersection 1


Determines when phase 1 starts of intersection 2

Table 4.10: Description of control parameters used in Hornsgatan optimiza-tion.

The chosen control parameters regulates each green time phase on both in-tersections, the offset value and the cycle length. To simplify the case, bothintersections have the same cycle length, giving a optimization problem withfive control parameters. The effects of each control parameter are given inTable 4.10, and a simple illustration of the signal plan with the control pa-rameters is given in Figure 4.7. As one can see, the parameters influence thewhole signal strategy.

Figure 4.7: Signal control description of case Hornsgatan.


53 Case Studies

To illustrate the optimization formulation, an optimization set up with theaverage delay and average stops as objectives is presented in Eqn. 4.2.

minS

(E(d(S, r)), E(s(S, r)) (4.2)

subject to49 ≤ C ≤ 144

10/144 ≤ g1/C ≤ 40/49

10/144 ≤ g2/C ≤ 30/44

25/144 ≤ g3/C ≤ 50/44

10/144 ≤ g4/C ≤ 30/44

10/144 ≤ g5/C ≤ 30/44

4∑i=1

gi + 24 = C

Here, E(d) and E(s) are the expected value of the delay and average stopsrespectively. The control parameters g1, g2, g3 , g4 and g5 are limited by thegreen split they control according to Table 4.10 and Figure 4.7.

This case study investigate the trade-off between the objectives presented inthe beginning of this section, i.e. average network delay, number of stops andfuel consumption. Also in this case, a compromise is needed between searchtime and convergence. In Figure 4.8 the convergence of a search process witha population size of 20 is presented. As one can see, after 20 generations onlyminor improvements are found. As a result, the presented search results areconducted with the following settings.

• population size of 20

• generation size of 20


54 Case Studies

Figure 4.8: Convergence of the objectives during evaluation generations inthe Hornsgatan case.

4.2.3 Results

The main result of this case study is presented below where each indepen-dent search displays the trade-off between two objectives. While controlparameters achieving compromise between objectives should be applied inreal decision making, the extreme solution from the estimated pareto front iscompared with approximated real case to analyse the advantages of the newstrategies. Here, the offset and cycle length will be shown together with themobility and impact measures. As in the previous case study, the additionalresults are presented in Appendix A.

Average delay vs Average stops

The best found fronts from the optimization approach regarding average net-work delay and average stops per vehicle is presented in Figure 4.9. Here onecan see how the fronts are moving toward the best front, where it stops andmultiplies. The search takes about 3.8 hours to perform and finds 8 pointsin the first front. The results shows that the strategies minimizing networkdelay and number of stop are not the same.

In Table 4.11 the extremes are presented. As one can see, the optimizationprocess finds better minimum values of the objectives compared to the real


55 Case Studies

Figure 4.9: Obtained first front of optimizing network delay and number ofstops (Hornsgatan).

case, with a decrease of about 4 percent for both strategies. The extremefrom the network delay finds the best emission and fuel measures of thesestrategies, where all of these measures are improved. The extreme fromaverage stops seems however to produce the worse result of the emissionmeasures, except for the NOx where it finds the best one.

Signalcase


offset/cycletime [s]

delay[h]

stops speed[km/h]

HC[g/km]

CO[g/km]

NOx

[g/km]Fuel[g/km]

Real case [19/89]avg. 22.14 0.883 27.75 0.093 1.95 0.267 78.30std. 0.58 0.018 0.27 0.0009 0.019 0.0026 0.58

minstops [17/106]avg. 26.30 0.850 25.46 0.094 1.96 0.261 82.04std. 0.66 0.014 0.28 0.0006 0.015 0.0011 0.39

mindelay [15/79]avg. 21.24 0.889 28.24 0.091 1.92 0.263 76.35std. 0.79 0.016 0.40 0.0007 0.015 0.0020 0.65

Table 4.11: Comparison of environmental impacts of approximated real caseand extremes from delay and stops optimization (Hornsgatan).

Average stops vs fuel consumption

The search process using stops and fuel consumption as objectives resultsin a nicely distributed first front, shown in Figure 4.10. As one can see, the


56 Case Studies

two best fronts contain many points indicating conflicting objectives. The 20generation search lasted about 19.4 hours and resulted in a first front consist-ing of 9 points. The difference between the best and worst point of the firstfront regarding stops and fuel consumption is 4.4 percent and 8.5 percentrespectively. The environmental impacts of the extremes can be comparedin Table 4.12.

Figure 4.10: Obtained first front of optimizing number of stops and fuelconsumption (Hornsgatan).

As one can see, the optimized objectives are reduced compared to the realcase. The extreme of fuel consumption obtains superior values on all mea-sures except average number of stops compared to the real case. Also in thiscomparison, the smallest NOx values is found for the strategy minimizingaverage number of stops.


57 Case Studies

Signalcase



delay[h]

stops speed[km/h]

HC[g/km]

CO[g/km]

NOx

[g/km]Fuel[g/km]

Real case [19/89]avg. 22.14 0.883 27.75 0.093 1.95 0.267 78.30std. 0.58 0.018 0.27 0.0009 0.019 0.0026 0.58

minstops [18/111]avg. 27.75 0.861 24.81 0.095 1.99 0.264 83.58std. 0.64 0.007 0.34 0.0005 0.013 0.0010 0.73

minfuel [16/79]avg. 21.21 0.901 28.26 0.092 1.92 0.265 76.48std. 0.52 0.009 0.23 0.0003 0.008 0.0015 0.33

Table 4.12: Comparison of environmental impacts of approximated real caseand extremes from stops and fuel consumption optimization (Hornsgatan).

Average delay vs average fuel consumption

The result from the minimization of average network delay and average fuelconsumption is presented below. The process took about 19.9 hours to per-form where only one point is found in the first front. In Figure 4.11 the sevenbest fronts are displayed, demonstrating how some fronts has several pointsand some fronts consists of only one point. The figure shows the difficulty tofind conflicting points thus indicating a convergence of these objective to asimilar solution. The result implies that minimizing network delay will alsominimize the fuel consumption.

In Table 4.13 the found point is compared with the real case. As one can see,the found strategy is superior in all measures. It should however be notedthat the improvement of the emission measures are below 2 percent whereasthe delay and fuel consumption improvements are about 5 percent and 2.8percent respectively.

Signalcase



delay[h]

stops speed[km/h]

HC[g/km]

CO[g/km]

NOx

[g/km]Fuel[g/km]

Real case [19/89]avg. 22.14 0.883 27.75 0.093 1.95 0.267 78.30std. 0.58 0.018 0.27 0.0009 0.019 0.0026 0.58

mindelay&fuel [17/81]avg. 21.03 0.881 28.42 0.092 1.92 0.264 76.12std. 0.37 0.012 0.23 0.0003 0.007 0.0015 0.44

Table 4.13: Comparison of environmental impacts of approximated real caseand best found point from delay and fuel consumption optimization (Horns-gatan).


58 Case Studies

Figure 4.11: Obtained first front of optimizing network delay and fuel con-sumption (Hornsgatan).

4.2.4 Discussion

The optimization framework leads to better traffic and impact performancein all cases in comparison to the approximated real situation. Minimizationof number of stops seems however to produce similar or inferior values of theother investigated measures, except for the emission of NOx. The strategyobtaining best NOx values is when the number of stops is to be minimized,thus indicating that its levels depends on how many times a vehicle needs tostops.

The study shows that the total average delay time for the network is morecorrelated to the fuel consumption. This might be that in a bigger net-work with many vehicles, a faster drive through is preferred to longer queueswhere stop-and-go vehicles consumes more fuel. As it can be seen, smallercycle length strategies are obtained when delay and fuel consumption areminimized. These strategies results in smoother flows with higher averagespeeds, also lowering the emissions of CO and HC. The obtained result ofonly one point may indicate that the search is not sufficiently long, and thatmore generations could find more solutions in the first front. But by ob-serving the result of the other search in this study, one can see that bothstrategies are very similar. It should also be noted that the greatest decreasein network delay and fuel consumption is found in the point obtained whenoptimizing both these objectives.


59 Case Studies

The reduction of the investigated measures is greatest for the delay and stops,where a maximum decrease of about 5 percent is found for average networkdelay and 3.7 percent for average stops per vehicle. These objectives arefollowed by a maximum decrease on fuel consumption of about 2.8 percent.The reduction of the emission measures does however not reach the samelevel, indicating that the emission does not have a simple dependence on ei-ther of the objectives or that the emissions does not have the potential to bereduced that much. This can be investigated by performing search processeswhere the emissions are used as objectives. It should be noted that the resultis statistically significant on the 5 percent level.

As one can see from the offset values, they do not change that much for eitherof the strategies, implying that similar offset should be optimal for signalcoordination regardless of minimization strategy. This can be explained bythat the offset is calculated from the static distance and the vehicular speedsbetween the intersections, thus it should not change unless there are dynamicspeed management between the intersections or there are many cars on thestretch limiting the vehicle speed. If however the search space is increasedfor the offset value, it might find other optimal offset solutions producing agreen wave on the other direction or finding a solution that compromises theflow on both directions.


Chapter 5

Conclusions andRecommendations

This study developed a methodology for optimizing traffic signal controlstowards a sustainable transportation system by integrating the VISSIM mi-croscopic traffic model, a NSGA-ii based stochastic optimizer and micro-scopic emission models. Additionally, two case studies where conducted toevaluate the effectiveness of the framework and search for trade-offs betweennetwork delay, number of stops and fuel consumption. The studies anal-ysed signal control strategies for different traffic situations where the firstcase study consisted of one single intersection in Wuhan and the other con-sisted of two coordinated intersections in Stockholm. For the Wuhan casethe vehicular emissions are calculated by the VT-Micro model and for theHornsgatan case CMEM is used as the emission model. In both cases, multi-objective optimization was performed to investigate the trade-offs betweendifferent objectives and demonstrate the best found solutions. Especially,the emissions from the best of each objective are presented to compare theenvironmental effect of these strategies.

In all investigated search processes, the framework was successful in findingstrategies reducing the objectives. As one can see from the Wuhan case, athree-objective optimization can reduce all investigated measures but doesnot find as good results as the extremes from the two-objective optimization.This indicates that with more objectives in the optimization process, a moreoverall solution will be found since more objectives are competing with eachother.

60

61 Conclusions and Recommendations

The results from the two different case studies show different trends for someof the investigated objectives. In the Wuhan case, one can see how the firstfront of the minimization of network delay and fuel consumption per vehiclecontains many points, indicating two conflicting objectives. The same objec-tives in the second case show converging solutions resulting in a first frontconsisting of one point. Moreover, by looking at the signal strategies onecan see that in the first case, a long cycle length is preferred when minimiz-ing fuel consumption whereas a short cycle length is preferred in the secondcase. This illustrates the difficulty and complexity in modelling vehicle fuelconsumption in urban environments. The strategies for minimizing networkdelay and number of stops seems to follow a similar strategy in both casesbut fuel consumption, as mentioned, does not.

The fuel consumption and emissions from vehicles are difficult to estimate,and to achieve accurate results a proper calibration is needed. The VT-Micromodel and CMEM are two models calculating the emissions in different ways.Even though these models are widely used, research has shown differences inthese methods. In [25], they show that CMEM may underestimate fuel andemission values for some driving states. This might also be a reason for thedifferences in the two case studies.

The optimization is a very time consuming process and, as one can see, thecomputational time significantly increases if the emission model is needed.This is due to the large vehicle record files from VISSIM that needs to bemodified to fit the emission inputs. For studies where more generations orlarger populations are needed, it might be necessary to implement the frame-work in a faster programming language such as C, C++ or Fortran, to achieveshorter computational times.

While the framework is successful in finding signal strategies that outper-forms the real approximated cases, some search processes only finds a fewsolutions in the first front. This limitation of solutions may be due to a prop-erty of the optimization process. As explained in Section 3.4, the diversitysearch (the crowding distance comparison) is only performed on the frontthat does not fit into the new population. This means that if the first frontdoes not contain enough solutions, it is not subjected to a diversity searchand all of these solutions are preserved. Of course the basic features of GAtries to find other competing solutions, but if too many fronts only contains afew similar points the crossover property may not produce sufficient diversity.


62 Conclusions and Recommendations

To summarize, the main conclusions and recommendations are:

• Traffic signal timing optimization strategy resulted in reduction of con-gestions, fuel consumption, and emissions when compared to the realcase.

• Apparent trade-offs existed between mobility and sustainability de-pending on the selection of objectives.

• More overall solutions will be found if more objectives are used in MOoptimizations.

• Fuel consumption and emissions are complex measure where differentsignal strategies are needed to minimize these in a single intersectionor coordinated intersections.

• It is very important to use calibrated models. In future research, cal-ibrated traffic model of Swedish intersections together with calibratedemission models with vehicles used in Sweden should be applied.

• The optimization process is very time consuming. For larger or morecomplicated networks, improvements of the performance of the softwareframework is highly recommended.

• The poor diversity of some solutions may be due to a NSGA ii property.Future research should investigate if other MO optimization methodsproduce more competing solutions in the first front.

Moreover, future research should investigate different levels of congestions toadequately appreciate the effect of the proposed framework. Also, other sig-nal control strategies such as vehicle actuated control should be investigatedwhere green time extension or maximum and minimum green time couldserve as control variables.


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Part I

Appendices

66

Appendix A

Additional Results

In this appendix the remaining result from the optimizations are given. Allsignal timing plans and objective functions from all fronts in the last popu-lation, calculated by the optimization process, are presented.

67

68 Additional Results

Traffic signal Objectives

Cycle length Phase 1 Phase 2 Phase 3 Phase 4 Delay Stops[s] [s] [s] [s] [s] [h]

142 11 89 11 12 22.6854 0.3952143 11 89 12 12 22.7622 0.3922126 10 73 12 12 21.0566 0.4058140 10 89 10 12 22.3484 0.3978103 10 53 10 11 18.9386 0.4348110 10 60 10 11 19.5 0.4198123 11 69 12 12 20.9946 0.4168142 10 89 12 12 22.7508 0.397156 15 96 12 14 24.856 0.4082113 10 60 12 12 19.9792 0.4254119 11 66 11 12 20.7586 0.425164 15 96 20 14 26.018 0.4186139 18 74 13 15 24.4322 0.4414163 15 96 18 15 25.5934 0.4132124 13 59 18 15 23.72 0.4696145 15 82 18 11 25.0824 0.4262113 11 60 11 12 20.0238 0.4258138 13 71 11 24 24.9362 0.453128 10 60 23 16 24.5206 0.4726131 12 63 17 20 24.7418 0.473

Table A.1: Traffic signal timing and resulting objectives from the optimiza-tion of network delay and number of stops (Wuhan).




Cycle length Phase 1 Phase 2 Phase 3 Phase 4 Delay Fuel Consumption[s] [s] [s] [s] [s] [h] [g/km]

103 11 52 10 11 19.1538 76.2648126 12 71 10 14 21.31 74.6245141 11 90 10 11 23.198 74.3056123 12 71 10 11 21.047 74.7333104 12 52 10 11 20.1812 76.2339142 12 90 10 11 23.3158 74.0885106 11 52 10 14 20.262 77.1952122 11 71 10 11 21.1012 74.7855124 11 71 12 11 21.3422 75.069124 12 71 11 11 21.403 74.9084125 12 71 12 11 21.694 74.9565125 11 71 10 14 21.3736 75.223129 12 56 23 19 25.7802 78.9107150 16 80 16 19 25.887 77.3823152 13 95 11 14 23.6732 75.537140 23 77 11 10 26.4968 76.5116128 12 53 22 22 26.453 79.6498137 12 63 20 23 26.5854 79.2287165 14 98 12 22 25.7282 75.5635166 20 98 12 17 26.1862 75.5575

Table A.2: Traffic signal timing and resulting objectives from the optimiza-tion of delay and fuel consumption (Wuhan).




Cycle length Phase 1 Phase 2 Phase 3 Phase 4 Stops Fuel Consumption[s] [s] [s] [s] [s] [g/km]

147 11 94 10 13 0.392 73.9455145 11 94 11 10 0.3986 73.607138 13 86 10 10 0.4172 74.3227148 11 94 11 13 0.3932 74.5946143 10 85 15 14 0.4062 74.7084156 12 99 12 14 0.3974 74.717152 12 96 10 15 0.3994 75.3477143 16 82 12 14 0.414 74.9331153 12 99 11 12 0.4012 74.9635138 12 82 12 13 0.4156 74.9388156 14 97 13 13 0.4064 75.0477154 12 97 13 13 0.4018 75.2335134 13 75 11 16 0.4244 75.8604148 15 83 17 14 0.4308 75.9576132 13 73 15 12 0.4428 76.5435135 16 75 15 10 0.4484 76.9652157 22 83 19 14 0.4526 77.6785138 18 65 22 14 0.4704 77.6672159 20 82 22 16 0.4616 77.8081158 17 82 22 18 0.4558 78.1009

Table A.3: Traffic signal timing and resulting objectives from the optimiza-tion of stops and fuel consumption (Wuhan).




Cycle length Phase 1 Phase 2 Phase 3 Phase 4 Delay Stops Fuel Consumption[s] [s] [s] [s] [s] [h] [g/km]

113 13 57 11 13 20.7254 0.4392 76.1997145 12 85 13 16 23.1382 0.4068 74.5439148 10 91 13 15 23.3522 0.4004 74.9161139 12 85 13 10 24.2306 0.4172 74.4938152 11 98 10 14 23.6316 0.395 74.8313125 11 72 11 12 21.3236 0.4174 74.8525127 12 69 17 10 22.9788 0.4384 76.0781136 13 77 14 13 23.014 0.4302 76.3472141 14 77 15 16 24.0754 0.4374 76.361143 16 75 19 14 25.0682 0.439 76.3773146 12 72 20 23 26.2816 0.4604 77.2818140 14 64 23 20 27.0136 0.485 78.4063146 10 88 12 17 23.3984 0.4072 74.8838178 19 97 18 25 29.6214 0.4414 77.8596164 19 86 21 19 27.6712 0.4484 77.4502163 12 99 14 19 24.9642 0.4052 75.1506138 13 75 13 18 23.907 0.4376 76.1364138 19 77 11 12 24.128 0.4304 75.7608147 17 85 12 14 24.2834 0.4208 75.3017166 21 91 20 15 27.6708 0.439 76.3609

Table A.4: Traffic signal timing and resulting objectives from the optimiza-tion of delay, stops and fuel consumption (Wuhan).



Traffic signal ObjectivesHornsgatan-Ringvagen Hornsgatan-

Rosenlundsgatan

Cycle length Phase 1 Phase 2 Phase 3 Phase 4 Phase 1 Phase 2 Delay Stops[s] [s] [s] [s] [s] [s] [s] [h]

101 28 24 25 30 12 76 25.0996 0.85587 26 12 25 30 12 62 21.5146 0.8656106 32 24 26 30 14 79 25.9732 0.854299 26 24 25 30 12 74 25.0198 0.855699 26 24 25 30 14 72 24.9266 0.8638106 32 24 26 30 12 81 26.3038 0.850497 24 24 25 30 12 72 24.8256 0.864879 19 11 25 30 10 56 21.2438 0.889489 28 12 25 30 12 64 21.925 0.871689 28 12 25 30 10 66 22.3092 0.869683 19 11 29 18 10 60 24.0764 0.938492 22 12 34 29 24 55 24.9446 1.015896 25 15 32 27 28 55 26.2266 1.053477 14 10 29 25 16 48 26.7508 1.056896 22 12 38 20 26 57 27.6846 1.0644103 25 15 39 25 28 62 28.8106 1.074290 17 17 32 27 24 53 30.0288 1.121102 19 26 33 19 22 67 34.7058 1.080891 17 20 30 20 29 49 30.8162 1.1748120 39 22 35 20 17 90 39.6234 1.1286

Table A.5: Traffic signal timing and resulting objectives from the optimiza-tion of network delay and number of stops (Hornsgatan).




Rosenlundsgatan

Cycle length Phase 1 Phase 2 Phase 3 Phase 4 Phase 1 Phase 2 stops fuel consumption[s] [s] [s] [s] [s] [s] [g/km]

106 33 24 25 28 13 80 0.8642 82.4726111 33 29 25 28 13 85 0.8608 83.580879 19 11 25 27 11 55 0.8998 76.588179 19 11 25 28 11 55 0.9012 76.475284 23 12 25 28 12 59 0.8832 76.93694 33 11 26 28 12 69 0.8692 79.34279 19 11 25 28 13 53 0.9076 76.451280 19 11 26 28 11 56 0.8926 76.690387 27 11 25 28 12 62 0.8694 77.372580 19 11 26 28 12 55 0.899 76.743880 19 11 26 27 12 55 0.8986 76.811887 27 11 25 27 13 61 0.8742 77.533787 27 11 25 27 12 62 0.871 77.5399105 27 29 25 28 13 79 0.8696 82.1799100 27 24 25 28 13 74 0.8698 81.334885 23 12 26 28 12 60 0.8842 77.441688 27 12 25 28 12 63 0.8734 77.771493 33 11 25 28 13 67 0.883 79.274793 33 11 25 27 11 69 0.8744 79.5014103 24 24 31 28 10 80 0.8962 83.9741

Table A.6: Traffic signal timing and resulting objectives from the optimiza-tion of number of stops and fuel consumption (Hornsgatan).




Rosenlundsgatan

Cycle length Phase 1 Phase 2 Phase 3 Phase 4 Phase 1 Phase 2 Delay fuel consumption[s] [s] [s] [s] [s] [s] [s] [g/km]

81 20 12 25 30 12 56 21.0262 76.117786 24 11 27 30 12 61 21.2792 76.655379 20 10 25 30 22 44 21.2856 76.860485 24 10 27 30 12 60 21.5904 76.938785 24 12 25 30 12 60 21.5858 76.999983 22 10 27 27 16 54 21.771 77.608985 24 10 27 27 12 60 21.8304 77.403983 24 10 25 30 22 48 21.6282 77.609781 20 12 25 30 22 46 21.9504 77.448784 22 11 27 30 22 49 22.0458 77.818387 21 10 32 30 12 62 22.641 77.714886 24 11 27 30 22 51 22.0808 77.811283 22 12 25 30 22 48 21.9918 77.884383 21 11 27 30 22 48 22.2488 78.03786 24 11 27 30 22 51 22.0808 77.8112104 25 19 36 17 24 67 42.4352 102.874120 25 25 46 26 17 90 32.6096 87.792690 21 20 25 17 11 66 27.6556 84.758988 21 11 32 30 22 53 23.9694 79.28592 21 19 28 17 29 50 28.5496 85.9689

Table A.7: Traffic signal timing and resulting objectives from the optimiza-tion of network delay and fuel consumption (Hornsgatan).


Appendix B

Signal plan Hornsgatan

Figure B.1: The city signal plan for Hornsgatan-Ringvagen.

75

76 Signal plan Hornsgatan

Figure B.2: The city signal plan for Hornsgatan-Rosenlundsgatan.


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