Express Minibus Services in the Lisbon Metropolitan Area ...martinez/PDF/FICO/Tese versão...

Express Minibus Services in the Lisbon Metropolitan Area:

an innovative concept and a feasibility analysis

Tomás Leite Clara de Sousa Eiró

Dissertação para obtenção do Grau de Mestre em

Engenharia Civil

Júri

Presidente: Prof. José Álvaro Pereira Antunes Ferreira

Orientador: Prof. José Manuel Caré Baptista Viegas

Co-orientador: Doutor Luís Miguel Garrido Martínez

Vogal: Prof. João António de Abreu e Silva

Novembro 2010

i

Abstract

The aim of this dissertation is to examine the viability of the implementation of a new

alternative intermediate transport mode in the Lisbon Metropolitan Area.

This new innovative system intends to combine the major strengths of both public transport

and private vehicles. Conventional public transport system can present efficient space and energy

consumption, while private vehicles have high levels of flexibility, are fast and always available.

This service will be mainly based on lower capacity buses which have the advantage of being

more manoeuvrable, more economic, flexible and are good on providing demand responsive

solutions.

For that purpose, this work presents a comprehensive methodology which encompasses the

potential demand estimation based on current transport demand data, and introducing spatial-

temporal constraint of the different service potential customers, the possible location of the

service’s stops, as well as, a detailed characterisation of the service operation, including routes

and schedules. The global objective of the model is to design a self-sustainable system that

maximises the operator’s profit and not to satisfy all the potential demand. All this procedure

includes a set of demand and supply parameters, which range of variation is analysed.

The obtained results suggest that this service might be significantly profitable to the operator,

for some of the demand scenarios tested and a good second best option mainly for private car

single drivers. The potential demand may be significant to produce a congestion relief on traffic

peak hours.

Keywords: Express Minibus service; demand responsive solutions; public transports; private

vehicles; linear optimisation.

iii

Resumo

O objectivo desta dissertação é estudar a viabilidade de implementação de um novo modo

alternativo de transporte na Área Metropolitana de Lisboa.

Este novo sistema inovador pretende combinar os pontos fortes do transporte público com os

do transporte privado. O transporte colectivo convencional pode apresentar um uso eficiente de

espaço e energia enquanto que os veículos privados têm um elevado nível de flexibilidade, são

rápidos e estão sempre disponíveis.

O serviço será baseado, principalmente, em autocarros de menor capacidade que têm a

vantagem de serem mais manobráveis, económicos, flexíveis e são adequados a sistemas de

procura variável.

Para esse efeito, este trabalho apresenta uma metodologia de avaliação que inclui a

estimação da procura potencial com base em dados de procura actual, onde se introduzem

restrições espácio-temporais do serviço para os diferentes clientes potenciais, a possível

localização das suas paragens, assim como, uma descrição detalhada dos parâmetros de

operação, nomeadamente, as rotas e horários de percursos. O objectivo global do modelo é

desenhar um sistema auto-sustentável que maximize o lucro do operador, e não satisfazer toda a

procura potencial. Todo este procedimento engloba um conjunto de parâmetros de procura e

oferta, cujo intervalo de variação é analisado.

Os resultados obtidos sugerem que este serviço pode ser significativamente rentável para o

operador para alguns dos cenários de procura testados, e uma boa opção, principalmente, para os

condutores de transporte individual. A procura potencial poderá levar a uma redução significativa

do congestionamento na hora de ponta.

Palavras-chave: Serviço de Minibus Expresso; sistemas de procura variável; transporte

público; veículo privado; optimização linear.

Express Minibus Services in the LMA: an innovative concept and a feasibility analysis

Acknowledgements

v

Acknowledgements

It is with great personal satisfaction that I may say that I have overtaken another big step of

my life.

The making of my dissertation was a really long process with a lot of obstacles. Obstacles that

range from: lacking of resources, changes in the theme, to computation problems and data

missing.

In all of this long and constructive process there were always some constants in the equation,

the people who surrounded me.

I would like to start by thanking to my supervisor, Professor José Manuel Viegas, for all of the

good advices, conversations, for constantly having an answer and for always being able to add

something new to my knowledge.

I would like to show my outmost gratitude to my co-supervisor, Luis Martínez, who ended up

becoming a big friend of mine. Without his guidance I would had never been able to finish this

dissertation. He was an excellent “teacher” with whom I learned a lot and I hope I can continue

learning with him.

To all of my colleagues of the room 4.25, Ana Raposo, Luis Caetano, Mariana D’Orey and

Tiago Ferreira, for being able to cheer me up when things weren’t going so well.

All of this process accompanied me everywhere, and sometimes it was necessary to bring

work and my mood, which was not always the best, home. Here, my parents Pedro and Ana, my

brother João, my sister Filipa and Sara were always comprehensive and supportive. A special

thanks, also, to all of my closest friends.

I would also like to acknowledge the contribution of the companies, EasyBus and Barraqueiro,

that through their operational managers, Ms. Leonor Gomes and Mr. Rui Gomes, respectively,

Acknowledgements

vi

provided me with some insightful data on the vehicle and operation information in the area of

this work.

My last thank goes to all the authors in whom I based my work. Without their knowledge, this

research would have never been possible.

Thank you all


List of Abbreviations

vii


ARTS Advanced Rural Transportation Systems

AT Activity Time

ATIS Advanced Traveller Information Systems

ATMS Advanced Transportation Management Systems

AVCS Advanced Vehicle Control Systems

CA Car Availability

CIVITAS CIty-VITAlity-Sustainability

CVO Commercial Vehicle Operations

DCCA Divide and Conquer in combination with Clustering Algorithm

DT Distance Travelled

ERP Electronic Road Pricing

EU European Union

FFT Fast Fourier Transform

GDP Gross Domestic Product

HVV Hamburger Verkehrsverbund

ICT Information And Communication Technology

ISTEA Intermodal Surface Transportation Efficiency Act

ITS Intelligent Transport Systems

LMA Lisbon Metropolitan Area


viii

MP Monthly Pass

NS Non Commute Subway Trip

NT Number of Trips

OICP Observation Interaction Clustering Problem

OP Orieentering Problem

RL Rodoviária de Lisboa

SOV Single Occupancy Vehicles

TDM Travel Demand Management

TOP Team Orienteering Problem

TSP Travelling Salesman Problem

TST Transportes Sul do Tejo

U.S. United States

VRP Vehicle Routing Problem

VRPTW Vehicle Routing Problems With Time Windows


Table of Contents

ix

Table of Contents

ABSTRACT .............................................................................................................................. I

RESUMO .............................................................................................................................. III

ACKNOWLEDGEMENTS .......................................................................................................... V

LIST OF ABBREVIATIONS ...................................................................................................... VII

TABLE OF CONTENTS............................................................................................................. IX

FIGURES ............................................................................................................................. XIII

TABLES .............................................................................................................................. XVII

I INTRODUCTION ............................................................................................................. 1

I.1. MOTIVATION ................................................................................................................... 1

I.2. OBJECTIVES ...................................................................................................................... 3

I.3. RESEARCH QUESTIONS ....................................................................................................... 4

I.4. METHODOLOGY AND STRUCTURE OF THE DISSERTATION .......................................................... 5

II STATE OF THE ART AND STATE OF THE PRACTICE ............................................................ 7

II.1. INTRODUCTION ............................................................................................................. 7

II.2. STATE OF THE WORLD: THE ROLE OF TRANSPORT IN THE URBAN CONTEXT ............................ 8

II.3. THE TRAVEL DEMAND MANAGEMENT APPROACH ............................................................ 12

II.3.1. Examples of Implemented TDM Measures ......................................................... 14

II.3.2. Intelligent Transport Systems ............................................................................. 17

II.3.3. Minibus Experiences ........................................................................................... 19

II.4. SUMMARY AND CONCLUSIONS ...................................................................................... 25

III STUDY AREA PRESENTATION ........................................................................................ 27

Table of Contents

x

III.1. INTRODUCTION ........................................................................................................... 27

III.2. CURRENT TRANSPORT NETWORK OF THE LMA ................................................................ 31

III.2.1. Bus Network ................................................................................................... 31

III.2.2. Ferry Network ................................................................................................. 31

III.2.3. Subway Network ............................................................................................. 31

III.2.4. Suburban Rail Network ................................................................................... 32

III.2.5. Road Network ................................................................................................. 33

III.3. CURRENT TRANSPORT DEMAND CHARACTERISATION ........................................................ 34

III.4. SUMMARY AND CONCLUSIONS ...................................................................................... 40

IV DESIGN OF A NEW SERVICE FOR THE LMA: THE EXPRESS MINIBUS ................................. 41

IV.1. INTRODUCTION ........................................................................................................... 41

IV.2. SERVICE ATTRIBUTES ................................................................................................... 42

IV.3. PRODUCTION MODELS ................................................................................................. 44

IV.4. ASSOCIATED COSTS ..................................................................................................... 44

IV.4.1. Human Resources ........................................................................................... 45

IV.4.2. Rolling Stock ................................................................................................... 46

IV.4.3. Fixed costs ...................................................................................................... 48

IV.5. PRICES ...................................................................................................................... 48

V MATHEMATICAL FORMULATION OF THE SEARCH FOR OPTIMAL EXPRESS MINIBUS

SERVICES FOR THE LMA ........................................................................................................ 49

V.1. INTRODUCTION ........................................................................................................... 49

V.2. BRIEF REVIEW OF THE MAIN OPERATIONAL RESEARCH PROBLEMS LINKED WITH THE CURRENT

RESEARCH 50

V.2.1. The p-median problem ....................................................................................... 50

V.2.2. Travelling salesman problem (TSP) .................................................................... 51

V.2.3. Vehicle Routing Problem (VRP) ........................................................................... 51

V.2.4. Team Orienteering Problem (TOP) ..................................................................... 52

V.3. METHODOLOGY FRAMEWORK ....................................................................................... 52

V.4. DEMAND ESTIMATION – PHASE 1 .................................................................................. 54

V.4.1. Introduction ........................................................................................................ 54

V.4.2. Decision Tree Estimation .................................................................................... 55

V.4.3. Simplified Delphi Method ................................................................................... 57


Table of Contents

xi

V.5. STOPS LOCATION – A “DIVIDE AND CONQUER” APPROACH – PHASE 2 ................................ 60

V.5.1. Introduction ........................................................................................................ 60

V.5.2. Clustering Algorithm (Divide) – Stage 1 ............................................................. 62

V.5.3. Definition of Stops’ Location (Conquer) – Stage 2 .............................................. 67

V.6. MINIBUS LINK LOAD ESTIMATION – PHASE 3................................................................... 70

V.7. MINIBUS ROUTING – PHASE 4 ...................................................................................... 72

V.7.1. Introduction ........................................................................................................ 72

V.7.2. Mathematical Formulation ................................................................................ 73

V.8. SUMMARY AND CONCLUSIONS ...................................................................................... 77

VI MODELLING THE EXPRESS MINIBUS SERVICE IN THE LMA ............................................. 79

VI.1. INTRODUCTION ........................................................................................................... 79

VI.2. ANALYSIS FRAMEWORK ................................................................................................ 79

VI.2.1. Express Minibus Tariff Systems ...................................................................... 80

VI.3. DISCUSSION OF RESULTS .............................................................................................. 82

VI.3.1. Demand Estimation ........................................................................................ 82

VI.3.2. Stops Location ................................................................................................ 89

VI.3.3. Minibus Link Load Estimation ......................................................................... 95

VI.3.4. Minibus Routing ............................................................................................. 97

VII CONCLUSIONS AND FUTURE DEVELOPMENTS............................................................. 107

VII.1. INTRODUCTION ......................................................................................................... 107

VII.2. STRENGTHS AND SHORTCOMINGS OF THE RESEARCH PRESENTED ...................................... 108

VII.3. POLICY IMPLICATION OF THE RESEARCH AND FUTURE DEVELOPMENTS............................... 109

VIII REFERENCES ........................................................................................................... 111


Figures

xiii

Figures

Figure I.1 - Dissertation structure ................................................................................................ 6

Figure II.1 - Population Growth (Source: (United Nations 2010a)) ............................................. 8

Figure II.2 - Night Sky in the world (Source: (Light Pollution Science and Technology Institute

2000)) ................................................................................................................................................. 9

Figure III.1 – The Lisbon Metropolitan Area .............................................................................. 27

Figure III.2 - Population evolution in the LMA (Source: (Martínez 2010) based on data from

Statistics Portugal – INE) .................................................................................................................. 28

Figure III.3 – Population annual variation in the different LMA municipalities (1991-2009)

(Source: Statistics Portugal (INE)) .................................................................................................... 29

Figure III.4 - Employment distribution in the LMA .................................................................... 30

Figure III.5 - Trip chain distribution (Source: LMA Mobility Survey, Tis.pt 1994) ...................... 30

Figure III.6 - Lisbon subway network in 2009 (Source: (Metropolitano de Lisboa 2010)) ......... 32

Figure III.7 – LMA current road network ................................................................................... 33

Figure III.8 - Mode distribution of commuting trips inside the LMA (Source: Statistics Portugal

– INE, 2001) ...................................................................................................................................... 34

Figure III.9 - Traffic flow on LMA's main roads at the morning peak hour ................................ 35

Figure III.10 - Average number of transfers for all LMA origins and a subset of the Lisbon’s

boroughs (Source: SCUSSE Project based on LMA Mobility Survey, Tis.pt 1994) ............................ 36

Figures

xiv

Figure III.11 - Average travel time for all LMA origins and a subset of the Lisbon’s boroughs

(Source: SCUSSE Project based on LMA Mobility Survey, Tis.pt 1994) ............................................ 36

Figure III.12 - Characterisation of the top twenty employment areas in the LMA (Source:

SCUSSE Project based on LMA Mobility Survey, Tis.pt 1994) .......................................................... 37

Figure III.13 - Parking pressure in the morning peak (Source: SCUSSE Project based on LMA

Mobility Survey, Tis.pt 1994) ............................................................................................................ 39

Figure III.14 - Parking pressure ratio between morning peak and night (Source: SCUSSE Project

based on LMA Mobility Survey, Tis.pt 1994) .................................................................................... 39

Figure IV.1 - Express Minibus maximum travel times ................................................................ 43

Figure V.1 - Methodology Flow chart ........................................................................................ 53

Figure V.2 - Decision tree ........................................................................................................... 56

Figure V.3 – The three scenarios of probability behaviour........................................................ 59

Figure V.4 - Elements of a barrier .............................................................................................. 64

Figure V.5 - "Labelled" and "scanned" nodes ............................................................................ 65

Figure V.6 - Barrier intersecting itself ........................................................................................ 65

Figure V.7 – Distance computation flowchart ........................................................................... 67

Figure V.8 - Logistic function chart ............................................................................................ 71

Figure V.9 - Regression to calibrate the inverse logistic function parameters to estimate the

demand-price elasticity .................................................................................................................... 73

Figure VI.1 - Distribution of the highest flows inside the LMA before behavioural constraints

(Concave demand scenario) ............................................................................................................. 83

Figure VI.2 Distribution of the highest flows inside the LMA after behavioural constraints


Figure VI.3 - Minibus mode share and its distribution through other transport modes (as trip

origin) ............................................................................................................................................... 88


Figures

xv

Figure VI.4 - Minibus mode share and its distribution through other transport modes (as trip

destination) ...................................................................................................................................... 89

Figure VI.5 - Clusters formed ..................................................................................................... 91

Figure VI.6 - Minibus' stops distribution for the LMA according to origin flows ....................... 93

Figure VI.7 - Minibus' stops distribution for the LMA according to destination flows .............. 94

Figure VI.8 - Distribution of the highest flows inside the LMA after the spatial constraints


Figure VI.9 - Manual selection of the Minibus' stops ................................................................ 99

Figure VI.10 - Example of a fixed tariff route ........................................................................... 101

Figure VI.11- Example of a taxi tariff scheme route ................................................................ 104


Tables

xvii

Tables

Table II.1 - Car ownership evolution in Europe (Source: 1990 and 2004 data (Allen 2006); 2007

data (The World Bank 2010)) ........................................................................................................... 10

Table II.2 - Car ownership in the World (Source: (The World Bank 2010)) ............................... 10

Table II.3 - CIVITAS past projects (Source: (CIVITAS 2010)) ....................................................... 15

Table II.4 - The Advanced Minibus Concept (Source: (Morlok et al. 1997)) .............................. 21

Table II.5 - Comparison between a feeder Minibus system and a conventional Bus system

(Source: (Morlok et al. 1997) cited in (Martínez & Geraldes 2005))................................................ 21

Table IV.1 – Nine Business Models Building Blocs (Source:(Osterwalder et al. 2005) ) ............ 42

Table IV.2 - Vehicles available (prices without Value Added Tax (VAT)) ................................... 47

Table IV.3 – Vehicle maintenance costs .................................................................................... 47

Table IV.4 - The best Minibuses in the Portuguese market ....................................................... 48

Table V.1 - Summary of the willingness to change to the Minibus service ............................... 59

Table V.2 - Probability of change according to the current transport mode ............................ 60

Table V.3 - Probability of change according to the trip purpose ............................................... 60

Table VI.1 - Summary of the fixed tariff calculation .................................................................. 81

Table VI.2 - Summary of the taxi scheme tariff ......................................................................... 82

Table VI.3 - Number of minibus customers according to each demand deduction .................. 85

Table VI.4 - Express Minibus service demand distribution in each municipality as origin ........ 85

Tables

xviii

Table VI.5 – Express Minibus service demand distribution in each municipality as destination

.......................................................................................................................................................... 85

Table VI.6 - Express Minibus service demand percentage from the initial trips database of each

municipality as origin ....................................................................................................................... 86

Table VI.7 – Express Minibus service demand percentage from the initial trips database of

each municipality as destination ...................................................................................................... 86

Table VI.8 - Statistical summary of the clustering procedure .................................................... 90

Table VI.9 - NSP and NST estimated values ............................................................................... 92

Table VI.10 - Summary of the stop's formation in the different demand scenarios ................. 92

Table VI.11 – Ratio between the demand on Phase 3 and Phase 1 of the model ..................... 96

Table VI.12 - Summary of the fixed tariff scheme for the concave demand scenario ............ 100

Table VI.13 - Summary of the fixed tariff scheme for the linear demand scenario ................ 101

Table VI.14 - Summary of the taxi tariff scheme for the concave demand scenario .............. 102

Table VI.15 - Summary of the taxi tariff scheme for the linear demand scenario .................. 103

Table VI.16 - Summary of the taxi tariff scheme for the convex demand scenario ................ 104

Table VI.17 – Estimates of number of passengers of the Express Minibus service during the

morning peak (Fixed Fare) .............................................................................................................. 106

Table VI.18 – Estimates of number of passengers of the Express Minibus service during the

morning peak (Taxi Tariff) .............................................................................................................. 106


Introduction

1

I Introduction

I.1. Motivation

In the last decades, several developed countries have acknowledged the existence of a severe

climate change problem generated by human activity, which has reflected on the creation of

international agreements to mend this problem, as the Kyoto Protocol in the 90’s and, more

recently, its review on the post-Copenhagen meeting.

The transportation sector is one of the economic activities more responsible for the increase

on pollution levels. According to (International Energy Agency 2009), the transportation sector, in

2007, was responsible for 23% of the World’s CO2 emissions and it is expected that this number

will rise up to 29% in 2030. However, there has been a strong direct link between the

transportation sector and the economic development (Grubb et al. 2006). Developed countries

have been tried, recently, to decouple energy consumption and economic growth. Yet, only some

countries have been able to weaken this relation, mainly due to a re-organisation of their

industrial and economic activity (i.e. Denmark), while in developing countries this reality is

different from case to case depending on local factors of each economy (Grubb et al. 2006).

The decoupling of this relationship has been pursued following two parallel paths: an increase

on the technology efficiency or by moving society towards more efficient organisation and

behaviour patterns.

The technological improvements may include the generation of cleaner energies,

improvements on the space impact of transportation modes and infra-structures, improvement in

the tele-activities, etc. The problem with these solutions is that they might not be effective

measures in a short or medium term.

There are several ways of improving the organisation and behaviour of the societies: a

rationalisation of the mobility prices internalising the external costs that are created, ensuring the

Introduction

2

access to mobility to the ones less able to pay, implementation of policies that stimulate the

increase in the transport load factor, changes in the land use policies towards a more efficient

territory occupation, logistic re-organisation, and the introduction of innovative transport

solutions.

All of these solutions have to reflect the current mobility needs providing an organisational

upgrade of the actual system. Within this context, the concept of second best option in the

transport mode choice arises. This term represents a solution which is both a near system

optimum (efficient for society) and a good solution for the individual and selfish selection.

The operationalisation of this concept in the transport sector may warrant an easier

acceptance of citizens and businesses of better solutions for the society.

Introducing the concept of second best option in the innovative transport solutions will allow

moving the transport sector, mainly in the urban context, towards more efficient and sustainable

answers.

This study will explore this concept by analysing the viability of a new innovative transport

service which explores current and emerging technologies and improves the organisational

standards of the tradition public transport services, allowing less intensive supply solutions and

more flexible and demand responsive.

The service that we propose in this study is a new low capacity bus service that will try to

attract users, principally, from private transport. These are the ones who are mostly responsible

for the generation of urban environmental problems. Yet, public transport users that might not be

satisfied with their actual level of service may also migrate to this new option.

In order to accomplish this, the service has to be attractive enough not only in terms of travel

time but also in aspects related to comfort, cost and flexibility.

Public transport, apart from the taxi, which might be included in the group of “individual

transport”, is not able to offer door to door services and present the same availability and

flexibility as the private vehicle does. This new service will try to get as close as possible to the

characteristics of a private vehicle, although it is conceived as operating in fixed routes and

schedules.

Therefore, this new service will be developed in a way that the travel times are close enough

to the ones verified in the private vehicle.


Introduction

3

As we intend to develop a self-sustainable system, without any type of subsidy, high

occupational levels of the vehicles is a requirement along its operation period, otherwise they will

not be economically sustainable. Also, we only intend to serve routes that will generate any

profit.

This system will be evaluated for the Lisbon Metropolitan Area (LMA), which will allow an

insightful analysis prior to the deployment of this type of service.

I.2. Objectives

The main objective of this dissertation is to present the concept of an innovative transport

service, which would use current technology and infrastructure, but that would address more

closely a significant segment of mobility needs of the population as a second best option. We also

intend to develop and apply optimisation tools that allow a preliminary test of its ability to

operate with great levels of efficiency and be economically self-sustainable. We will designate this

service as Express Minibus.

The assessment of the potential impact of the new service on modal shift and congestion

relief will also be a crucial point on this dissertation. When presenting a new service, it is decisive

to have a clear vision of how much will it cost and how the costs are supported. The fare system is

also a topic that must be covered. The lack of an appropriate survey prevented a realistic

estimation of the demand curve for different travel attributes, which range from the mode

attributes, to personal characteristics, mobility patterns and fare levels. Yet, we will assess

different tariff specification as well as modal shift estimates that can be assumed to be on the

safe side, i.e. rather conservative.

It is also the intention of this dissertation to study the potential demand of this new transport

service and its spatial distribution, and also to identify the most viable service connections within

the Lisbon Metropolitan Area (LMA).

To implement a new service there are certain regulations that have to be fulfilled.

The current regulation of public transport in Portugal is still based on a Law of 1945, and so

has no mention of intermediate public transport modes, not even of the concept of Metropolitan

Introduction

4

Area. So, when we are dealing with a service that has attributes that place it somewhere between

a taxi and a regular bus service, in vehicle dimension as well as on the specification of the services,

it is obviously beyond the scope of that regulation. However, since it is consensual that such

regulation has to be replaced soon (apart from other reasons) this incompatibility with the

existing framework should not deter this study.

Different options regarding service specification (from full supply side to full demand side)

have to be explored, in search of a pattern that can be attractive to a sufficient number of clients,

both in service and in price, with little or no need for subsidy.

The application area for the evaluation will be the LMA and there is the intention to identify

the corridors and sub-areas where the service could be implemented.

I.3. Research Questions

Many people, on a daily basis, complain a lot about the time they spend on traffic. New

service solutions are regularly tried by the Public Transport companies and the municipalities in

order to reduce the number of cars and to ease the traffic.

Some Minibus services have been implemented successfully around the world, although with

different service specifications that can bring this service closer to the private car. Furthermore,

there are few studies related to the Lisbon Metropolitan Area and there is no big relevance given

to this topic. Hence this study intends to encourage the research on this field by answering some

questions:

Will this new Express Minibus service be able to attract people from other means of

transport, in particular from the private vehicle?

If the service is able to attract customers:

Will it be economically viable?

In what areas is it profitable to operate?

What type of service is profitable? With few stops and long distances? With more

stops but shorter paths?

Which travel time difference, when compared with the private vehicle, is it tolerable

by the potential users?


Introduction

5

The following methodology intends to pursue the answer to these questions.

I.4. Methodology and Structure of the dissertation

The research methodology was developed in order to answer the questions that were stated

above. This dissertation was divided in seven main parts that cover different topics of the

developed work. The interaction between the different stages of the dissertation is represented in

Figure I.1.

After this brief introduction, Chapter II encompasses a brief description of the current state of

the art and practice, including the main policies developed by some countries to try to solve

traffic problems, the technologies behind the development of new innovative transport systems

and the current practices of services with similar specifications to the one here proposed.

Chapter III will present and describe the study area that is being targeted. We will give a

general overview of the current transport network of the LMA, as well as the current travel

demand and travel patterns within the study area.

Following this, a brief assessment of the service will be done through the description of the

main attributes of the system, like its specific characteristics, production model, associated costs

and prices.

Chapter V will describe the entire model that was developed, which encompasses various

traditional problems of Operations Research. Each part of the model is preceded by a brief

description of the components behind its formation, followed by a detailed presentation of all the

assumptions and the mathematical formulation of the algorithms. The modelling approach will

include four different phases that range from the estimation of the potential demand for the

service to the actual definition of the service deployment. This process will be done through the

introduction of a “Divide and Conquer” approach.

After the description of the problem formulation, we will finally present the results that were

obtained for the study area, for different demands and service specifications. All of the necessary

parameters’ estimations will be explained and presented and the results of each phase will be

discussed.

Introduction

6

Finally, conclusions will be drawn from the previous analyses regarding the viability, or not, of

the service as well as a reference to future improvements to the current research.

Figure I.1 - Dissertation structure


State of the Art and State of the Practice

7

II State of the Art and State of

the Practice

II.1. Introduction

This Chapter develops a comprehensive review of the current research and experience on the

Travel Demand Management (TDM) measures, and the current practice on the deployment of

small and intermediate bus services, designated in this dissertation as Minibuses. The current

review encompasses a considerable amount of different research fields, ranging from Urban

Economic Theory to Operations Research.

The Chapter will assess the following topics:

the current situation of urban transport (traffic congestion and transport mode share

assessment );

the main policies envisaged by the European Union (EU) and the United States (U.S.)

towards sustainable development within the urban transport sector;

TDM applications towards public transport enhancement;

the technologies that have been developing and allow the implementation of new

innovative transport systems;

Minibus’ system current deployment;


8

II.2. State of the World: The Role of Transport in the Urban

Context

Mobility is a central element of quality of life and it is the core principle for the organisation

and structuring of societies. But also an aggravating factor of many societal problems, mainly

amplified by such strong dominance of the automobile in the developed countries mobility.

The evolution of the population may increase the severity of mobility externalities. In every

continent except Europe, the world population is increasing and it is expected to remain like that,

as it can be seen below (Figure II.1):

Figure II.1 - Population Growth (Source: (United Nations 2010a))

Alongside this increase in the total number of inhabitants, it is being observed an urbanisation

process. It is expected, in 2025, that 56.6% of the population will be living in urban areas and

10.3% of it will be leaving in “megacities”1 (United Nations 2010b).

This strong urbanisation process has led to new arrangements in the structure of the

morphology of cities, characterised by a significant urban sprawl, as it can be seen in Figure II.2.

1 This term refers to cities with more than 10 million inhabitants.

10

100

1000

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1950 1960 1970 1980 1990 2000 2010 2020 2030 2040 2050

Ln (M

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on

s o

f In

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inta

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)

Years

World

Central America

South America

Northern America

Africa

Asia

Europe

Oceania



9

In the last decades, several cities around the world have been developing policies to fight

urban sprawl and develop more efficient spatial development of metropolitan areas which led to

the creation of new external agglomerations in the fringes of major cities, as an attempt of solving

the saturation of the main urban areas (Bontje & Burdack 2005).

Some metropolitan areas have envisaged this process and tried to plan polycentric

functionally independent areas in order to reduce big economic dependence on the centre and

daily mobility requirements. Most of these attempts have partially failed, usually because of the

inability of replacing the employment status of the major urban centres (Loo 2007). In some cases

not enough employment was created in the new urban areas and the commuting movements to

the city centre were increased (Tuppen 1979).

Figure II.2 - Night Sky in the world (Source: (Light Pollution Science and Technology Institute 2000))

This tendency for people to move to rather disperse locations creates major problems for

transport planners as they have the duty to offer equal and acceptable levels of service to all the

population. In small agglomerations, it is rather difficult to guarantee that acceptable transport

infrastructures and public transport services will be self-sustainable. So, many times, areas with

disperse occupation are left with lower levels of service leading to an increase in the private

transport share.

Even in places with a good land-use and transport integration and a high accessibility to heavy

transport modes, the private car mode share continues to be really high (Kitamura et al. 1997).

But it is not only a problem of poor quality in public transport services, as in the past years,

many factors have contributed to this high automobile dependency. Not only policies are


10

favouring the use of cars, with more road infrastructures, but also with the rapid development of

technology and increasing purchasing power so that, in many countries, the growth of the Gross

Domestic Product (GDP) is higher than the growth in the cost of transportation (Glaeser &

Kohlhase 2003), increasing the disposable income and thus making cars more easily available.

Proof of this is the increase in car ownership that is being verified (with only a few exceptions)

((Table II.1) and (Table II.2)).

Table II.1 - Car ownership evolution in Europe (Source: 1990 and 2004 data (Allen 2006); 2007 data (The World Bank 2010))

Table II.2 - Car ownership in the World (Source: (The World Bank 2010))

Country

Number of cars per 1 000

inhabitants

% increase 1990 to

2007 1990 2007

Austria 388 511 32 Cyprus 304 481 58

Czech Republic 234 414 77 Denmark 309 370 20 Estonia 154 390 153 Finland 388 483 24 France 414 498 20

Germany 445 566 27 Greece 170 429 152 Iceland 468 667 43 Ireland 226 437 93

Italy 483 601 24 Luxembourg 477 441 -8 Netherlands 367 441 20

Norway 380 458 21 Poland 138 383 178

Portugal 258 572(2004)

122 Spain 309 485 57

Sweden 419 465 11 Switzerland 442 524 19

United Kingdom 359 463 29

Country

Number of cars per 1 000

inhabitants

% increase 2005 to

2007 2005 2007

Australia 542 545 1 Brazil - 158

Bulgaria - 257

Canada - 372

Cape Verde - 67

China 15 22 47 Japan - 325

Romania 156 -

Russia 188 (2006) 206

South Africa 98 108 10

Turkey 80 88 10 Ukraine 118 128 8

United States 461 451 -2

Not only are the values of car ownership high but also its typical occupancy is very low.

According to (Shaheen et al. 1999), in 1990, the Single Occupancy Vehicles (SOV) represented 90%

of the work trips and 58% of the non-work trips in the USA.

In Europe, the average load factor is 1.6 persons per vehicle and if are only considered the

work-home trips, this load factor goes down to 1.1-1.2 persons per vehicle. These values have

been dropping along the years. In the early 1970s the value was 2.0-2.1 and in the early 1990s it

was 1.5-1.6. All thanks to “…higher car penetration (hence, more independent trips), greater use of



11

the car for commuting (where the load factor is the lowest), smaller household size, and more

single-person households.” (International Energy Agency 1997)

The more intuitive solution to solve this car use increase would be to always enhance the

road network capacity for it to be able to accommodate all the demand. Until the 80’s or 90’s

(depending on which country or region), the transport planning philosophy was to “predict and

provide”, where through predicting models transport planners estimated the dimension of the

needed infrastructures and provided the population with it.

But after a few decades, planners started to realise that if the road supply was enhanced, the

demand would also increase and the system would find a new equilibrium point at a higher level,

due to latent and induced demand. So, developing the network was not solving the supply side

problem in the long term.

It is also difficult to increase the existing network, not only because it is expensive but also

due to the lack of space and their environmental impacts. The solution has to involve some form

of demand management – overall reduction of mobility, different distribution in time and or in

space, transfers towards modes of higher efficiency in the occupation of space, higher occupancy

of vehicles, or a combination of these.

Hence, rather recently, transport planning evolved to a new approach designated as “aim and

manage”, where transport planners instead of only intervening in the supply side, started to take

into consideration the demand side. It was understood that the solution was to control the

demand and to search for new transport alternatives.

The United States of America (U.S.A.) is suffering from many transport and environmental

issues. Concerns about the sustainable development are increasingly under discussion in the

United States. The interest in sustainable development is being motivated by many factors: a

desire to reduce carbon loading (the U.S.A. produces 30% of the world’s total greenhouse

emissions and the transportation accounts for 25% for those emissions), worries about other

environmental harms, the effects of growing dependence on the automobile, rapid urbanisation

and sprawl development (Deakin 2002).

During the 90’s, the US did also acknowledge the problems described above and, in 1991, the

Intermodal Surface Transportation Efficiency Act of 1991 (ISTEA) was approved, and the new

transport mode solutions (carpooling and carsharing) and paratransit services were definitely


12

introduced. This act also limited the expansion of highways in order “…to solve the apparent

disparity between urban transportation system supply and travel demand” (Taylor et al. 1997).

Europe has also recognised this problem. According to European Commission (2007), the

congestion generated in Europe is responsible for the loss of 100 billion Euros per year (1% of the

EU’s Gross Domestic Product (GDP)) and urban traffic is responsible for 40% of Carbon Dioxide

(CO2) emissions and 70% of emissions of other road transport pollutants. All of this contributes to

climate changing/global warming, increased health problems, bottlenecks in the logistic chain,

high energy consumption, etc.

In the Green Paper on urban mobility (European Commission 2007), many solutions are

discussed in order to solve traffic problems. Some solutions that are presented include improving

the safety and attractiveness of other alternatives to the private car like, walking, cycling,

collective transport, motorbikes and scooters. Enhancing transfers from the private car to

different transport modes and intelligent and adaptive traffic management systems have also

proved to be efficient ways to deal with congestion problems.

All of these policies are trying to ensure equity among citizens to the access to all the

transportation systems available, giving a special attention to people with reduced mobility,

disabled people, children, etc. With the ageing of the population all over Europe, new smart and

more efficient transport solutions are becoming necessary.

A possible way of doing this is by using travel demand management measures.

II.3. The Travel Demand Management Approach

Travel demand management (TDM) measures can be defined as follows: “Transportation

Demand Management (TDM) is a strategy to reduce demand for single occupancy vehicle use on

the regional transportation network. As a regional strategy to improve transportation system

performance, TDM can reduce highway congestion and traveller delay; improve air quality; and

improve access to jobs, schools, and other opportunities.” (Rodriguez & Murtha 2009)

There are many ways to categorise TDM measures. Tanaboriboon (1992) cited in (Taylor et al.

1997) proposed 6 categories: traffic constrains, public transportation improvements, peak-period

dispersion, ride sharing, parking controls and land-use control techniques. Taylor et al. (1997) in



13

his work only considered four categories: travel constraints, stimulation of alternative mode

usage, alternative work arrangements and land-use planning.

A more recent categorisation was proposed by (Rodriguez & Murtha 2009):

Traveller information – users are provided with traveller information to support their

decisions and to choose the most adequate mode, route, time-of-day for the trip;

Employer and Campus Transportation Demand Management – this measure is really

useful for companies to attract and retain employees as they provide them

commuting trips, to reduce the on-side parking demand, to reduce taxes and other

expenses, to improve the environment and reduce energy consumption;

Auxiliary Transit Services – these services include: ridesharing for markets where,

when, or for whom traditional transit would not be economical desirable; and

services such as carsharing and “guaranteed ride home” that facilitate transit use;

Market and Financial Incentives – transportation is a derived demand because

“…demanding transport only reflects a demand for something else; transport is simply

a mean to overcome distance, a mean by which consumer and supplier - of whatever

good or service we are analyzing - can find each other on the same spot.

Consequently, the magnitude and shape of transport demand is basically an extension

of the demand for other product/service, meaning the benefits one can measure in the

transport market are no other than the benefits of consuming such product/service.

Transport demand is derived from other demands.” The general cost of travelling is

not the only one that has to be considered, also the time spent and other items that

influence the utility. Nevertheless, monetary prices have a great impact in travel

demand. For instance, when there was a gasoline price increase of 33.9% in 2008,

there was a substantial decline in highway traffic congestion in major cities of the USA

(congested hours fell from 5 hours, 25 minutes in 2007 to 4 hours, 21 minutes in

2008). There are many strategies like “Pay-as-you drive” and congestion prices.

The TDM definitions do not include the type of service that is being developed but it could be

inserted in the auxiliary transit services as it is an alternative to the private transport and is a

more efficient public transport solution.

Many countries have already implemented and tested several TDM measures.


14

II.3.1. Examples of Implemented TDM Measures

II.3.1.1. The European Experience

As we already mentioned, Europe has recognised its limitations and is researching for new

demand management policies. The areas that are being targeted go from promotion of walking,

cycling, collective transport use, enhancement of transfers from the private car to different

transport modes and development of intelligent and adaptive traffic management systems.

We now present some examples of traffic demand management measures and studies that

have been found in Europe.

The promotion of walking and cycling can be done through initiatives in cities, companies and

school but these modes have to be totally integrated in the mobility plan. Pucher and Buehler

(2008), in their work, present some good examples of how actual cycling practices have worked in

Netherland, Denmark and Germany, and use these examples as a promotion to the

implementation of this mode of transport in the U.S.A.

To reduce the car-dependent lifestyles many alternatives can be used either by reducing the

number of cars through the use of car-pooling and car-sharing or by providing the option of

“virtual mobility” (tele-working, tele-shopping, etc.). Another important issue that has to be

addressed when thinking on reducing car-dependent lifestyles is parking policies. The increase in

parking costs is an effective policy to control the number of private vehicles that are coming into

the city ((Marsden 2006) and (Viegas 2005)).

Intelligent Transport Systems (ITS) will also have an important role in traffic solutions. ITS

systems provide information to travellers and to supply tools for effective use of road space.

According to (European Commission 2007) an effective use of road space might increase its

capacity by 20 to 30%.

One measure that is suggested in (European Commission 2007) is the promotion of“...less

costly collective transport solutions, such as bus rapid transit, as an alternative to the more

expensive tram and metro systems. "Bus rapid transit" systems offer fast and frequent public bus

transport services along dedicated corridors, usually with stations that have metro-type

characteristics.”

CIVITAS



15

In order to provide cleaner and better transport in cities, the European Union started to co-

finance, in 2002, an initiative called CIVITAS (CIty-VITAlity-Sustainability).

According to (CIVITAS 2010), the objective of the program is “to promote and implement

sustainable, clean and (energy) efficient urban transport measures; to implement integrated

packages of technology and policy measures in the field of energy and transport in 8 categories of

measures; to build up critical mass and markets for innovation.”

This initiative supports and evaluates the implementation of ambitious integrated sustainable

urban transport strategies in many different cities, which range from public transport promotion

to the introduction of technical and organisational innovations.

Some of the programs that have been implemented in the past are summarised in Table II.3.

Table II.3 - CIVITAS past projects (Source: (CIVITAS 2010))

2002-2006 (CIVITAS I)

Cities Project

Barcelona

CIVITAS MIRACLES Cork

Winchester

Roma

Rotterdam

CIVITAS TELLUS

Berlin

Göteborg

Gdynia

Bukaresti

Nantes

CIVITAS VIVALDI

Bristol

Bremen

Kaunas

Alborg

Lille

CIVITAS TRENSETTER

Praha

Graz

Stockholm

Pécs

2005-2009 (CIVITAS II)

Cities Project

Preston

CIVITAS SUCCESS La Rochelle

Ploiesti

Genova

CIVITAS CARAVEL Kraków

Burgos

Stuttgart

Toulouse

CIVITAS MOBILIS

Debrecen

Venezia

Odense

Ljubljana

Norwich

CIVITAS SMILE

Suceava

Potenza

Malmö

Tallinn

II.3.1.2. The United States of America Experience

One popular TDM measure implemented in the United States and that has similar concepts of

the topic of this dissertation is paratransit.

“The Transportation Research Board’s Committee on Paratransit states that “paratransit”

means alongside transit. It includes all public and private mass transportation in the spectrum


16

between private automobile and conventional transit. Paratransit modes are usually demand

responsive and provide shared rides.” (Goodwill & Carapella 2008)

This term was first referred to around 1965, when suburbanisation was in full blossom. Due to

the wide spread of population around the main city, and being these suburbs scarcely populated,

the great variety of movement patterns generated became impractical to serve everyone with

acceptable frequencies with regular scheduled buses operating fixed routes. These zones started

to be dependent on private transportation. Those who were not allowed to drive or were unable

to afford a car, like elders and young people and people with low income jobs serving the affluent

families in those areas, started to be restrained to their own neighbourhoods.

A new transport service was needed: one that was as flexible as the private vehicle and also

had the economic and efficiency benefits of a public transport. “Thus arose a family of

transportation services collectively known as “paratransit” (the prefix “para” means “closely

resembling” or “akin to”).” (Orski 1975)

Paratransit is a rather new concept and most of the United States’ paratransit companies only

provide the obligatory elderly and disabled people services that are legally required.

Sometimes it is the most efficient way to provide a minimal transport service and it is not

seen as a service for profit.

There are several examples of paratransit services in different fields: community paratransit

service (Orski 1975); services to elderly or disabled people ((Simon 1998) and (Nelson\Nygaard

Consulting Associates 2007)); door to door services (Nelson\Nygaard Consulting Associates 2007);

feeder services (Weiner 2008); and Demand Responsive/Point Deviation Connector Service

(Weiner 2008).

Other examples of paratransit applications are presented by Mann (1974) cited in (Orski

1975) who proposed a new transportation concept called Auto Rapid Transit (ART). Basically, it

consists on a mix between car pooling and taxi services. Drivers travelling to and from their

workplaces would have a special license and an identification plate indicating where the vehicle

was heading to. This license would allow them to pick-up people at designated downtown pick-up

points and at suburban terminals and take them to the selected place. These extra costs would be

covered by a fixed fare.



17

II.3.1.3. Congestion Charging Around the World

Several cities have been implementing a TDM measure called congestion charging.

Congestion charging consists in charging vehicles that circulate inside a certain area of a city.

Singapore was the first city in the world to introduce this type of systems during the 70’s.

Singapore’s current system is characterised by having a lot of gantries spread inside a defined

cordon and each time a car passes under a gantry, according to the hour of the day, road users

are automatically charged. The Electronic Road Pricing (ERP) uses a short-range radio

communication system to deduct the charge from CashCards (Land Transport Authority -

Singapore Government 2010).

In London, congestion charges were first introduced in 2003 and it consists on a single tax of

£8 per day (9.15€) (£5 initially, equivalent to 7.12€) and it allows to enter and leave the city as

many times as a driver needs. This was the only solution found by the London Government to the

continuous growth of traffic on the busiest hours ((Transport Select Committee 2003) cited in

(Glaister & Graham 2005)).

In Stockholm, after a trial period from January 2006 until July 2006, congestion charging was

permanently introduced in August 2007. Instead of having a single fee, like London, charges vary

depending on the time of the day (Albalate & Bel 2009).

All of the cities are having very positive results in reducing their congestion despite,

sometimes, they are not very popular measures ((Transport for London (TfL) 2009), (Albalate &

Bel 2009)), (Menon 2002), ((Stockholmsforsöket 2006) cited in (Albalate & Bel 2009)) and

((Eliasson & Mattsson 2006) cited in (Albalate & Bel 2009))).

II.3.2. Intelligent Transport Systems

Some years ago, sophisticated TDM services were really difficult to be implemented as

information and communication technology (ICT) was not very developed and available at low

prices. Some of the main functionalities of TDM operations were either unfeasible or very

expensive to be made as it was impossible to coordinate everything.

With the increase in traffic congestion, in the 1960s, the concept of Intelligent Transport

Systems (ITS) was created with the purpose of making use of advanced information and


18

communication technologies to improve the performance, efficiency and safety in transport

systems. By adding information and communications technology to transport infrastructures and

vehicles it is possible to manage vehicles, loads and routes efficiently thus improving safety,

reducing vehicle wear, transportation times and fuel consumption.

The ITS program of the United States is divided into six major categories (Transit Cooperative

Research 2001):

Advanced Rural Transportation Systems (ARTS);

Advanced Traveller Information Systems (ATIS);

Advanced Transportation Management Systems (ATMS);

Advanced Vehicle Control Systems (AVCS);

Commercial Vehicle Operations (CVO)

The category that is related to public transport and to paratransit in particular, is Advanced

Public Transportation Systems (APTS).

According to (Casey et al. 2000), APTS technologies have the purpose to increase the

efficiency and safety of public transport systems and to provide a better access to information on

system operation. Not only it has the objective to offer better information for decision-makers to

make effective decisions on systems and operations but also to increase traveller’s convenience

and ridership.

Radin (2005) conducted a survey, which is done every two years in the U.S.A., to evaluate the

state of the existing and planned deployments of Advanced Public Transportation Systems (APTS)

technologies and services in the United States.

She identifies the following technologies as potentially supportive of ridership:

Electronic fare payment data used in route and service planning;

Electronic fare payment interoperability with other transit agencies;

Vehicles equipped with automatic vehicle location;

Vehicles equipped with automatic passenger counters;

Advanced traveller information systems.



19

Yet, some of these technologies are mainly linked with the improvement of the system’s

information, enhancing the quality of the service for current users, and promoting a more

efficient system operation, rather that directly impact the systems ridership.

In recent times, cell phones are starting to be used as a big source of life information. Many

applications have been developed to promote urban mobility and life organisation.

The penetration of Global Positioning Systems (GPS) and the use of mapping software are

enabling what is called “Location Based Services”, where a user with his cell phone can identify

theatres, museums, restaurants and even get directions to desired places. Companies that

provide these types of services are: Nokia (Nokia Maps), Google (Google Mobile), and Apple

(Iphone Travelocity).

Researchers from Nokia Research Centre Palo Alto, Navteq, and UC Berkeley with support

from Caltrans and US DOT, have developed a software which is capable to collect real-time data

from GPS-equipped mobile phones to estimate real-time traffic conditions (Work & Bayen 2008).

It is even possible, with some applications, to identify the nearest stop of the public transport

network.

The future of this area is highly promising and, given today’s demands, its development

rhythm is likely to increase.

II.3.3. Minibus Experiences

II.3.3.1. Introduction

With the growing and sprawling of cities, conventional public transport started to be unable

to satisfy, with good levels of service, all the mobility requirements. The suburbs as usually do not

have substantial transport demand, especially during peak hours, are left with minimal levels of

service. Usually, the headways of suburban bus services are 30 to 60 minutes.

Also, the need to provide a more personalised service that would cover passenger’s needs

and that would be attractive, encouraged transport planners to find new transport alternatives.

As a result, the Minibus concept was born.


20

A Minibus is defined as a motor vehicle similar to a conventional bus but with a reduced

capacity. “The size of minibuses has grown from 16-20 seats in earlier conversions to about 25-30

seats in more recent deliveries” (White et al. 1991). There are also smaller Minibuses with 9 seats,

including the driver. Of course, the bigger the Minibus gets the less manoeuvrable it is but the

comfort on-board increases.

As in any other transport mode there are various disadvantages and advantages.

One of the major advantages of a Minibus service is its flexibility both in time and in space

and its ability to perform a more personalised service. They are suited for dial-a-ride and “hail and

ride” services because Minibuses can adapt more easily to route changes.

Saying that a Minibus service offers better travel times might be misleading. Although

Minibus’ services might have fewer stops, have better acceleration and deceleration, their travel

time may be enlarged due to the increase in stopping time. Regular buses normally have two

doors, one used for entrance and another for exit. Minibuses have only one door which has to

deal with entrances and exits in succession.

Adding to this is the boarding difficulties that Minibuses present. Not only the entrance is

narrower than a regular bus but also its steps are higher. “Fowkes and Watkins (1986) report that

only 75% of the population can manage a 200 mm step. On minibuses a typical step height from

the ground level to the first step is 380 mm, with second and third steps of 220 mm and 115 mm,

respectively (Hawkins 1986).” (Banister & Mackett 1990)

Although Minibus services are able to provide a better service with a higher route coverage

and area penetration, to be able to fulfil a regular bus demand, more Minibuses would be needed

and that may cause more traffic congestion. This fact demonstrates that Minibus vehicles belong

to a different market niche than conventional buses. One possible application for this type of

vehicles, considering its attributes, would be to try to attract current private vehicle users which

might reflect on an improvement of traffic conditions.

Another possible solution to solve the need of many Minibuses to satisfy the peak hour

demand would be to coordinate Minibuses with traditional bus services by using the Minibuses as

the main feeders of a bus with a higher capacity. This inability to satisfy higher demands is the

reason that Morlok et al. (1997) use to justify the fact that Minibuses have not had a greater use

in the past.



21

According to (Banister & Mackett 1990), “A minibus requires the same number of staff to

operate it as a large bus, so the operating costs of a fleet of small buses is likely to be higher than

a fleet of large buses offering the same number of passenger seats.”

Morlok et al. (1997) agree with (Banister & Mackett 1990) when they say that: “The reasons

why small buses have not been used much in the past are several. These include the policy of

paying small bus operators the same wages as large bus operators. Since labor is the dominant

cost, the savings were minimal.” Morlok et al. (1997), in their work, summarise the Minibus

concept (Table II.4):

Table II.4 - The Advanced Minibus Concept (Source: (Morlok et al. 1997))

A small vehicle (10-25 seats) that has an AVMC System, or Advanced Vehicle Monitoring and Communications System

This vehicle is centrally controlled, and

its exact location is known at all times.

Serves a fixed route at higher speed than a conventional bus,

Or, can deviate from its route for door service

Operates at shorter headways because of lower cost per vehicle-mile

Can be integrated with conventional transit through: Passenger information Timed transfers Joint fares

Can be integrated with paratransit such as: Car pools Van pools

Reduces peak to base ratio when used in the base times, making transit more economical

Particularly applicable to low demand areas

More likely to generate new riders than buses

As Martínez and Geraldes (2005) sum up in their research paper, there are several advantages

when comparing Minibus service with the conventional Bus service (Table II.5).

The objective of providing a Minibus service is not to substitute the current bus services but

to try to recover the users that, due to low quality of the public transport service, had already

shifted to the private vehicle.

Table II.5 - Comparison between a feeder Minibus system and a conventional Bus system (Source: (Morlok et al. 1997) cited in (Martínez & Geraldes 2005))

Characteristics Minibus system

Conventional Bus system

Efficiency for medium or low levels of demands for transportation + -

Commercial speed thanks to less number of stops and maneuvering facility + -

Environment impacts (lower sound profile, less vibration, less visual impact) + -

On-board comfort + -


22

Service frequency + -

Service flexibility + -

Cost per place-km - +

Lifetime - +

Number of vehicles for the same demand - +

On-board capacity - +

II.3.3.2. Minibus Experiences in Great Britain

“Prior to the 1985 Transport Act there were about 40 locations served by over 400 minibuses.

By the end of 1987 a further 5200 minibuses were serving an additional 350 locations.” (Banister

& Mackett 1990).

With the deregulation of the passenger public transports, as the bus operators were allowed

to compete freely to provide services to the general population, the Minibus market has

expanded and new services have appeared in different parts of Great Britain.

Watts et al. (1990) cited in (White et al. 1991) studied 4 cities that substituted conventional

buses by Minibuses with capacity of 25 and 30 people:

One area that was analysed was located in Newbury. That part of the city had high

levels of car ownership and a lot of traffic and parking problems. The traditional bus

route that went through the city was replaced by a new Minibus system that was able

to duplicate the service frequency, from 30 minutes to 15 minutes intervals between

Minibuses. The number of trips increased 21% and the passengers, in a conducted

survey, expressed that the best benefit of the new service was its frequency;

Another line in Leeds was also analysed. The new service frequency was also doubled,

as it was in Newbury, but this time the increase in trips was only 5%. The best benefit

from the new service was also the improvements in the service’s frequency;

The route in South Yorkshire was characterised by a route that leaves from the centre

of the city and goes to a suburban mountainous area. The Minibus service kept the

same frequency (20 minutes) but the regular route size was increased by 20% and it

enabled a higher penetration in the city centre. The number of trips increased 12%

and its best characteristic was considered to be its ability to penetrate in narrower

areas;

Swansea was the other analysed area where several lines that connected the city

centre to the suburb were characterised. Both the penetration of the service and its



23

frequency were increased. The service frequency was increased to a bus every five

minutes. All this alterations produced a 51% increase in the demand and the

frequency was again considered the most valued attribute;

Although all the cases have shown an increase in the demand (number of trips and not

passengers), it is not referred if it was derived from the reduction in the use of private transport.

II.3.3.3. Minibus Experiences in Austria, Germany and Switzerland

In the mid-1960s, the public transport services in Hamburg were offered by many different

private and public companies which were not very well coordinated and integrated in terms of

routes, station stops, timetables and fares. According to (Doerel et al. 1993), cited in (Pucher &

Kurth 1996), “Getting from one end of Hamburg to the other could take up to seven different

tickets.”

This poor public transport service allied with an increase in car ownership and adverse

demographic trends was partly responsible for the 16% decline in total ridership in Hamburg from

1956 to 1965 (Pucher & Kurth 1996).

All of these critical conditions led to the creation of an entity, called Hamburger

Verkehrsverbund (HVV), in 1967, responsible for coordinating and integrating all of the public

transports in the region but still preserving the individual identities of the component firms. The

Verkehrsverbund was able to ensure “...that the customer needs only one ticket and one

integrated timetable for the entire trip from origin to destination.” (Pucher & Kurth 1996)

This system was so successful that it was spread to other German cities and also to Swiss and

Austrian cities. Although there are small variations in the procedures for revenue, cost accounting

and the relative importance of different levels of government, the structure of the Verbund

system is the same in virtually all cities of the three countries.

In this system, Minibuses (as well as diesel bus, trolley bus and van services) have an

important role of acting as feeders to the rail network, the main structure of the Verbund

systems.

This idea is complemented by (Morlok et al. 1997), where he states that, in Germany,

Minibuses “... are seen to be part of a hierarchal system ranging from taxis at the low capacity end


24

of the spectrum to rapid transit at the high. In general, minibus services are designed to provide

timed transfers for at least one location, and usually have integrated fare structures with other

operators.”

II.3.3.4. Minibus Experiences in Brazil

The current operating Minibus services, in its initial times, had an illegal genesis. Many

common citizens (many of them unemployed) saw a business opportunity in the inefficient public

transport service and bought their own private Minibus and started to appear in places with

strong concentration of people and offered transport routes to the city centres, in exact overlap

with the traditional bus routes.

Anyone willing to go to the Minibus’ destination would hail for the service and pay a fare.

These services became so popular that they grabbed a significant market share from the regular

Bus routes.

After complaints from the official transport operators, and to avoid continued entries into the

market, the Administration in many Brazilian cities has legalised these special Minibus services,

integrating them in the Brazilian public transport system, sometimes acting as feeders of the high

capacity buses, sometimes as express routes to the city centres (Bertozzi 2009).

II.3.3.5. Minibus Experiences in the United States of America

The Minibus use in the U.S. is widely spread. Lots of companies have been formed and are

responsible for paratransit services like picking up children from school, airport shuttles, elderly

transport, as it was already referred in previous Chapters, is also using Minibuses.

The more relevant services in the U.S. are services of scholar transport and single case

services. Companies like Kids Kab, Supershutle, Royal Transportation Co., Kitsap Transit, etc.,

provide these type of services ((Chandler 1993), (Morlok et al. 1997), (Kids Kab 2010), (Kitsap

Transit 2010) and (SuperShuttle 2010)).

II.3.3.6. Minibus Experiences in Developing Countries

Several developing countries cities created their initial public transport services giving

concessions of the system to developed countries conventional bus operators, which brought

with them high quality services guided by their standards. These operators used initially cross-



25

subsidisation between different routes, using high demand routes profit to cover the operation

costs of more remote routes.

Initially, these concessions were being lucrative but, with the increase in the demand and

spreading of the cities the operators did not have enough capital to expand their fleet and started

to use the same number of buses to cover a wider area. This was translated in a reduction of the

quality of service (less frequent services), which opened opportunities for small private companies

to provide unregulated Minibus services that completed the gaps in the major services.

As these services were illegal, they were able to practice unregulated prices that despite being

high, there was still enough demand available to pay them due to the lack of supply.

The government of these countries started to try to regulate this market but as there were

too many different companies, although prices were capped, there was not enough control to

actually force these tariffs. As stated above there were some cases that were able to integrate

these initial illegal services in the public transport system (Brazil).

All of this culminates in services with low quality and high prices and as these private services

continue to steal clients from the regular bus services these are becoming more and more

deteriorated and are starting to have great needs to be subsidised.

There are some exceptions, as in the case of Kuala Lumpur where, during the 1990s, the

opposite happened: Minibuses were replaced by conventional bus services (Iles 2005).

There are many local names for the use of Minibuses for paratransit services in developing

countries, such as: dala-dala (Tanzania); dolmus (Turkey); emergency taxi or ET (Zimbabwe);

jeepney (Philippines); matatu (Kenya); public light bus or PLB (Hong Kong); robot (Jamaica); silor

(Thailand); tempo (Bangladesh); and tro-tro (Ghana) (Iles 2005).

II.4. Summary and Conclusions

With this Chapter it can be concluded that, as time is passing by, with the current economic

and social situation, and taking into consideration the tendencies that are being projected, cities

are becoming saturated and new innovative measures are being needed to manage all the chaos

that is being generated in all transportation systems.


26

Governments are starting to give more attention to these mobility issues and TDM measures,

alongside with ITS solutions, are gaining more and more relevance.

We identified several policies developed with some measures implemented and others are

still thought and in early stages of operations. The CIVITAS program is a good example.

Regarding the Minibus services it can be said that there are many in developing countries,

frequently in unregulated markets, and also that are already some systems functioning in Europe

and that they are having some positive results. Moreover, we observed that the majority of the

existing systems are either for children’s services or occasional services. There are not those many

generalised Express Minibus’ systems.

Also, in all the reviewed literature, there is not a single reference of the effect that this type of

service towards private vehicle users, which is one of the major subjects that this study intends to

tackle: the attraction of the private car users, especially in densely populated areas, to a more

personalised, efficient and quicker service than the conventional bus and other mass public

transportation options.

Therefore it seems relevant to further explore this type of service which might become a

decisive solution for relieving some of the most pressing urban transportation problems, namely

congestion.


Study Area Presentation

27

III Study Area Presentation

III.1. Introduction

The study area that is being considered in this work is the Lisbon Metropolitan Area (LMA). The

LMA (Figure III.1) is divided into 18 municipalities: Alcochete, Almada, Amadora, Barreiro, Cascais,

Lisbon, Loures, Mafra, Moita, Montijo, Odivelas, Oeiras, Palmela, Seixal, Sesimbra, Setúbal, Sintra

and Vila Franca de Xira. In many studies the area of Azambuja is also considered as being part of

the LMA. So this work will enclose 19 different municipalities.

Figure III.1 – The Lisbon Metropolitan Area


28

The set of these municipalities are home to approximately, 2.8 million inhabitants and cover a

surface of 2,962.6 km2. Lisbon, the capital of Portugal, has the highest population share (21.05%)

and Alcochete the lowest (0.48%).

According to the census data of 2001, we can observe that after a period of huge growth of

Lisbon during the first half of the XX century, in the last decades, this tendency has been changing

and Lisbon’s population has started to decrease, while other municipalities, as Sintra, have been

experiencing a fast growth process. People are spreading out and the more outside areas are

starting to grow (Figure III.2).

Figure III.2 - Population evolution in the LMA (Source: (Martínez 2010) based on data from Statistics Portugal – INE)

A more detailed assess of the recent population evolution is presented in Figure III.3, where

we can identify a significant decrease in the rate of growth, especially inside Lisbon (with a

negative growth) and some municipalities closer to Lisbon (highlighted lines in the figure). The

ones that present a higher growth are the municipalities located further away from Lisbon (i.e.

Sesimbra and Mafra), or municipalities that have experienced a significant accessibility

improvement to the LMA centre (i.e. Alcochete).

0

100.000

200.000

300.000

400.000

500.000

600.000

700.000

800.000

900.000

1864 1878 1890 1900 1911 1920 1930 1940 1950 1960 1970 1981 1991 2001

Inh

abin

tan

ts

Census Years

Alcochete

Almada

Amadora

Azambuja

Barreiro

Cascais

Lisboa

Loures

Mafra

Moita

Montijo

Odivelas

Oeiras

Palmela

Seixal

Sesimbra

Setúbal

Sintra

Vila Franca de Xira



29

Figure III.3 – Population annual variation in the different LMA municipalities (1991-2009) (Source: Statistics Portugal (INE))

Although people are spreading out, the concentration of employment has not changed that

much in the past years. The main employment concentration continues to be in Lisbon and new

centralities close to Lisbon, as Oeiras (Figure III.4).

This suburbanisation process combined with the distribution of employment has led to a

dominance of simple commuting trips (those travelling between home and work or school) in the

travel patterns of the LMA, as it can be seen from Figure III.5. Yet, we should also acknowledge

the phenomena of underreporting of some sporadic trips in mobility surveys, which may bias the

obtained results towards simpler trip chains (Brög & Erl 1999).

According to (INE 2003), Lisbon is considered to be the main destination of all the commuting

trips representing the destination of 48% of all the commuting trips in Odivelas, 45% in Amadora,

43% in Loures and 42% in Oeiras. All of this represents an entry in Lisbon of 341,620 people for

work or study every day.

Lisbon has 7 main entry corridors: Cascais, Sintra/Amadora, Oeste, Norte, Ponte Vasco da

Gama and Ponte 25 de Abril which are responsible for the generation of the majority of Lisbon’s

traffic.

-3,00%

-2,00%

-1,00%

0,00%

1,00%

2,00%

3,00%

4,00%

5,00%

6,00%

1991 1993 1995 1997 1999 2001 2003 2005 2007 2009

Amadora

Cascais

Lisboa

Loures

Mafra

Odivelas

Oeiras

Sintra

Vila Franca de Xira

Alcochete

Almada

Barreiro

Moita

Montijo

Palmela

Seixal

Sesimbra

Setúbal

Azambuja


30

Figure III.4 - Employment distribution in the LMA

Figure III.5 - Trip chain distribution (Source: LMA Mobility Survey, Tis.pt 1994)

Being simple commuting the most common travel pattern in the LMA along with the

population sprawl linked with a preservation of employment concentration in Lisbon, has led in

recent years to longer travelling distances and travel times and greater levels of traffic congestion.

44,24%

11,10%

9,38%4,91%

30,36%

Simple commuting tour

Shopping home-based tour

Personal matters home-

based tour

Commuting with an

intermediate meal tour

Others



31

III.2. Current Transport Network of the LMA

This section presents a brief characterisation of the LMA transport networks, covering both

the road network and the public transport services. The public transport services that are worth

mentioning are: rail, bus, ferry and subway.

III.2.1. Bus Network

Bus services have also benefited from a considerable improvement in the last decades, at the

regional level with the creation and development of suburban bus services. The largest bus

operator in the AML is Carris, which is responsible for the operations inside Lisbon. Other

companies like Rodoviária de Lisboa (RL), Transportes Sul do Tejo (TST), Vimeca, Scotturb,

Transportes Colectivos do Barreiro, SulFertagus, are responsible for providing the services

between Lisbon and other municipalities and within each municipality.

III.2.2. Ferry Network

Before the construction of the rail connection between Lisbon and the South municipalities,

the main public transport connection between the two margins of the Tagus was the ferry system.

Currently, ferries are operated by Transtejo and Soflusa (the latter only on the Barreiro –

Lisbon line). One line between Cacilhas and Lisbon transports road vehicles besides passengers,

but the total volume of vehicles transported by ferry is less than 1% of those that use the two

existing bridges.

There are five main connections that connect both margins of the Tagus: one line which links

Terreiro do Paço to Montijo; three lines that link Cais do Sodré to Cacilhas, Seixal and Montijo;

and a connection between Belém to Trafaria which stops in Porto Brandão.

III.2.3. Subway Network

The subway network was the last network to be developed. It was inaugurated in 1959 and

since then it has been growing mainly within the city of Lisbon, and trying to meet the inner-city


32

transport demand. The operator responsible for the subway network in Lisbon is Metropolitano

de Lisboa (Figure III.6).

Figure III.6 - Lisbon subway network in 2009 (Source: (Metropolitano de Lisboa 2010))

III.2.4. Suburban Rail Network

Railways were the first main public transport in Portugal. In its early times, there was a big

investment in its development which led to the rapid construction of the first lines. Many of them

remain operating nowadays.

The most recent developments were the construction of the Oriente intermodal station, the

connection to the south end of the Tagus and the extension of the network to Setúbal.

The current configuration of the railway network in the LMA is mainly operated by CP,

although a private company (Fertagus) has been operating the south bank suburban rail, after

having won an international tender for this concession in the mid-nineties.

There are four main lines that are responsible for the mass public transport access to Lisbon’s

city centre: Azambuja, Cascais, Sintra and Eixo Norte-Sul. All of these lines have good connections

to the subway network as shown below.



33

III.2.5. Road Network

The LMA road network system has observed a very strong expansion in the last decades,

including the development of motorways, bridges, intercity and inner-city roads, which led to

major changes in the accessibility patterns inside the LMA and in its relations with the

surrounding regions. During the 90’s a comprehensive highway plan was delineated at the

national level to improve the connectivity and safety of the intercity and regional traffic: the Plano

Rodoviário Nacional 2000 (National Road Network Plan 2000). Several of these highways were

developed inside the LMA, improving the access to Lisbon city and many are promoting easier

movements within the LMA. The current network configuration is represented in Figure III.7.

Figure III.7 – LMA current road network


34

III.3. Current Transport Demand Characterisation

After the presentation of the different transport networks and their spatial configuration

within the LMA, we will now characterise the current transport demand.

The current transport demand mode share for commuting trips inside the LMA is presented in

Figure III.8. This demand is constrained by the existing supply for the different LMA connections.

The private car as driver is clearly the one with the highest share. This high percentage

suggests a mode share biased towards the private car. This fact is aggravated by a low car

occupancy rate of 1.13 (INE 2003), which leads to high levels of traffic congestion and its

associated externalities.

Figure III.9 presents the traffic loads of the main road network links, were we can observe

significant flows on the following road segments: Ponte 25 de Abril, Ponte Vasco da Gama, 2ª

Circular, A5 and IC19, which are the main enter corridors of Lisbon.

Figure III.8 - Mode distribution of commuting trips inside the LMA (Source: Statistics Portugal – INE, 2001)

This fact also has a significant impact on the efficiency of bus services which also rely on the

road network in areas that do not present dedicated corridors, considerably deteriorating their

level of service.

16%

22%

3%10%

2%

39%

5%

1% 2%

Walking

Bus

Subway or Light rail

Train

Employer or School Transport

Private car as driver

Private car as passenger

Motorbike or Bicycle

Other



35

The road network expansion produced higher levels of accessibility within the LMA, which has

promoted urban sprawl, leading to situations of low accessibility to public transport in remote and

low density areas.

Although the residential location has been spreading along the LMA in the last decades, the

activity centre of the LMA remains in Lisbon, which concentrates 43% (INE 2003) of the

destinations of commuting trips.

Being commuting trips the ones with the highest rate in the LMA, we have developed four

accessibility indexes for the top twenty employment areas (Figure III.12). Two of them show the

average number of transfers and travel time2 in public transport between these high employment

zones and the entire LMA, and the other two illustrate the same indicators but only between the

identified areas and the boroughs within Lisbon. All of the indexes were weighted by the number

of inhabitants in each source area to take into consideration the different importance that each

origin has (Figure III.10 and Figure III.11).

Figure III.9 - Traffic flow on LMA's main roads at the morning peak hour

2 The travel time includes in-vehicle travel time, out-of-vehicle travel time (access time, waiting time

and transfer time).


36

Figure III.10 - Average number of transfers for all LMA origins and a subset of the Lisbon’s boroughs (Source: SCUSSE Project based on LMA Mobility Survey, Tis.pt 1994)

Figure III.11 - Average travel time for all LMA origins and a subset of the Lisbon’s boroughs (Source: SCUSSE Project based on LMA Mobility Survey, Tis.pt 1994)

0

0,5

1

1,5

2

2,5

3

3,5

4

Ave

nid

as N

ova

s (2

6)

Ave

nid

as N

ova

s (2

5)

Ave

nid

as N

ova

s (2

7)

Car

nax

ide

(156

)

Alv

erc

a d

o R

ibat

ejo

(182

)

Po

rto

Sal

vo (1

62)

Setú

bal

(Ce

ntr

o) (

261)

Esto

ril (

280)

Alg

ue

irão

-Me

m M

arti

ns

(165

)

Lin

da-

a-V

elh

a (1

61)

Ae

rop

ort

o (1

09)

Ave

nid

a (8

2)

San

ta M

arta

(33

)

Ave

nid

a (8

4)

Ori

en

te (1

01)

Alg

és

(159

)

Qu

inta

do

An

jo (2

49)

Rio

de

Mo

uro

(171

)

AA

A (6

5)

Cas

cais

(279

)

Ave

rage

nu

mb

er

of t

ran

sfer

s

Transfers with origins in the LMA Transfers with origins only inside Lisbon

0

20

40

60

80

100

120

Ave

nid

as N

ova

s (2

6)

Ave

nid

as N

ova

s (2

5)

Ave

nid

as N

ova

s (2

7)

Car

nax

ide

(156

)

Alv

erc

a d

o R

ibat

ejo

(182

)

Po

rto

Sal

vo (1

62)

Setú

bal

(Ce

ntr

o) (

261)

Esto

ril (

280)

Alg

ue

irão

-Me

m M

arti

ns

(165

)

Lin

da-

a-V

elh

a (1

61)

Ae

rop

ort

o (1

09)

Ave

nid

a (8

2)

San

ta M

arta

(33

)

Ave

nid

a (8

4)

Ori

en

te (1

01)

Alg

és

(159

)

Qu

inta

do

An

jo (2

49)

Rio

de

Mo

uro

(171

)

AA

A (6

5)

Cas

cais

(279

)

Ave

rage

tra

vel t

ime

[min

ute

s]

Average Travel Time with origins in the LMA Average Travel Time with origins only inside Lisbon



37

Figure III.12 - Characterisation of the top twenty employment areas in the LMA (Source: SCUSSE Project based on LMA Mobility Survey, Tis.pt 1994)

Express Minibus in the Lisbon Metropolitan Area: an innovative concept and a feasibility


38

As it can be observed, when looking at situations where there are people coming from outside

Lisbon to the main Employment areas like Avenidas Novas (zones 26, 25 e 27), even though the

average number of transfers is relatively low (1.53, 1.11 and 2.05 transfers respectively) when

compared with the average for all the areas (2.25 transfers), this factor has a high impact on the

attractiveness of public transport use. According to a mode share discrete choice model

developed in the Lisbon Mobility Plan by Tis.pt, in 2004, the marginal effect of an additional

transfer on a journey represents a 68.8% in-vehicle travel time penalty.

Also the average travel times (56.83, 51.84 and 59.14 minutes), when compared with the

average of all the LMA (72 minutes), are low but if we compare them with the actual private

vehicle travel times they are much higher (33.88, 30.71 and 33.61 minutes)3. This is also

encouraging people to use the private vehicle.

Both average transfers and travel times values are reduced when we only consider origins

inside the Lisbon area. This reduction is more significant in the employment areas inside Lisbon

and is mainly due to the presence of a higher density of transport supply that covers most of

Lisbon’s main employment and origin areas. This poses a big constraint when one thinks on using

the public transport system, promoting substantially the private car use, especially for more

disperse and less public transport accessible locations.

We also assessed the parking pressure4 in the Lisbon municipality in the morning period and

the evening, in order to identify the main areas with parking problems, which might be potential

sources/destinations areas of the service under analysis.

As we can observe, the parking demand is relatively high during the morning peak hour (10

a.m.) in the main employment areas in the centre (Figure III.13). Analysing the ratio between the

morning peak and night (Figure III.14), we can observe that the parking demand in the main

employment areas during the night is much lower than during the day, showing a tendency for

mono-functional areas (i.e. Avenidas Novas) when compared to other more mixed areas

(residential and non-residential, i.e. Telheiras).

3 Data obtained through the project SOTUR - Strategic OpTions for Urban Revitalisation based on

Innovative Transport Solutions (Martinez & Viegas 2009). 4 Parking pressure is defined by the ratio between the parking demand and the parking legal supply

(not consider illegal which can be up to 32% during the day and 30% during the night (Câmara Municipal de Lisboa 2005)) at each hour of the day. This pressure was computed considering influence of the parking demand and supply of the surrounding blocks using a decreasing distance factor (inverse logistic function).



39

Figure III.13 - Parking pressure in the morning peak (Source: SCUSSE Project based on LMA Mobility Survey, Tis.pt 1994)

Figure III.14 - Parking pressure ratio between morning peak and night (Source: SCUSSE Project based on LMA Mobility Survey, Tis.pt 1994)



40

III.4. Summary and Conclusions

The majority of the outside areas of Lisbon are growing at a steady rate contrasted by a

decrease in the population of Lisbon and some neighbour municipalities. Nevertheless, the main

employment centres have not evolved in the same way and continue to be located in centre

Lisbon (apart from some exceptions like industrial and office parks outside Lisbon as Tagus Park in

Oeiras). All of this combined is leading to high volumes of commuting trips having Lisbon as the

main destination.

Although the LMA’s transport network has a considerable size and new transport solutions

are appearing regularly, the public transport service is still not able to provide an appropriate

coverage of all the LMA.

This is leading people to use their private vehicles, generating huge traffic congestions and

high parking pressures.

Within this context it seems appropriate to develop a new innovative transport service, like

the one presented in this work, to try to fill the gap between the mass public transports that are

only being able to provide an efficient service in densely populated corridors, and the current

transport demand.


Design of a New Service for the LMA: the Express Minibus

41

IV Design of a New Service for

the LMA: the Express Minibus

IV.1. Introduction

Prior to a new business implementation, a business is created to generate profit, or at least be

self-sustainable. In order to do this it is necessary to have a plan and a proper structure.

The appropriate tool to structure a business is a business model.

According to (Osterwalder et al. 2005), “A business model is a conceptual tool containing a set

of objects, concepts and their relationships with the objective to express the business logic of a

specific firm. Therefore we must consider which concepts and relationships allow a simplified

description and representation of what value is provided to customers, how this is done and with

which financial consequences.”

Osterwalder et al. (2005) divide the Business models into nine building blocks that should be

addressed when building a Business Model (Table IV.1).

In this Chapter, although the development of the Business Model is not the main topic of this

dissertation, we provide a short description of the key items in the Business model for this new

service, namely:

Service attributes, which define the product we are placing in the market;

Production model, which describe how the product or service is produced;

Associated costs, which encompass all the costs expected in the production of the

new product or service;

Prices, which defines the price setting method;



42

Table IV.1 – Nine Business Models Building Blocs (Source:(Osterwalder et al. 2005) )

Pillar Business Model Building Block

Description

Product Value Proposition Gives an overall view of a company's bundle of products and services.

Customer interface

Target Customer Describes the segments of customers a company wants to offer value to.

Distribution Channel

Describes the various means of the company to get in touch with its customers.

Relation Ship Explains the kind of links a company establishes between itself and its different customer segments.

Infrastructure Management

Value Configuration

Describes the arrangement of activities and resources.

Core Competency Outlines the competencies necessary to execute the company's Infrastructure business model.

Partner Network Portrays the network of cooperative agreements with other companies necessary to efficiently offer and commercialise value.

Financial Aspects

Cost Structure Sums up the monetary consequences of the means employed in the business model.

Revenue Model Describes the way a company makes money through a variety of revenue flows.

Most of the data used was collected through an interview to Ms. Leonor Gomes, the

responsible of a private Minibus operator, acting mostly in the school market, called Easy Bus; and

to Mr. Rui Gomes, a fleet manager of the largest Portuguese bus operating group, Barraqueiro.

The obtained data ranges from the fixed cost structure (vehicles acquisition and maintenance) to

the variable cost structure as staff.

IV.2. Service Attributes

As already mentioned, the main goal of this new Express Minibus service is to fill a market

niche that would be attractive as a second best option to private car users mainly for drivers with

unsatisfactory public transport options to perform their daily trips. As a consequence, if the

transfer volumes are significant, this system may help in reducing traffic congestion.

There is a considerable body of literature that analyses the main advantages of private car

over traditional public transport options (Hiscock et al. 2002). They can be mainly summarised in:

flexibility, comfort and availability.



43

The number of stops in each route of the proposed service is not a fixed parameter but it is

limited by the fact that the total time that a passenger will stay on board should be similar to its

travel time if a private vehicle was used. The definition of this parameter may be one the key

factor of success of the proposed system. We established the following tolerances to the total

travel time (Figure IV.1):

Figure IV.1 - Express Minibus maximum travel times

The service will be established in order to serve as many potential users as commercially

viable. When establishing the possible Minibus’ stops, we will define a decreasing function for

walking time acceptability characterised by an inverted logistic. Moreover, in a given Minibus

route there will be a minimum separation (distance) to be imposed between consecutive stops.

0

10

20

30

40

50

60

0 10 20 30 40 50 60

Exp

ress

Min

ibu

s M

axim

um

Tra

vel

Tim

e

Real Travel Time (TTreal) by Private Vehicle

TTreal + 5 5 + TTreal + (1/7) * TTreal

10 + TTreal + (1/9) * TTreal Travel Time by private vehicle



44

The capacity of the Minibus vehicles considered will vary between 8 and 24 passengers,

selected according to the estimated demand of each route. In a real world venture we must

recognise that there will be economic advantages in operating a fleet of all identical vehicles, but

this is only an exploratory study.

This being a more personalised service than a common bus service, and having profitability

requirements, all the routes must have sufficient demand. Based on this, the operating hours will

be dependent on the expected demand.

For the current study, we will focus on the morning peak period between, 07:00 a.m. and

10:00 a.m., to test the system viability. Nevertheless, we are aware that the system should have

similar services outside this period (at least in the evening peak) in order to have a better value

proposition and rolling stock usage. In between peaks, there is space to search for other types of

service with marginal profit but that will not be covered in this dissertation.

IV.3. Production Models

The production model that is going to be developed is based on an own acquired (or leased

on a long term contract) fleet with contracted personnel to perform the driving and managing of

the service. The maintenance part will be done by a specialised contracted company.

IV.4. Associated Costs

When developing a new service, it is crucial to define the costs incurred in developing the

service.

The cost structure knowledge may be a decisive factor when it comes to the profitability of a

new business. In this section it is intended to present all the costs associated with the

implementation of the Express Minibus service. The main items in which the costs may be divided

are: Human Resources, Rolling Stock, Fixed Costs



45

IV.4.1. Human Resources

The human resources item comprehends all the costs of the employees of the company. The

required employees to run this service are: back office staff and the vehicle drivers.

Back-office staff

The back-office staff would be responsible to coordinate all the bus fleet and to take care of

all the bureaucracies that a service like this requires. In average, a single worker is able to handle

5 vehicles in the busiest hour of the day5.

The fleet managers would have to have a good knowledge in how to handle with ITS systems.

There has to be a person responsible to coordinate, regularly, probably with the support of a

consultancy company, the analysis of the system’s demand in order to ensure that the system is

flexible and demand responsive. This analysis may result on modification in time schedules,

supplied routes or capacity changes of current routes or expand the system to new ones.

To estimate the average salary of a back-office employer we used the data from Statistics

Portugal (INE), where the average month net income of technicians and associate professionals is

1,035€ (second semester of 2010).

Drivers

As a Minibus consists in a vehicle of 8 to 24 seats, legally, a common driver’s license is enough

to operate these vehicles and this is one of the characteristics that make this service attractive.

The drivers would be responsible for the cleanliness of their allocated vehicle. It would be

necessary, according to previous experience, a cleaning session once a week6.

The average levels of absenteeism that are verified in this sector in other bus companies, like

Carris, are 5.4%.

To estimate the average salary of the drivers we used the data from Statistics Portugal (INE),

where the average month net income of technicians and associate professionals is 1035€ (second

semester of 2010).

5 Data obtained in the meeting with Easy Bus

6 Information obtained in the meeting with Easy Bus



46

IV.4.2. Rolling Stock7

The rolling stock would consist in Minibuses that, according to the current market supply,

would vary between 8 to 24 seats depending on the demand.

The costs associated with the vehicle would not only be the cost of its acquisition but also all

the maintenance costs they require and the costs with fuel and other consumables.

Before referring to the actual costs it is worth mentioning some important legal regulations

that limit the type of used Minibus:

There are 3 types of buses, independent of their size:

o Class I - Urban – An access to wheel chairs is obligatory and the bus has to

have, at least, 1/3 of seated places;

o Class II - Inter-Urban – Along the area with seated places there has to be a

corridor of at least 35 cm width if it is not carrying standing people or a 45 cm

width if there are people standing;

o Class III – Tourism;

Directive 2001/85/EC of European Parliament stated that only Buses with more than

45 passengers have to have two entry doors. This gives a big advantage to the

Minibuses because they gain 2 places for a given vehicle size;

The dimension used to calculate the capacity of standing places in buses is 1500 cm2

(about 6.5 pax/m2).

In the Portuguese market there are currently several options for Minibuses in different sizes.

Table IV.2 summarises all the options, their acquisition prices and who are the suppliers.

Currently in the Portuguese market, passenger transport operators do not usually rent

vehicles through the suppliers due to high prices charged. According to Mr. Rui Gomes, the most

common solution is the renting through an intermediate player.

7 All the data and information in this section was obtained in the meeting at Barraqueiro.



47

Table IV.2 - Vehicles available (prices without Value Added Tax (VAT))

Number of seats

Brand Cost of

acquisition

8

Ford Transit € 32,800

Renault Traffic € 30,100

Volkswagen Transporter

€ 37,364

Toyota Hiace € 33,100

168 Volkswagen € 67,120

Mercedes 519 XCDI € 68,280

249 Iveco 65 C18 € 74,500

Estimated maintenance costs, life spans and fuel consumptions are presented in Table IV.3:

Table IV.3 – Vehicle maintenance costs

Number of seats

8 16 24

Periodicity [thousands of

km] Cost


km] Cost


km] Cost

Maintenance

General Inspection (oil change included)

20 300 € 30 600 € 30 500 €

Brake Pads 40 127 € 30 95.35 € 30 89.50 €

Brake Discs 120 222 € 90 280 € 90 220 €

Tires 60 424 € 50 to 60 520 € 50 to 60 620 €

Motor 450 2,600 € 450 5,400 € 450 4,200 €

Battery 2 years 105 € 2 years 111.44 € 2 years 164 €

Consumption [litres / 100km] 10 to 12 14 to 16 16 to 18

Average Life Span [Years] 8 to 10 10 to 12 10 to 12

According to the opinion of Mr. Rui Gomes, a Barraqueiro fleet manager, and considering all

the limitations and offers in the Portuguese National market, the best options when thinking on

acquiring Minibuses are (Table IV.4):

8 The minibus with 16 seats may carry up to 20 people. It depends on the configuration: 14 seated

places + 4 standing places + wheel chair place + driver; 15 seated places + 4 standing places + driver. If the vehicle has 16 seated places it will change to class II vehicles, it won’t have the need to have a place for wheel chairs and its cost changes to 62,000€.

9 The minibus with 24 seats may carry up to 29 people depending on the configuration but with a

maximum of 24 seated places.



48

Table IV.4 - The best Minibuses in the Portuguese market

Number of seats Choice Comments

8 Volkswagen Transporter

Toyota Hiace

The Volkswagen is more comfortable but the Toyota is a better car, more economic, reliable and with a longer life span

16 Mercedes 519 XCDI The Mercedes is a more reliable vehicle

24 Iveco 65 C18 There are no other options in the Portuguese Market

IV.4.3. Fixed costs

As in any other service, there are costs associated with the office space, software and

hardware equipment, telecommunications, printers, furniture and everything necessary in a

traditional office. These costs were estimated to be between 12% and 15% of the Human

Resources in the Back-office.

Adding to this there would be fleet Parking costs associated. Depending on vehicle size and

location of the depot, this could cost between 50 and 150 Euros per vehicle per month.

A detailed estimation of these costs should be also carried out prior to the system

deployment.

IV.5. Prices

The price charged to a customer is, normally, a decisive factor when thinking on acquiring or

not a service.

In this dissertation two approaches are going to be tested:

A fixed cost, independent of the distance travelled;

A variable cost dependent on the number of kilometres travelled by the passenger. A

system much like a common taxi service;

Both of them will be evaluated and only then a decision, on which system should be adopted,

will be taken.


Mathematical Formulation of the Search for Optimal Express Minibus Services for the LMA

49

V Mathematical Formulation of

the Search for Optimal Express

Minibus Services for the LMA

V.1. Introduction

This Chapter intends to explain the modelling approach that was used to estimate the

potential demand and best configuration of an Express Minibus Service on the LMA, based on a

detailed assessment of the behavioural attitudes towards this new service and spatial-temporal

constraints.

The modelling approach used was based on traditional Operations Research linear

optimisation problems, with the necessary adaptations to the problem formulation.

The first part of this Chapter presents a review of the existing traditional Operations Research

problems and combinatory optimisation commonly applied to the transport sector that were used

as conceptual base to solve the existing problem.

Afterwards, there is an explanation of the adopted methodology and a detailed

characterisation of the implementation process.

Each subsequent section represents each step of the model built with a small introduction to

the bases on what it was created, followed by a detailed description of the actually used

algorithm.



50

V.2. Brief Review of the Main Operational Research Problems

Linked with the Current Research

There has always been a great tradition of using Operational Research as a tool to analyse

transportation systems problems. The most widespread formulations and algorithm, linked with

the current research, are presented next, including the contours of the definition, their history,

the main field of application and mathematical formulation.

V.2.1. The p-median problem

The p-median problem is a classical location optimisation problem in graphs were we want to

determine the p-nodes of the graph that minimise the distance to reach all the other graph nodes.

This mathematical formulation is used in problems where it is desired to define supply points and

location of facilities, where we want to minimise the sum of distances from each demand point to

its closest supplier. The p-median problem has existed, at least, since the 17th century where

Pierre de Fermat posed the 1-median problem with 3 demand points but its origin is still a matter

of debates (Rouskas 2009).

Kariv & Hakimi (1979) proved in their work that the p-median problem is a NP-Hard problem10

even in a simple structured network.

There are several adaptations of the basic algorithm for applications on discrete facilities

allocation. Teixeira and Antunes (2008) used an adaptation of the p-median problem to a

hierarchical facilities location model, also adding minimum and maximum capacity constraints and

not considering a value of p as the total number of open facilities. The authors acknowledge that

p-median capacitated problems may lead in some situations to uneven spatial solutions when the

capacity constraints are active in the problem.

10

NP-complete or NP-hard combinatorial problems have the property of having its complexity increase exponentially with the increase of the number of elements to be analyzed, which results in an increased computational time.



51

V.2.2. Travelling salesman problem (TSP)

The TSP consists in determining the minimum cost circuit passing by all the nodes in a graph,

only once. This circuit is known as Hamiltonian circuit (or cycle).

The TSP is one of the most widely studied combinatorial optimisation problems. Although a

book had already been published in Germany, in 1832, where it reaches the firs essences of the

TSP, according to (Lawler et al. 1985), the TSP was first referred to around 1931-1932 when

Merrill Flood publicised it in mathematical and operations research circles.

Laporte (1991) refers in his work many examples where the TSP was used for Computer wiring

(Lenstra & Kan 1975); Wallpaper cutting (Garfinkel 1977); Hole punching (Reinelt 1989); Job

sequencing; Dartboard design (Eiselt & Laporte 1991); Crystallography (Bland & Shallcross 1989).

V.2.3. Vehicle Routing Problem (VRP)

The VRP is an adaptation of the TSP to multiple vehicles with capacity constraints. In the VRP

there are a certain number of customers that have demand for goods. The VRP tries to minimise

the number of vehicles used to perform the duty, the total distance travelled or a combination of

both. The vehicles have limited capacity and can only perform one tour starting at a fixed depot.

Dantzig & Ramser (1959) were the first ones to solve this problem and referred to it as the

“Truck Dispatching Problem”.

Solomon (1987), in his paper, refers to a variation of the VRP, which was not, at the time,

widely studied, where time windows are introduced as a constraint to the routing problem. This

problem is designated as the vehicle routing problems with time windows (VRPTW).

What distinguishes the VRP from the TSP is the fact that in the VRP is necessary to use several

vehicles that fulfil the needs of their targets, while in a simple TSP the only objective is to find the

shortest way to visit each destination a single time.



52

V.2.4. Team Orienteering Problem (TOP)

Orienteering is an outdoor sport, normally practiced in a mountainous or heavily forested

area. The sport consists in reaching a final point and on the way pass by as many as possible check

points. This sport can also be played in teams, where the members of each team will have to

reach the same destination but have to do so in a way that they cover as many checkpoints as

possible without repeating them.

This problem was first defined by (Chao et al. 1996) and it is called Team Orienteering

Problem (TOP). The TOP is an extension of the Orieentering Problem (OP), where multiple tours

are solved instead of a single tour (Archetti et al. 2007).

The TOP is also considered a variation of the TSP.

What makes the TOP different is the fact that it does not have to visit all the needed

destinations in the solution. In a TOP the objective is to maximise the collected total profit, not to

deliver universal service the profit is obtained through the specification of a value to each served

client.

V.3. Methodology Framework

In this dissertation we intend to develop a comprehensive methodology which encompasses

several stages that go from an initial assessment of the potential demand of the new service, to

the detailed definition of routes, their vehicles specification and the stops’ schedules. The

different components of this all-inclusive model use some several algorithms of traditional

Operational Research and problems and combinatory optimisation.

The problem under analysis presents a high complexity and a large set of decision variables,

which range from identification of potential users and the most suitable location of the stops for

the vehicle, to the schedule of different Minibus routes. This problem can be considered a NP-

complete problem, which prevented us to use a single optimisation problem to include all the

strands of the problem.

The developed model phases can be summarised in:



53

An initial phase which assessed the behaviour of potential users in the study area,

using a decision tree model to estimate the predisposition of travellers to use this

new service, based on attributes of their current trip chain configuration and lifestyle.

This phase was designated as Demand Estimation.

After this phase we define the potential location of the stops of the system, based on

the estimated potential demand of the different places in the study area and demand

periods. This phase was designated as Stops Location.

The following phase of the model estimates the potential demand of each link

between the defined Minibus stops, and set the system potential O/D matrix. This

phase was designated as Minibus Link Load Estimation.

The last phase of the model, computes the most profitable Minibus routes for the

given O/D matrix, and defines the path of each vehicle and its occupation during the

analysis time period. This phase was designated as Minibus Routing.

The resulting modelling approach is presented in Figure V.1:

Figure V.1 - Methodology Flow chart



54

V.4. Demand Estimation – Phase 1

V.4.1. Introduction

In order to estimate the potential demand for the new Express Minibus service, we used a

synthetic travel simulation model developed and calibrated for the Lisbon Metropolitan Area

(LMA). The demand data used on this model is based on a mobility survey of the LMA performed

in 1994, with approximately 60,000 trips and 23,000 persons surveyed, and an activity database

of 2009 that was used to update the travel patterns observed in the initial survey. This is a rule

based model, which uses the reported travels by respondents and their connections along the

day, to disaggregate the total population of trips of the LMA based on the current activity

generation (trip generation coefficients for different activities along the day) and transport

network, generating specific origin and destination points, transport mode used and starting time

of each trip carried out (Viegas & Martínez 2010).

The synthetic travel model generated 4,827,642 daily trips inside the LMA, 1,126,230

during the morning peak period (7:00 am to 10:00 am), 38.4% of which in private car.

The initial filter performed to the database was the consideration of trips during the

morning peak (7:00 am to 10:00 am) and longer than 2,000 meters (this filter restricted the

number of trips to 761,592 trips). These filters derive from the nature of the proposed service

which is supposed to be a second best option to private car users, so it is imperative that it

consumes as little time as possible and is well differentiated from the service of regular buses. So,

all the trips that were below a distance of 2,000 meters were removed (too short for the Express

Minibus) as well as those for which the preferred mode was walking (still some above 2,000 m).

Also, we only considered trips that occurred in the morning peak period (7:00 am to 10:00 am)

because there had to exist sufficient demand for the service to be profitable and it was not

possible to analyse the entire day due to the excessive computing time it would entail. So, the

morning peak period was preferred to the afternoon one.

We also assessed the current O/D matrix flows using as base the Lisbon Mobility Survey of

2004 which presents a 66 zoning scheme of the LMA (Câmara Municipal de Lisboa 2005). We only

considered, for this study, the O/D pairs that had, at least, 1,000 trips during the morning peak.

This value was established in order to guarantee that there would be enough demand, even for a



55

small mode share of this service. This filter generated another reduction of trips to 431,141, which

represents 38% of the total trips, in the LMA, during the morning peak, where 51% of them are

done by private vehicle.

Of course that, all this demand will not shift to the new service. So, to estimate the

possible users we used an econometric demand estimation model. Due to the lack of a stated

preferences survey that included this mode as an option to calibrate a discrete choice model, we

followed a simplified methodology that tried to measure the impacts of some attributes over the

mode choice of the Express Minibus service. This methodology encompassed two stages: the first

one was to consider a decision tree model in order to estimate the variables that could have more

influence in the mode choice decision process of changing or not to the new service; and in the

second phase we used a simplified Delphi method11 to estimate the weight that each selected

attribute would have on the choice. The trip purpose and the chosen mode of the trip were also

taken into consideration, apart from the variables chosen in the decision tree model.

V.4.2. Decision Tree Estimation

Each obtained trip, from the initial survey, was characterised by a set of 25 different

attributes, which range from the current travel patterns to household characteristic and public

transportation accessibility. Some of these variables are: car availability, public transport pass

availability, number of trips in a day, number of transfers, and distance to stations of the subway

or commuter rail.

Prior to the development of the decision tree for the Express Minibus service, we

estimated a four level decision tree that better explained the current modal spit, considering

three main aggregated modes: walking, public transport and private car. This analysis was used to

give us some insights on the most relevant variables for travel mode choice. From the whole set

of available variables, we selected some from the previous analysis and others that were

envisaged as relevant attributes for Express Minibus service selection. The obtained tree is shown

in Figure V.2.

11

The Delphi method was developed at RAND Corporation in the 1950s and is an interactive forecasting method that relies on the knowledge of a board of experts on the theme that is being studied. The method consists in asking each expert, independently, their opinion and, through a guided discussion and an iterative assessment of opinions, reach a single value that might be assumed as the best estimate.



56

Figure V.2 - Decision tree

The variables that were used in the decision tree are:

Number of trips (NT), which stands for the total number of trips performed in the

day. This variable was considered to be the initial division on the decision tree and

categorised as: 2 trips, which resembles a simple commuting trip; 4 trips, which

resembles a commuting trip plus an extra pendular trip during the day; and other

than 2 or 4 that resembles non-commuting trips;

Monthly pass (MP), which represents the ownership or not of a monthly public

transport pass;

Distance travelled (DT), which accounts for the kilometres travelled during the whole

day. This variable was divided into 4 categories: less than 16.5 km, between 16.5 and

39.5 km, between 39.5 and 74 km, and more than 74 km; 12

Car availability (CA), which characterises the availability of a car or a motorcycle for

the individual daily use;

Activity time (AT), which represents the expected total daily activity time, considering

the time spent in work, in shopping, eating, etc., except travelling time. This variable

12

These intervals were obtained through the utilisation of clusters in the data from the surveys where we identified the limits of each cluster.

2 Other than 2 or 44

Distance travelled Distance travelled Monthly pass

Car availability Non commute

subway trip Car availability

Activity time Activity time

Mode Choice

Number of trips

Yes

Yes Yes

Monthly pass

Yes No

Monthly pass

Yes No

No

No No Yes No

<16.5 km > 74 km<16.5 km > 74 km

Distance travelled

<16.5 km > 74 km

< 5h30 > 10h30 < 5h30 > 10h30



57

was divided into three different classes: less than 5h30, between 5:30 am and 10:30

am, and more than 10:30 am; 12

Non commute subway trip (NS), which accounts for the existence or not of a non

commuting trip performed by subway in a day.

With this decision tree we were able to generate 112 different combinations that had to be

classified with a probability of changing or not to the Minibus service.

V.4.3. Simplified Delphi Method

As it was already defined, a Delphi method uses a focus group to reach a conclusion of what

values are considered to be significant. As Armstrong and Green (2005) refer in their work, Delphi

methods are good estimating processes when thinking on forecasting market sizes or market

shares of new products.

This process, when talking about a huge number of variables to estimate, might be very costly

and time-consuming. That is why we used a simplified version of the Delphi Method, skipping the

discussion part and only using a statistical analysis of the results that were obtained from each

individual answers in the focus group.

The simplified process was composed by a first part with a thorough presentation of the

Express Minibus concept, followed by a small survey which tried to depict the relevance of the

selected variables for the Minibus mode choice and their trade-offs. The survey also assessed the

probability of change to this mode according to the current mode choices and trip purposes.

From the survey we were able to extract an average of the rating of each selected attribute

and its interaction with the Minibus choice (positive or negative). In the case of the distance

travelled and activity time, we had already divided them in four and three categories,

respectively, so we also obtained the average of the ranking between the different classes.

We decided to compute a linear equation (RMinibus), considering the attributes as variables, in

order to estimate a classification for each situation obtained in the Decision tree model.

For the development of our equation, we needed the relative importance that each attribute

had according to the survey. For this, we standardised the average values of each attribute, rating



58

in a scale from 0.1 to 0.9. We used this scale in order to take into consideration that no attribute

should be discarded as well as no attribute should have an absolute dominance.

In the equation, each binary attribute was counted with the value of its coefficient rating with

weights 1 or 0 depending whether the answer was Yes or No, respectively. While, in the attribute

of distance travelled and activity time each of them was weighted using the measured values of

their attribute rankings and a correction according to the number of categories of each variable (3

and 4 respectively). Finally, for the number of trips in a day, which was perceived to have a

negative impact in the change to the Minibus service, though, this effect was discretised

considering a different effect of commuting tours (two trips for simple commuting tour and four

trips for commuting tour with an intermediate trip) and the other types of more complex trip

chains, which may be more unattractive for the Express Minibus service. With this consideration,

we performed a trial and error process trying to find plausible estimates, resulting in coefficient of

1 for 2 trips, 1.25 for 4 trips and 2 for the other cases. All of the variables contribution to the

linear equation followed the impact signs identified by the Delphi method.

So, the final equation for the definition of the value of each case is as follows:

(V.1)

(V.2)

The results of this equation were than standardised, and divided into five classifications,

ranging from A (very likely to change) to E (very unlikely to change), according to the five

percentiles. This classification relates to the probability of one being interested in the Minibus

service in each node of the decision tree.

The aggregate results for the distribution of the generated trips, according to this

classification, is presented in Table V.1 where the number of trips reported is that in the original

database morning peak trips in the LMA.



59

Table V.1 - Summary of the willingness to change to the Minibus service

A B C D E

Total Trips

% Total Trips

% Total Trips

% Total Trips

% Total Trips

%

Number of trips in each case

34,859 2.05 457,777 26.94 464,231 27.32 242,090 14.24 500,571 29.45

For the assignment of probabilities of change, three possibilities of transition were defined:

linear, concave and convex (Figure V.3).

Figure V.3 – The three scenarios of probability behaviour

Then, to calculate the possible flow of each O/D pair we used a simple expression where each

trip, according to its characteristics would be multiplied by the corresponding variables: trip

purpose, mode used and the value that resulted from its classification.

The summary of the probabilities reduction of the different modes and purposes is presented

in Table V.2 and Table V.3:

0

10

20

30

40

50

60

70

80

90

100

A B C D E

Pro

bab

ility

of

chan

ge [

%]

Linear

Convex

Concave



60

Table V.2 - Probability of change according to the current transport mode

Table V.3 - Probability of change according to the trip purpose

Mode Reduction

Ferry 0.900

Other Transport 0.420

Private car 0.750

Suburban Bus 0.750

Subway 0.300

Taxi 0.100

Train 0.600

Urban Bus 0.380

Purpose Reduction

Commuting (Leave home) 1.000

Commuting (Return home) 1.000

In service 0.000

Meal 0.075

Other 0.500

Personal matters 0.400

Pick/Drop familiar 0.050

Shopping/Leisure 0.200

V.5. Stops Location – A “Divide and Conquer” Approach – Phase 2

V.5.1. Introduction

In this phase, as it was already mentioned, we intend to estimate the location of the potential

Minibus stops.

To accomplish this, we used the census blocks as spatial disaggregation unit of the LMA,

which normally represents, at urban scale, a block of approximately 1 ha, while in rural areas this

value can go up to 100 ha. All potential travellers are aggregated into these spatial units that will

represent their origins/destinations. The LMA is divided into 32,763 blocks where only

approximately 22,000 have activity.

Due to the high complexity and combinatorial scale of the problem, owing to the existence of

too many census blocks, we opted to split the estimation of the Minibus’ stops into two different

stages: first the LMA physical area was divided into smaller sub-areas and only then the potential

stops were established. To do this we introduced an approach, based on the “Divide and Conquer”

heuristic.

The “Divide and Conquer” approach consists in taking a problem, divide it into smaller sub-

problems, solving them independently and combining these solutions to get a global solution. This

technique is the basis for many kinds of problems like sorting (quick sort, merge sort), multiplying

large number, syntactic analysis, searching (binary search depth-first search) and computing the

discrete Fast Fourier Transform (FFT) (Dinh & Mamun 2004).



61

The first person to define clearly “Divide and Conquer” algorithms was John Mauchly in 1946.

Nevertheless, the use of sorted lists dates back to 200 BC in Babylonia (Knuth 1998).

According to (Smith 1985) and (Rugina & Rinard 2001) the “Divide and Conquer” algorithms

have several advantages:

Their structure is really simple and efficient;

When the problem is divided into sub-problems, they tend to be independent of each

other therefore enabling the possibility of solving them independently, although they

are combined in the end;

The approach is computationally efficient. As long as a sub-problem can be fitted in

the cache of a computer the program reuses the cached data until its completion. This

is an important characteristic because it makes possible the solution of problems in

not so powerful computers;

The approach is really flexible and can be applied to various problems.

A recently proposed practice, to solve real sized problems, defined, sometimes, by its huge

dimension, which uses “Divide and Conquer” design is the combination of clustering techniques

and metaheuristics. This combination is formally called DCCA (Divide and Conquer in combination

with Clustering Algorithm)-based implementation (Dinh & Mamun 2004).

The only problem regarding this approach is the fact that, if the sub-problems are not

significantly independent, it might lead to considerable sub-optimisations. Hence, it should be

guaranteed that the interdependence level is minimal.

This technique of using clustering techniques to divide a problem into smaller ones and the

use of metaheuristics to find the solutions can produce satisfactory solutions to real NP-hard

optimisation problems in a short runtime. Examples of the application of DCCA are: Vehicle

Routing Problem ((Taillard 1993) and (Reimann et al. 2004) cited in (Dinh & Mamun 2004)) and

Travelling Salesman Problem ((Mulder & Wunsch 2003) cited in (Dinh & Mamun 2004) and

(Correia & Viegas 2010)).

In the following sections, we will describe how we computed the two steps of this approach:

the definition of the different sub-areas, clustering algorithm - Divide, and the estimation of the

potential Minibus stops, using an adaptation of a p-median algorithm - Conquer.



62

V.5.2. Clustering Algorithm (Divide) – Stage 1

The objective of cluster analysis is to group data with similar defined characteristics based

solely on the information in the data. “The greater the similarity (or homogeneity) within a group

and the greater the difference between groups the better or more distinct the clustering

(MacQueen 1967).”

Clustering techniques are very powerful methods to organise and sort data, so they are used

in numerous areas of study: Biology, Information Retrieval (Internet), Climate, Psychology and

Medicine, Business, etc.

We can identify in the literature two main types of clustering procedures:

Hierarchical Clustering Algorithms where in the initial state every element is a cluster

setting an optimal aggregation schedule for the different elements given an

aggregation method (i.e. distance between cluster groups or minimum variance

method (Ward Jr. 1963)) and variables’ distance measurement type;

Partitional Algorithms: these types of algorithms are used when it is computationally

impossible to build a dendrogram due to the big size of the problem. In partitional

algorithms the algorithm obtains a single partition of the data which is dependent on

the initial solution imputed to the problem.

According to (Murray & Estivill-Castro 1998), there are 3 ways of solving clustering problems:

1. Observation interaction clustering problem (OICP) where the objective is to minimise

total weighted difference in the assignment of observations to clusters, where the

distance to the furthest element of the cluster can be used as selection criteria;

2. Centre point clustering where the objective is to minimise the total distance of the

cluster’s objects to its centre;

3. Median clustering is really similar to the centre point approach but in median

clustering the cluster membership is defined based on assigning observations to a

representative observation which means that the potentials median are known a

priori as they correspond do the set of observations;



63

In this work, in the divide phase, we used the OICP adapted version, where the distance to the

other elements of the cluster is minimised, constrained to a maximum distance to any cluster

member and to the centre point.

In this dissertation we established three constraints to the cluster formation:

1. The number of objects (city blocks) in each group cannot exceed 200 elements;

2. The distance from each object to the centre of the cluster has to be less than 2000

meters;

3. The highest distance between members of a cluster has to be lower than 2500

meters.

In the literature we may find several procedures to compute the distance between cluster’s

elements (Hair Jr. et al. 2009):

Euclidean distance is the most famous one and may be also referred to as straight-

line distance. For a 2D space, It is calculated through the following equation:

(V.3)

The Euclidean distance is considered, by (Murray & Estivill-Castro 1998), to be one of

the most used method for automated pattern spotting and knowledge discovery in

spatially referenced data;

Squared (or absolute) Euclidean is similar to the Euclidean distance with the

difference that the square root is not calculated. This absence has the advantage of

speeding-up computation processes;

City-block (Manhattan) distance instead of calculating the hypotenuse of a squared

triangle, like the Euclidean distance, sums the size of the two sides of the right

triangle. It is a simpler procedure but, according to (Shephard 1966), it may lead to

invalid clusters if the variables are highly correlated and it is highly sensible to the

definition of the direction of the Cartesian axis;

Mahalanobis distance (D2) “is a generalized distance measure that accounts for the

correlations among variables in a way that weights each variable equally.”



64

The clustering variable used in this work was the Euclidean distance, but adding one feature,

namely the consideration of physical barriers to walking displacements.

The distance between the census blocks used in the clustering procedure was computed

considering the existence of physical barriers which might prevent a direct connection in space.

There might be census blocks that physically are close, but if they have physical geographic

separators placed on territory as railways, rivers, motorways, etc., as well as common urban

mobility barriers between them, that may limit their connectivity, not allowing straight

connection and demanding walking around obstacles. For this purpose, we considered as barriers

the existing transportation networks as highways, motorways and railroads.

Prior to a detail description of the algorithm, we will present some basic concepts that are

used in its formulation.

In the algorithm, a barrier consists of a physical object that does not allow for people to cross

it. A barrier is formed by a set of linear segments that are linked together and only allow the

passage of people on the barriers’ end points (identified as End in Figure V.4).

Figure V.4 - Elements of a barrier

The algorithm originally presented in (Viegas & Hansen 1985) uses a shortest path algorithm

formulation (Djisktra algorithm), where the graph is not an input and it is formed during the

algorithm run. The graph is formed initially only by the origin and destination points, and during

the simulation the barriers ends, and the intermediate barriers segments points may be added as

vertices in the graph. During the model run, when the graph is being expanded, the graph node

can be characterised in two different types:

A “labelled” node, which is a node that has already been tried to reach by the current

origin in the algorithm and added to the algorithm graph (Figure V.5);



65

A “scanned” node, which is a node that was already “labelled” and has a direct

connection to the origin or an already formed barrier free connection to the origin

point, (Figure V.5);

Figure V.5 - "Labelled" and "scanned" nodes

The algorithm flowchart is presented in Figure V.7 and its workflow can be described as

follows.

Given two nodes, an origin and a destination node, the algorithm tries to make a direct

connection between them. If the connection does not intersect any barrier, the algorithm

retrieves their Euclidean distance. Otherwise, if the connection intersects one or more barriers,

the algorithm will generate new nodes to the graph that correspond to the ends of each barrier it

has intersected, and introduces them in a “labelled” nodes array.

It might happen that, when the algorithm tries to reach its destination through the end of a

barrier, it intersects the barrier to which the origin point belongs to (Figure V.6). In this case, all of

the ends of the segments of the intersected barrier will be added to the “labelled” nodes vector

and have to be tested. To access each end point of the added segments, the algorithm contours

the barrier going along the different segments until it reaches the target node without

intersecting the barrier.

Figure V.6 - Barrier intersecting itself

Origin

Destination

Impossible to reach the destination. Two new nodes are “labelled” (blue nodes)

Origin

Destination

Node 1 is possible to be reached. Node 1 is marked as “scanned”.

Node 2

Node 1

Node 2

Node 1

Phase 1 Phase 2



66

After having defined all the ends of the barriers between the origin and the destination

nodes, the algorithm tries to reach the first node from the “labelled” nodes array of the graph

from the origin. Two things might happen when trying to reach a node: there is no barrier

between them and the target node is added to the “scanned” nodes array and the distance from

the origin to the node is updated if the distance is less than the current estimate; or, there is one

or more barriers between these new pair of nodes and so, the algorithm adds more nodes to the

graph that become new possible destinations of the current origin and labels them as possible

targets.

This process is repeated until all possible nodes have been “labelled”. Afterwards, the

algorithm advances for the first possible “scanned” node and repeats the all process again.

The algorithm stops when the number of “labelled” nodes is equal to the number of the

“scanned” nodes already used in the algorithm. After this procedure, it is possible to know the

shortest distance between the two initial nodes.

This procedure has enabled the calculation of the distance between each element of a cluster,

taking into consideration the presence of physical barriers. With this algorithm to assess the

distance between members of the clusters, we were able to run the clustering procedure using

the constraints that were presented above.

As it was already mentioned, the objective of the clustering was to reduce the size of the

problem when trying to establish the potential Minibus’ stops. The resulting clusters’ structure

may relate to the LMA urban structure and its different agglomerations. After the application of

this procedure to reduce the size of the stop’s location problem, we are now able to determine

their location within each group and aggregate the results to reach a global solution.



67

Figure V.7 – Distance computation flowchart

V.5.3. Definition of Stops’ Location (Conquer) – Stage 2

V.5.3.1. Introduction

The localisation of the stops was based on an adaptation of the p-median algorithm where the

p value is not set and a cost of stops’ formation is added to the objective function, and instead of

minimising distance to the p nodes, the algorithm maximises the profit that can be generated by

that stop creation, measured by the number of people that can potentially use that stop.

This step of the model will be used to define the location of the potential stops of the Minibus

which are to be reached, by the users, on foot. Therefore, in the definition of the stops, it was



68

considered that a user would be no further than 1250 meters (approximately a 15 minutes’ walk)

from the stop.

In order to ensure the computation of the demand levels for each potential stop during the

three hours of the analysed period, time for generation of demand was considered to be discrete,

dividing the 3-hour period (7:00 a.m. to 10:00 a.m.) in 12 steps of 15 minutes.

It was also defined that the stops would have to be separated by a minimum distance, in

order to avoid the creation of too many stops, which would degrade the performance of the

service that intends to be more efficient than the regular bus service.

V.5.3.2. Mathematical Formulation

To compute the stop’s locations, we used optimisation software called Xpress-MP. This

software uses a programming language called Mosel.

The mathematical formulation of the problem is the following:

Sets: N = {1,…,C} set of all the available nodes where a Minibus Stop can exist and also

represents the location of the origins and destinations of the flows, where C is the maximum

number of nodes; A = {1,…,K} set of all the available arcs between nodes where K is the maximum

number of arcs; T = {1...,12} set of all the considered time steps.

Decision variables: : binary variable for the existence of a stop in node , at time step ,

where є N; : continuous variable that represents the percentage of people who come from

node , at time step , and use the stop for their trip, where є N; : binary variable

responsible for the existence of a stop in the node , in any time step, where є N.

Data: : matrix that represents the walking distance between each pair of network nodes

where є N; : matrix that represents the demand in arc with the starting point of the trip

in the node , at time step , where є A and є N; : vector that represents the number of

arcs, at time step , that have its origin in the node where є N; : vector that represents

the total number of arcs that leave from node , regardless of the time step, where є N.

Constants: : maximal walking distance that is acceptable between a trip starting/end

point and the origin/destination stop location.



69

With this notation, the objective function is described by the following expression:

(V.4)

NSP and NST are parameters to be adjusted. NSP represents the average number of

passengers that have to exist in order to justify the creation of a new stop and NST stands for the

minimal number of passengers, in a fixed time step, that justify the creation of different stops.

This function maximises the potential demand generated in an area with the least stops

possible in all the existing time steps and takes into consideration three parts:

1. The number of people that use the defined stops;

2. A deduction considering the cost of creating a stop;

3. A penalty in using a different set of stops in different time steps. This deduction has the

objective to try to homogenise the location of the stops in each area across the period of

operation.

This solution space is constrained by the following equations:

(V.5)

Ensures that the demand is not exceeded;

(V.6)

Guarantees that the demand is only allocated to existing stops;

(V.7)

Ensures that the variable exists if the node is used as a stop at any time step;

(V.8)



70

Assures that the existing stops are separated, at least, by meters (a parameter to be

adjusted);

(V.9)

The decision variable is binary;

(V.10)

The decision variable is binary;

is real.

Running this algorithm enabled the estimation of all the potential viable Minibus’ stops.

Nevertheless, the stops identified in this algorithm may not be all used in the routing phase of the

model.

V.6. Minibus Link Load Estimation – Phase 3

From the O/D matrix obtained in the potential demand estimation phase, whose origins and

destinations were census blocks of the study area, we should convert this demand to the

estimated set of potential stops obtained in the previous phase. This procedure allows the

prediction of a real demand matrix between the Minibus’ potential stops.

As not everybody will have a Minibus stops very close to their home, we took into

consideration the demand that is lost if one has to walk a certain distance until the departing stop

and the demand loss if one has to walk from the arrival station to its final destination.

To model this demand loss we used an inverse logistic curve taking values between 1 and 0.

The value of the inverse logistic curve for the walking distance between home and the Minibus’

stop represents the fraction of the potential demand that will be willing to walk that distance to

catch the Minibus.

The inverse logistic curve is presented in the following equation:



71

(V.11)

Where a and b are calibrated by considering two different point in the curve (e.g. “close”, 5

minutes walking distance –Y =0.90, and “far”, 15 minutes walking distance –Y =0.10). These

reference values were based on an accessibility study developed for the Lisbon subway system

(Martínez 2010). The values obtained were: a= -4.4607 and b=0.4461. The resulting curve is

presented in Figure V.8.

Figure V.8 - Logistic function chart

Previously to assigning the demand to the Minibus’ stops O/D pair, the algorithm assesses the

estimated travel time between the stops in order to verify that both the origin and destination

stops exist for the required time interval. This takes into consideration the walking time from the

census block to the origin stop, the Minibus estimated travel time and the walking time from the

end stop to the census block destination using a discrete time specification (from 1 to 12 time

intervals).

Once again this phase uses the algorithm of the barriers, described above, to compute the

distances between census blocks and stops.

0,00

0,10

0,20

0,30

0,40

0,50

0,60

0,70

0,80

0,90

1,00

0 5 10 15 20 25 30

Imp

ed

ance

Travel time [minutes]



72

V.7. Minibus Routing – Phase 4

V.7.1. Introduction

The definition of the Minibus’ routes is based on a variation of the Vehicle Routing problem

(VRP).

Again, due to operational constraints, the time was considered discrete and the three hour

period that was considered in the simulation process was divided into 12 steps, where each time

step represents a quarter of an hour.

As this service intends to be self-sustainable, we defined that not all the potential demand

had to be satisfied. Instead, the algorithm will try to find the most profitable solution.

The formation of each route will ensure that the travel time will not exceed the limits already

defined in the service attributes.

In this stage of the algorithm, due to lack of computer memory that only allowed the

calculation of eight Minibuses in the same run, we used a greedy algorithm.

A greedy algorithm does not produce the optimal solution because in each step of the run it

calculates an optimal next step but it does not guarantee that the combination of those steps will

lead to the optimal global solution.

Given the very large dimension of the problem and the preliminary nature of this research, we

admitted that the routes obtained with the greedy algorithm would be good enough to allow a

critical analysis of the results in the perspective of the potential benefit of such a service in the

LMA, and knowing that the optimal result would always be more favourable than the one

obtained with this algorithm.

The algorithm stops when it generates the first non profitable route.

In order to develop a more realistic market model, we estimated the demand elasticity to the

service fare price.



73

This elasticity was modelled using, once again, an inverse logistic function. This function was

calibrated using as reference the current daily trip cost of a public transport pass holder as a

lower bound, with a 98% of price acceptance, and the equivalent taxi trip price as the upper

bound, with a 2% of price acceptance. These probabilities bounds were set to express an almost

full acceptance of the price of the service (98%) to an almost rejection (2%) when we consider,

respectively, the bus and the taxi fare (a good calibration of a logistic function does not accept the

use of 100% and 0%). This relation is dependent on the trip’s nature due to the distance and time

dependence on taxi‘s fare. In order to establish an association between the inverse logistic

function parameters and the travel distance, we estimated three types of relations: a regression

between the trip distance and the average speed of the taxi, a regression between the average

speed and the percentage of time under 30 km/h (speed limit considered to start taking into

account the time fare component), and, finally, the regression between the distance and the

inverse logistic function parameters. The results of the polynomial regression for the inverse

logistic parameters are presented in Figure V.9.

Figure V.9 - Regression to calibrate the inverse logistic function parameters to estimate the demand-price elasticity

This simple estimation of the demand-price elasticity will allow a more realistic estimation of

the service’s market potential for different ticket fare levels.

V.7.2. Mathematical Formulation

Once more, the software Xpress-MP was used and the constraints and objective function used

in the algorithm are described below:

y = 0,0002x3 - 0,0163x2 + 0,3815x - 8,5755R² = 0,937

y = 0,0002x3 - 0,014x2 + 0,3271x - 4,016R² = 0,937

-9

-8

-7

-6

-5

-4

-3

-2

-1

0

0 5 10 15 20 25 30 35 40 45

Val

ue

s o

f a

and

b p

aram

ete

rs

Distance [kilometers]

a

b

Poly. (a)

Poly. (b)



74

Sets: N = {1,…,C} set of all the available nodes where a Minibus Stop may exist and also

represents the location of the origins and destinations of the flows, where C is the maximum

number of nodes; A = {1,…,K} set of all the available arcs between nodes where K is the maximum

number of arcs; T = {1,...,12} set of all the considered time steps;

Decision variables: : continuous variable that represents the number of people that are

travelling in arc , at time step , inside the Minibus, where є A; : binary variable

responsible for the existence of a trip in the arc , in each time step , by the Minibus, where є

A; : continuous variable that quantifies the percentage of the total arc’s demand assigned, at

time step , inside the Minibus, where є A; : binary variable that represents the existence,

or not, of demand in arc , in time step , where є A.

Data: : matrix that represents the distance between each pair of network nodes where

є N; : vector that represents the number of quarters of hour that arc takes to travel, where

є A; : vector that represents the real travel time of arc , where є A; : vector

that represents the potential demand in the arc , at time step where є A; :

continuous variable, between 0 and 1, that represents the percentage of clients of arc that are

willing to use the service for the given tariff (dependent of as presented above on the price

demand elasticity index), where є A; : vector that represents the maximum additional time

accepted by clients when comparing the service with the car travel time, where a є A;

Constants: : maximal capacity of a single Minibus; : fixed component of the

ticket price charged to the passengers for a single trip; : variable fee charged to the

user by kilometre travelled; : fixed cost of operation of the Minibus; : variable

cost of each kilometre travelled by each Minibus

With this notation, the objective function is described by the following expression:

(V.12)

Where i and j are, respectively, the origin and destination of arc .



75

This equation maximises the total profit in all the existing time steps and takes into

consideration two parts:

1. The profit obtained per user, where two possible fare systems can be tested: a fixed

fare component and a distance dependent tariff, where, while running the fixed fare

plan price, the variable part is not considered;

2. The cost of using a Minibus.

This solution space is subject to the following constraints:

(V.13)

Ensures that the capacity of a Minibus is not exceeded;

(V.14)

Guarantees that one Minibus at a time step is in a single arc. This constraint introduces a

limitation to the system preventing that one Minibus may make more than one stop in the same

time step (15 minutes). This simplification was not considered to be relevant because of the

nature of the system, which favours routes with few stops;

(V.15)

Assures that the real demand for every arc is not exceeded;

(V.16)

Ensures that the passengers at a stop that are travelling to one of the Minibus’ destinations

get in;

(V.17)

where the destination of arc is the same as the origin of arc in the respective time step.

This function warrants that the passengers that enter in one stop are the same, or less, that exist

in the Minibus’ destination at the time step plus the travel time between stops. The time limit

corresponds to 13 intervals to give the possibility of a Minibus finishing his route despite it is



76

outside the defined period. We considered that concluding the route a maximum of 15 minutes

after the defined hour would be acceptable;

(V.18)

where the destination of arc and are the same in the respective time steps and where -

1 + round(

) represents, respectively, the upper limit of the 15 minutes

intervals. This function assures that the passengers travelling only exist if the path exists.

(V.19)

where the destination of arc and are the same in the respective time steps and where -

1 + round(

) represents, respectively, the upper limit of the 15 minutes

intervals. This constraint is not a service constraint but a model workflow constraint which

warrants that whenever demand is assigned to an arc, the travel time tolerance will be measured.

(V.20)

Ensures that the passenger’s travel time is below the tolerable limits. The value of 1,000 used

in this expression is imposed as a bonus value to ensure that only arcs with demand will respect

the constraint;

(V.21)

(V.22)

The decision variables and

are binary;

and

are real.

At the end of this algorithm we have all the different stages of the system planning available,

going from demand estimation to stops’ location and all the operational parameters of the



77

Minibus system (size of the fleet and capacity of the different vehicles, routes and corresponding

stopping schedules).

V.8. Summary and conclusions

This Chapter has presented a detailed description of a complex method which encompasses

several different phases.

The model starts by estimating the system’s potential demand based on a simplified version

of a Delphi Method incorporated in a Decision tree model. Afterwards, an analysis of the spatial-

temporal constraints of this service is performed through the estimation of the Minibus’ stops

location. Due to the complexity of this problem, a heuristic had to be used to reduce its

dimension. This was performed through a “Divide and Conquer” heuristic using a clustering

procedure.

The next step of the model consists on the estimation of the potential link flows which was

done based on travel time estimates and a degradation of demand linked with the walking

distance to the stops, modeled by an inverted logistic function that took into consideration the

cost of not having a door to door service.

The final phase of the model is formed by a routing algorithm that estimates the optimal

Minibus’ routes, along with their schedules and passengers transported during the operating

hours using an adaptation of a VRP using a greedy approach.

With all the methodology thoroughly described, we will, in the following Chapter, present the

obtained results for different demand scenarios and system’s configuration.


Modelling the Express Minibus Service in the LMA

79

VI Modelling the Express

Minibus Service in the LMA

VI.1. Introduction

In this Chapter we will discuss all the results that we obtained through all the steps of the

model.

This assessment will be divided in two main sections. In the first one we will give a brief

overview about the different types of scenarios that were analysed: demand distribution, tariffs

and vehicle’s capacity analysis. The second part will present all of the results obtained in each

different phase.

VI.2. Analysis Framework

Our general framework of analysis took into consideration three different attributes of the

model: the demand estimation for the Minibus service, the capacity of the Minibus and the fare

system.

As it was already explained above, we analysed three different case scenarios for the

reduction in the demand for the new service: linear, convex and concave.

We also studied the profitability of using each type of Minibus when calculating each different

route. The capacities that were taken into consideration were the ones already stated: 8, 16 and

24 seats.



80

The other variable that was taken into consideration was the tariff system. Two possibilities

were thought and analysed: fixed price independently of the size and time of the trip and a

system close to the taxi model. Each of them is going to be detailed below.

VI.2.1. Express Minibus Tariff Systems

The definition of the two types of tariffs will now be assessed. The objective of this

differentiation was to identify how the optimal configuration of the system would be affected

when considering a fixed fare against a distance based pricing.

In both approaches we used the same cost definition of the service for the different vehicles,

always considering that an acceptable profit for the operator would be the cost coverage plus a

20% margin over the average travel configuration (distance and speed).

VI.2.1.1. Fixed Price Ticket

The first and simplest approach was to use a simple single ticket tariff, where a user is charged

only for using the service, independently of the length he travels.

In this tariff system, the cost of the service is distributed equally among all the users so,

although the cost of using a Minibus of higher capacity is bigger, when we take into consideration

the number of passenger transported, the final cost of the ticket will be necessarily lower.

To calculate the ticket price we assessed our trip generated data, calculated the average

distance of all the trips and used it to define the average travel time using a commercial speed of

30 km/h. The estimation of the average distance was done considering an additional component

of empty travelling of 33%, which intends to include the distance of the Minibus from the depot

to the first stop, the return of the vehicle to the depot, and some displacements of the Minibus

during its operational time. We considered this value as a conservative estimate. With the

average travel time and using an average occupancy level of 2/3 of each type of Minibus, we were

able to estimate an approximate value for the number of passengers in the three hours of the

service. Taking into consideration this average number of passengers, the fixed costs, the

variables costs and the intention of having a 20% profit, we were able to calculate how much

should be charged to each user to run a Minibus route.



81

The estimates of this tariff plan are present in Table VI.1.

Table VI.1 - Summary of the fixed tariff calculation

Fare components attributes Minibus

8 16 24

Daily Cost of Minibus operation 167.88 € 194.47 € 199.75 €

Cost supported by the 3h service (40%) 67.15 € 77.79 € 79.90 €

Estimated average number of people in one Minibus 5.33 10.67 16.00

Average travel distance (database average + 33% empty travelling) 12726.60 metres

Average time travelled 0.42 hours

Average number of passengers in 3h 31.43 62.86 92.29

Fixed cost of the Minibus’ operation (per passenger) 2.14 € 1.24€ 0.85 €

Variable cost of the Minibus’ operation (per passenger) 0.31 € 0.22 € 0.16 €

Total Cost (per passenger) 2.45 € 1.45 € 1.01 €

Fare (20% 0f profit) 2.94 € 1.74 € 1.21 €

VI.2.1.2. Taxi Tariff Scheme

The second tariff system, as mentioned above, was based on the cost estimations presented

in the previous tariff scheme. However, in this case, part of the fixed costs (vehicle and staff) and

the variable costs were assigned to a variable fare component dependent on the travel distance.

This tariff system tries to resemble the general taxi tariff system, where a user is charged in two

parcels: a base fee, and a variable component along his/her trip, that depends on the distance

travelled and the time spent in speeds under 30 km/h.

The variable part of the time included on the taxi fare system was not used. The main reason

to ignore this component was because of the travel time risk in congestion situations that would

be totally transferred to the user of the system. This situation could drive people away from the

service after a bad experience of getting delayed and paying an extra cost.

After some trials, we identified that the most balanced way of spreading the fixed costs on

the tariff system would be to allocate 30% to the fixed parcel and the remaining 70% to the

variable component. The variable part also considered all of the Minibus’ operations costs (gas

and maintenance).

The results are presented below (Table VI.2).



82

Table VI.2 - Summary of the taxi scheme tariff

Tariff components Minibus number of seats

8 16 24

Daily Cost of Minibus operation 167.88 € 194.47 € 199.74€

Cost supported by the 3h service 67.15 € 77.79 € 79.90 €

Average number of passengers in one Minibus 5.33 10.67 16.00

Average travel distance (database average + 33% empty travelling) 12726.60 metres

Fixed cost of the Minibus’ operation (per passenger) 2.14 € 1.24€ 0.85 €

Variable cost of the Minibus operation (per passenger) 0.31 € 0.22 € 0.16 €

Fixed fare component (20% of profit) 0.77 € 0.45 € 0.31 €

Fare per kilometre (20% of profit) 0.109 € 0.066 € 0.046 €

VI.3. Discussion of Results

In this section we are going to present all of the calibration steps that were used in all the

calculation process and all the assumptions that were made, sometimes to guarantee the

feasibility of the model.

After all the variables have been correctly defined and all the assumptions justified we will

present the results for the different scenarios of demand and tariff.

VI.3.1. Demand Estimation

This section analyses the changes to the original demand that resulted from the consideration

of the behavioural characteristics of each traveller. As we already explained, in a previous

Chapter, nine trip attributes were considered in the calculation of the demand: car availability,

monthly pass availability, number of trips made, distance travelled, activity time, presence, or not,

of a non-commute subway trip, chosen mode and trip purpose.

Prior to the presentation of the decision tree model results, we should acknowledge that our

initial subset of trips (431,142) represented approximately 38% of the total of the morning peak

demand. The estimates that will be presented are aggregated at the municipal level, instead of

the census block level, in order to provide a better insight and a greater statistical significance.



83

Before analysing the potential demand of the Express Minibus service, we should present the

initial distribution of the flows in the morning peak period in the LMA to serve as baseline for our

analyses (Figure VI.1). We can observe, as it would be expected, that Lisbon is the main demand

pole, both as origin and destination, and Setúbal also attracts a noteworthy trips from the

neighbour municipalities.

Figure VI.1 - Distribution of the highest flows inside the LMA before behavioural constraints (Concave demand scenario)

By considering all of the referred attributes in the decision tree, we were able to estimate the

potential impact on the current demand of the transport system, during the morning peak hour

that would result from the introduction of the Express Minibus service for the different demand

scenarios. As the other scenarios presented similar results we will only analyse the linear demand

scenario which is illustrated in Figure VI.2 and that presents the two highest O/D flows observed

for each municipality as travel source.



84

As expected, when compared with the initial flows, Lisbon remains as the major source and

attraction point of all the trips inside the LMA. We can also observe that Setúbal, although not

having the same relevance as Lisbon, is also responsible for some movements in the south side of

the LMA as it was initially. When comparing the initial flows and the flows after the behavioural

constraints we can observe that the major arcs were kept the same and only reduced their value.

Figure VI.2 Distribution of the highest flows inside the LMA after behavioural constraints (Concave demand scenario)

The total potential share of the Express Minibus service, during the morning peak period is

presented in Table VI.3 for the different demand scenarios. The obtained results show a very high

potential (between 12.93% and 23.09% for our current trip subset, which represents 4.9% and

8.8% of the total morning peak demand) for the Express Minibus service.



85

Table VI.3 - Number of minibus customers according to each demand deduction

Concave Linear Convex

Total number of trips 99,554.21 81,652.96 55,764.53

% of the considered LMA trips 23.09% 18.94% 12.93%

The total share that each municipality has on the total potential Minibus’ trips is presented on

the following tables (Table VI.4 and Table VI.5).

Lisbon is clearly the municipality with the highest percentage of potential Minibus users as

origin and destination and Alcochete is the one with the lowest percentage.

Table VI.4 - Express Minibus service demand distribution in each municipality as origin

Municipality Type of demand scenario


Alcochete 0.29% 0.30% 0.30%

Almada 7.39% 7.23% 7.06%

Amadora 6.65% 6.72% 6.73%

Azambuja 0.73% 0.74% 0.75%

Barreiro 2.85% 2.81% 2.74%

Cascais 8.39% 8.49% 8.68%

Lisbon 21.84% 21.77% 21.97%

Loures 8.57% 8.69% 8.79%

Mafra 1.63% 1.58% 1.54%

Moita 1.68% 1.63% 1.52%

Montijo 0.82% 0.79% 0.76%

Odivelas 5.23% 5.33% 5.38%

Oeiras 6.48% 6.54% 6.63%

Palmela 1.94% 1.90% 1.84%

Seixal 5.02% 5.00% 4.96%

Sesimbra 1.20% 1.20% 1.18%

Setúbal 2.32% 2.31% 2.32%

Sintra 11.93% 11.90% 11.85%

Vila Franca de Xira

5.05% 5.06% 5.02%

Total number of Minibus

trips 99,554.21 81,652.95 55,763.53

Table VI.5 – Express Minibus service demand distribution in each municipality as destination



Alcochete 0.22% 0.21% 0.17%

Almada 6.17% 6.28% 6.40%

Amadora 4.48% 4.64% 4.84%

Azambuja 0.42% 0.41% 0.38%

Barreiro 2.52% 2.42% 2.26%

Cascais 7.26% 7.34% 7.39%

Lisbon 39.73% 39.73% 39.89%

Loures 6.39% 6.44% 6.43%

Mafra 1.46% 1.45% 1.40%

Moita 0.88% 0.87% 0.81%

Montijo 0.75% 0.73% 0.69%

Odivelas 3.33% 3.40% 3.47%

Oeiras 4.95% 4.84% 4.75%

Palmela 1.23% 1.26% 1.32%

Seixal 3.87% 3.74% 3.57%

Sesimbra 1.23% 1.23% 1.20%

Setúbal 3.69% 3.57% 3.52%

Sintra 7.46% 7.49% 7.60%

Vila Franca de Xira

3.95% 3.96% 3.90%

Total number of Minibus

trips 99,554.21 81,652.95 55,763.53



86

The following tables (Table VI.6 and Table VI.7) represent the percentage of people in the

morning peak period that would be willing to change to the Express Minibus service, in each

municipality, as an origin or destination, considering only the subset of trips described above.

The municipalities which present higher share of trips, that can be reallocated to the Express

Minibus are: Azambuja, Vila Franca de Xira and Barreiro as origins, and Setúbal, Lisbon and

Sesimbra as destinations. Nevertheless, some of these municipalities represent a small share of

the total number of potential Minibus trips as shown in Table VI.4 and Table VI.5.

Table VI.6 - Express Minibus service demand percentage from the initial trips database of each municipality as origin



Alcochete 24.78% 20.69% 14.08%

Almada 24.85% 19.96% 13.30%

Amadora 24.01% 19.89% 13.62%

Azambuja 30.43% 25.05% 17.34%

Barreiro 28.01% 22.72% 15.08%

Cascais 22.25% 18.45% 12.89%

Lisbon 19.40% 15.86% 10.93%

Loures 24.31% 20.21% 13.96%

Mafra 26.89% 21.45% 14.22%

Moita 27.02% 21.57% 13.73%

Montijo 24.54% 19.51% 12.78%

Odivelas 24.59% 20.58% 14.17%

Oeiras 22.25% 18.44% 12.75%

Palmela 22.35% 17.90% 11.83%

Seixal 25.66% 20.98% 14.20%

Sesimbra 27.60% 22.74% 15.18%

Setúbal 23.87% 19.45% 13.38%

Sintra 23.36% 19.11% 13.00%

Vila Franca de Xira

29.75% 24.46% 16.57%

Average 25.05% 20.47% 13.84%

Table VI.7 – Express Minibus service demand percentage from the initial trips database of each municipality as destination



Alcochete 18.85% 14.21% 8.09%

Almada 20.76% 17.33% 12.06%

Amadora 16.18% 13.72% 9.78%

Azambuja 17.43% 13.90% 8.87%

Barreiro 24.78% 19.50% 12.48%

Cascais 19.25% 15.96% 10.98%

Lisbon 35.30% 28.95% 19.85%

Loures 18.12% 14.97% 10.22%

Mafra 24.19% 19.65% 12.91%

Moita 14.09% 11.42% 7.32%

Montijo 22.41% 18.03% 11.64%

Odivelas 15.68% 13.11% 9.14%

Oeiras 17.00% 13.63% 9.14%

Palmela 14.12% 11.90% 8.48%

Seixal 19.77% 15.70% 10.23%

Sesimbra 28.41% 23.25% 15.50%

Setúbal 37.89% 30.10% 20.25%

Sintra 14.62% 12.03% 8.33%

Vila Franca de Xira

23.30% 19.16% 12.88%

Average 21.17% 17.19% 11.48%

The results of the origins are somehow expected due to the lack of public transport supply in

some of these municipalities. For the destinations, in the case of Lisbon and Setúbal, might be due

to their nature as the main activity centres in both banks of the LMA, and even though they might

have a lot of internal trips, there is a high public transport supply. The difference between Lisbon



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and Setúbal may be explained, not only because of Lisbon’s higher importance in terms of

employment, but also by the inexistence of a mass public transport system in Setúbal. For

Sesimbra, the high share of trips can be justified by the low supply of public transports and

activity dependence on other municipalities.

Figure VI.3 and Figure VI.4 analyse all the transport modes from which the Express Minibus

service may capture its users, for the linear demand scenario. The classification used in the legend

of the figures is as follows: mass transport represents subway and train systems and other

transport represents mainly bus services.

From Figure VI.3 we can extract the following considerations:

The mode from which the Express Minibus service would attract more potential

clients are the bus services (other in the figure) (45.58%), which results from the

significant share of this mode in areas like Loures, Almada and Seixal (prior to the

opening of the Metro Sul do Tejo). These users might be willing to change to an

improved service as the one being studied. The private vehicle also has a high share

(41.48%) derived from its relevance on the total morning peak trips inside the LMA.

We can also observe that the Express Minibus service is not able to capture a high

share (12.81%) from the mass transport services (except in municipalities with

suburban rail connections to Lisbon), which results, not only from an overall small

mode share, but also from the low percentage of users that were considered to be

potential Express Minibus clients;

The area with a higher percentage of potential Minibus trips is Sesimbra due to

reasons that were already presented, where we would be able to capture a large

percentage from the current suburban bus users.

The more balanced distribution among the different modes were obtained on the

largest municipalities of the LMA’s north bank, which stresses an already existent

more balanced mode share distribution than the south bank.



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Figure VI.3 - Minibus mode share and its distribution through other transport modes (as trip origin)

When evaluating the municipalities has destinations (Figure VI.4) the situation remains

practically the same: bus services (other in the figure) have the highest share (45.58%) and the

private car remains in second place (41.48%). This is coherent with the analysis presented above,

where bus service users are the ones more willing to find alternative improved solutions. The

mass transport has the same global representativeness in origins and destinations (12.81%) and

with a very similar distribution.

Areas like Alcochete and Mafra, where the availability of public transport is bad and its

accessibility is not that good, rely very much on the private vehicle to travel. So the Express

Minibus service could only get its users from it. Nevertheless, the overall representativeness of

these areas is low.



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Figure VI.4 - Minibus mode share and its distribution through other transport modes (as trip destination)

From this first analysis we can highlight the existence of a promising demand for the Express

Minibus service, and the existence of some areas that might the best candidates for the

implementation of this service. The following phases will use the presented results as inputs for

the stops location and the estimation of their demand.

VI.3.2. Stops Location

As presented in the previous Chapter, this phase of the model intends to estimate the

Minibus’ potential stops and was divided into two stages based on a “Divide and Conquer”

heuristic. The result of each stage of this phase is presented below.



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VI.3.2.1. Clustering Algorithm

In this stage, we calculated all of the clusters for the three different types of demand

scenarios. As the algorithm was formulated, each clustering process presented the same 531

clusters with the same elements but different results in the potential flows. Due to the high

extent of the data we will not present the resulting O/D matrices.

From the total number of cluster we observed that 283 are located on the North bank and the

remaining 248 were located on the South bank. The clusters in the North bank tend to be smaller

but with a higher number of elements, especially in municipalities like Amadora, Lisbon and

Odivelas, and a more disperse pattern in municipalities like Mafra and Loures which present wider

cluster and with a small number of elements. This last pattern is also observed in the majority of

the municipalities in the South bank, with the exception of Almada and Setúbal that present

higher number of inhabitants and also activity. The cluster’s spatial distribution is presented in

Figure VI.5.

The following table sums up the general statistics of the formed clusters (Table VI.8).

Table VI.8 - Statistical summary of the clustering procedure

Statistical indicator Cluster’s area [ha.] Distance to the centroid [m]

Average 471.02 587.24

Standard deviation 800.88 315.05

Maximum 12,530.56 2424.67

Minimum 6.56 0.00



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Figure VI.5 - Clusters formed

VI.3.2.2. Definition of Stops’ Location

Having already defined the clusters, we advanced to the next step of the model and the

Minibus potential stops’ locations were calculated.

As we have defined in the formulation of the problem, there were two variables (defined as

NSP and NST in Chapter V) that had to be estimated. As we have to run this phase for the

different demand scenarios we computed three sets of values.

The NSP, that symbolises the average number of passengers that have to exist in order to

justify the creation of a new stop, was estimated through the calculation of the aggregate average



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of the total demand of each arc over the three hours of operation, plus a constant (α) times the

aggregate standard deviation of the flow of each arc during the three hours. The value of α was

established in a trial and error process, where with a simple example, we tested different values,

reaching the value of α=4.6 as the most balanced situation for the stops’ distribution.

The estimation of NST, that represents the minimal number of passengers in a fixed time step

that justify the creation of different stops, was done in the same way as NSP but, instead of using

the flows of each arc along the three hours, we used the total flow of each time step.

The results obtained are presented in the table below (Table VI.9).

Table VI.9 - NSP and NST estimated values

Type of demand estimation

Linear Concave Convex

NSP 1.3701 1.6377 0.9709

NST 0.3621 0.4368 0.2533

The minimal distance between stops was defined to be between the conventional stops’

distance of traditional bus services and the ones used in the subway and railway services. This

value was set to 500 meters.

The result of the stops’ location algorithm for the concave demand scenario is shown in Figure

VI.6, for the number of trips as origin, and Figure VI.7 for the number of trips as destination. Due

to the high extent of the data and also because of the similarities between all the scenarios, we

will only show a summary of some statistical attributes of the other two scenarios (Table VI.10).

Table VI.10 - Summary of the stop's formation in the different demand scenarios

Statistical attribute Demand Scenario


Total number of formed stops 1353 1365 1291

% of clusters without stops 36.53 35.59 37.29

Average number of intervals that the stops are active 3.18 3.08 2.96

Average number of stops in one cluster 4.01 3.99 3.88

Standard deviation of the number of stops in one cluster 3.78 3.92 3.87

Maximum number of stops in one cluster 30 36 31



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Firstly, we can identify an absence of stops, in both situations, in areas like Azambuja, Mafra,

Palmela and Vila Franca de Xira. This can be partially explained by the disperse occupation

patterns and also because of their reduced flows. On the other hand, Lisbon is the municipality

with the higher concentration of stops, both as origin and destination, and the flows are higher as

a destination, mainly because of reasons already stated.

Figure VI.6 - Minibus' stops distribution for the LMA according to origin flows



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It is also possible to observe a linear distribution of stops, with high flows as destinations,

along three main corridors: Cascais line, North highway and Sintra line. This is coherent with the

real characteristics of these corridors that are primarily residential areas but that have been

recently evolving to new employment centralities in the LMA.

Some of the municipalities located near the Lisbon’s fringe (i.e. Amadora and Odivelas)

present stops with high flows as origins. This was expected due to their residential nature.

Figure VI.7 - Minibus' stops distribution for the LMA according to destination flows



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VI.3.3. Minibus Link Load Estimation

In this phase of the model we introduced a new reduction on the potential demand, this time

related to spatial constraints. With the estimation of the potential stops, we were capable of

calculating the value of degradation of the flow taking into consideration the distance between

the new stops and the origin/destination of each trip, using the inverse logistic function previously

described.

Once again, we start by analysing the total reduction on the initial potential demand of the

Express Minibus service for the different LMA O/D pairs. Figure VI.8 illustrates the same demand

patterns as in the previous phases of our study, only observing a reduction on the absolute values

of the flows.

Figure VI.8 - Distribution of the highest flows inside the LMA after the spatial constraints (Concave demand scenario)



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A more detailed assessment of the changes between the previous configuration of the flows

and the one obtained in this phase is presented in Table VI.11. The results show a very significant

demand reduction derived from spatial-temporal constraints introduced by the concentration of

demand in the Express Minibus’ stops. This reduction is not homogeneous among the different

demand scenarios due to their different stops’ location. This reduction is more drastic on

municipalities with a more disperse territorial occupation as Mafra, Palmela and Sesimbra.

We should also acknowledge a considerable reduction in the municipality of Lisbon, the main

demand generator/attractor, which can be explained by the fact that some densely suburbs near

Lisbon’s borders, as Odivelas, Amadora and Oeiras (Algés), are taking demand from Lisbon’s

neighbourhoods, close to those borders, to stops located in their municipalities. This fact can be

verified by the increase of demand in some of these municipalities like Odivelas (concave and

linear scenario) and in Seixal that captures part of the Almada’s demand close to the border.

Table VI.11 – Ratio between the demand on Phase 3 and Phase 1 of the model

Municipalities

Demand Scenario


Origin Destination Origin Destination Origin Destination

Alcochete 2,16% 3,14% 2,25% 4,16% 0,54% 1,04%

Almada 41,51% 44,45% 47,28% 51,89% 8,28% 6,34%

Amadora 35,11% 41,89% 40,59% 49,73% 2,71% 9,92%

Azambuja 20,55% 11,48% 26,62% 14,69% 20,68% 2,82%

Barreiro 36,54% 28,37% 44,40% 34,21% 7,59% 2,14%

Cascais 34,09% 40,17% 40,85% 48,22% 7,38% 7,62%

Lisbon 16,82% 14,98% 17,84% 16,71% 6,75% 4,96%

Loures 51,71% 42,64% 60,11% 49,55% 8,14% 6,57%

Mafra 3,03% 12,06% 3,52% 11,72% 1,92% 1,29%

Moita 43,31% 15,23% 58,07% 23,29% 2,48% 1,55%

Montijo 10,09% 17,46% 10,35% 21,71% 7,82% 15,78%

Odivelas 134,74% 53,49% 160,42% 65,05% 9,22% 6,70%

Oeiras 29,39% 28,56% 34,85% 33,07% 11,33% 7,42%

Palmela 6,99% 17,04% 7,85% 18,89% 0,53% 8,64%

Seixal 93,53% 47,64% 116,47% 59,44% 10,94% 0,85%

Sesimbra 19,01% 27,34% 22,53% 32,81% 1,65% 43,99%

Setúbal 42,14% 29,38% 48,35% 34,06% 5,66% 0,00%

Sintra 30,72% 29,48% 36,77% 34,49% 3,18% 3,26%

Vila Franca de Xira 22,75% 34,19% 27,78% 42,11% 8,23% 10,14%



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This phase revealed a significant demand reduction derived from the spatial-temporal

constraints which stresses the relevance of a good definition of the service stops’ location in order

to develop a viable system.

VI.3.4. Minibus Routing

In this section we present an application of the Minibus routing algorithm to the study area

using the inputs from the previous phases of the model.

The algorithm greedy was run using all the variations of the size and tariff system, inputted

has parameters, for each demand scenario. This allowed a sensitivity analysis of the resulting

system configuration.

The first approach was to try to use all of the obtained stops in the previous phase of the

model (approximately 57,000 arcs on the O/D matrix). Unfortunately, due to the huge size of the

problem, this approach was computationally infeasible (lack of memory on the processing

computer). Therefore, we had to try a different approach to attempt to reduce the size of the

problem.

The solution passed by trying to reduce the number of stops, thus reducing the number of

arcs, which was the main dimension of the problem that was preventing it to be solved. So, in

order to select the potential profitable stops, we estimated the demand that each stop was able

to aggregate, both as origin and destination, using the inverse logistic function specified in

Chapter V. Afterwards, we standardised both the aggregated demands and defined the ratio

between the demand as origin and destination. In order to standardise this last indicator, we

defined a standardisation function that attributes to values below 0.2 and above 5 a standardised

value of 0 and uses linear equations between the values of 0.2 and 1 (positive slope) and between

1 and 5 (negative slope).

With these three standardised indicators we computed a compensatory function that

attributed different weights to the indicators. For this analysis we considered a 0.4 weight for the

demand variables and 0.2 for the ration. With the estimates of this compensatory function we

were able to sort the stops and we selected the top 100.



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This approach did not take into consideration the proximity between each of the 100 stops

which might had two consequences: first, it would mean that it was possible to walk between

them, secondly, the distribution of the surrounding demand would be divided among the two

stops instead of concentrating in one of them.

To make a more refined selection of the stops, taking this problem into consideration, we

started by identifying the stops that were distanced by less than 1250 meters (acceptable walking

distance) and that were located, within this threshold distance, next to a higher ranked stop.

These last stops were removed from the 100 stops’ set reducing considerably the problem size.

This process was able to reduce the number of stops to, approximately, 43 (1806 arcs),

depending on each demand scenario. Even this number was too high for the computation of the

algorithm.

Seeing that this process was computationally infeasible, we decided to create a possible and

simple scenario for the LMA to demonstrate the utility of the routing algorithm as a planning tool.

We decided to select manually the stops that were visually seen as the most promising ones.

The selection process was based on the stops that had resulted from the sorting procedure,

where we tried to spread them over the entire LMA and also taking into consideration the

percentage of Express Minibus trips initially measured for each municipality, ensuring at least one

stop in the main demand centres. The result of the stops’ selection process is presented in Figure

VI.9.

This configuration of stops was the base to compute the routing algorithm for all the different

demand scenarios and different pricing schemes.

Even though we were able to reduce the size of the problem to a set of 22 stops, the

algorithm processing time was still too long. To enable the computation process, we had to limit

the time that the optimisation algorithm was allowed to run, fixed at a maximum of 1000 seconds

(17 minutes). We restricted the computation error to be less than 10%, which was a value

sufficiently accurate for an exploratory study.

We will divide the presentation of the obtained results in three parts: first we will assess the

results from the fixed tariff scheme, then the ones obtained for the taxi scheme and finally we will

make a comparison between both of them.



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Figure VI.9 - Manual selection of the Minibus' stops

VI.3.4.1. Fixed Tariff Results

The results from the fixed tariff scheme, for the different demand scenarios, are presented in

Table VI.13 and Table VI.12.

The tables presented are sorted by the order of formation of the Minibuses when running the

greedy algorithm. As it can be seen, in some cases, there are later solutions that improve the prior

solution’s profit. This fact derives from a sub-optimal solution in some of the iterations that was

limited by the 1000 seconds as discussed above.

From this summary we can first conclude that the service is economically viable in the case of

the linear and concave scenarios, but it does not generate any profit in the convex demand

scenario (reason because it was not presented). This inability of generating profit was derived



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from the low flows that the convex scenario presented, which is the source of income on this

tariff scheme. As it was expected, the results between the concave and linear approach did not

vary significantly as they had similar flow’s configurations.

The type of vehicle preferred in both situations was the one with 16 available seats. As this

tariff system is only dependent on a single tariff, the Minibus will have to transport the higher

number of passengers during his operation period. If there was a high demand in all the

operations’ hours, the Minibus of 24 places would have probably been selected, but, given the

current situation, which did not present demand in several periods between all stops, the service

demand was not enough to fill all the 24 seats of the Minibus. Also, as the cost of using this type

of Minibus is much higher, the 16 seats’ Minibus was preferred.

As the distance travelled by the Minibus is only a cost source, smaller distanced trips were

preferred, which resulted in low average distances. As expected, due to the model specification,

although we allowed an extra time step after 10 a.m., the Minibus’ services closed their

operation, normally, at the tenth time interval, which represent 2h30 of operation time.

The total and average number of passengers transported did not vary between the two

scenarios, the main difference between the solutions was in its travelled distance, where the

concave scenario presents a smaller value, which compensates a slighter smaller occupancy levels

and leads to higher profits.

Table VI.12 - Summary of the fixed tariff scheme for the concave demand scenario

Minibus number

Total passengers transported

Operation time

Average passenger per bus

Minibus capacity

Profit *€+ Estimated travelled

distance [km]

1 104.25 9 11.58 16 95.61 59.17

2 146.24 9 16.25 24 89.54 51.49

3 77.97 9 8.66 16 78.54 53.40

4 95.87 9 10.65 16 80.83 66.68

5 83.90 8 10.49 16 60.67 39.82

6 81.93 11 7.45 16 56.40 48.59

7 70.12 8 8.77 16 39.60 42.66

8 72.23 9 8.03 16 37.31 44.66

9 59.78 9 6.64 16 22.11 95.42

10 58.23 8 7.28 16 8.07 68.68

11 50.40 9 5.60 16 0.57 0.00

Total 900.93 - - Total 569.25 570.56

Average 81.90 8.91 9.22 Average 51.75 51.87



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Table VI.13 - Summary of the fixed tariff scheme for the linear demand scenario

Minibus number


Operation time


Minibus capacity


distance [km]

1 147.91 9 16.43 24 92.70 36.70

2 105.45 9 11.72 16 96.60 60.22

3 97.93 9 10.88 16 85.83 52.48

4 88.94 9 9.88 16 69.71 55.08

5 80.49 8 10.06 16 56.19 48.61

6 81.74 11 7.43 16 50.27 98.27

7 69.16 8 8.64 16 36.56 48.06

8 68.56 9 7.62 16 35.34 49.00

9 61.32 9 6.81 16 21.05 57.57

10 57.74 8 7.22 16 8.21 89.91

11 49.67 9 5.52 16 0.52 59.86

Total 908.90 - - Total 552.97 655.76

Average 82.63 8.91 9.29 Average 50.27 59.61

Examples of routes of this tariff scheme can be found in Figure VI.10, where the service visits

five different municipalities (Amadora, Lisboa, Sintra, Almada and Cascais) during the operation

time, indicating a complex demand distribution in space and time.

Figure VI.10 - Example of a fixed tariff route



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VI.3.4.2. Taxi Tariff Scheme

Due to the nature of this scheme, the operator objective function is more linked to travelling

longer distances with high occupancy levels. As the 8 seats’ Minibus does also present the highest

profitability for the variable component, the operator will tend to select this vehicle if is not able

to ensure full occupancy of larger vehicles (see Table VI.14, Table VI.15 and Table VI.16).

In this tariff scheme, all of the demand scenarios were able to generate some routes. Again,

due to the low demand on the convex scenario, the number of formed Minibus was substantially

lower than in the other scenarios where 28 Minibuses were formed.

Again, this scheme also proved to be a profitable solution in all the demand’s approaches.

Table VI.14 - Summary of the taxi tariff scheme for the concave demand scenario

Minibus number


Operation time

Average passengers per bus

Minibus capacity


distance [km]

1 54.01 9 6.00 8 38.24 71.18

2 114.00 8 14.25 16 31.64 57.50

3 60.82 10 6.08 8 44.11 72.95

4 97.00 10 9.70 16 26.00 68.69

5 66.00 10 6.60 8 31.00 65.63

6 63.98 11 5.82 8 27.74 69.47

7 68.84 7 9.83 16 24.43 69.55

8 56.00 7 8.00 8 22.60 62.23

9 60.93 8 7.62 8 20.46 45.41

10 53.96 8 6.74 8 22.38 61.08

11 40.00 6 6.67 8 17.87 47.81

12 55.00 8 6.88 8 24.11 57.89

13 40.00 5 8.00 8 18.26 56.06

14 65.00 5 13.00 16 14.80 53.33

15 57.91 10 5.79 8 13.63 69.17

16 144.00 7 20.57 24 9.87 49.93

17 45.47 8 5.68 8 14.02 71.48

18 50.85 8 6.36 8 12.93 54.34

19 46.00 9 5.11 8 11.39 62.33

20 28.00 5 5.60 8 7.63 63.24

21 59.24 8 7.41 8 9.86 48.59

22 40.73 7 5.82 8 7.44 58.09

23 53.17 7 7.60 8 7.68 45.86

24 37.00 5 7.40 8 12.01 57.80

25 44.00 7 6.29 8 7.61 64.05



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Minibus number


Operation time


Minibus capacity


distance [km]

26 64.00 5 12.80 16 1.73 56.10

27 36.96 5 7.39 8 5.75 49.87

28 44.00 7 6.29 8 6.67 46.56

29 52.09 8 6.51 8 8.26 61.14

Total 1698.95 - - - 500,13 1717.33

Average 58.58 7.52 7.99 - 17,25 59.22

Table VI.15 - Summary of the taxi tariff scheme for the linear demand scenario

Minibus number


Operation time


Minibus capacity


distance [km]

1 61,00 9 6,78 8 48,77 76.31

2 106,01 9 11,78 16 42,68 69.53

3 59,29 9 6,59 8 41,27 74.03

4 31,37 9 3,49 8 31,97 73.25

5 39,74 7 5,68 8 30,55 69.55

6 58,00 9 6,44 8 29,07 56.86

7 52,07 8 6,51 8 28,76 68.77

8 112,00 9 12,44 16 25,72 68.06

9 31,43 9 3,49 8 21,49 90.00

10 78,36 8 9,79 16 17,67 52.38

11 63,02 9 7,00 8 21,99 49.02

12 56,00 7 8,00 8 19,79 45.52

13 58,25 9 6,47 8 20,82 68.01

14 12,00 5 2,40 8 19,57 69.90

15 53,74 9 5,97 8 24,59 56.74

16 93,00 8 11,63 16 10,93 48.54

17 24,00 5 4,80 8 17,21 64.55

18 51,56 9 5,73 8 14,74 60.58

19 37,00 5 7,40 8 12,01 57.80

20 52,00 6 8,67 8 11,62 69.88

21 47,00 8 5,88 8 15,88 53.96

22 37,00 5 7,40 8 7,73 53.94

23 43,00 8 5,38 8 10,75 66.95

24 43,17 8 5,40 8 8,01 54.61

25 37,00 4 9,25 8 7,16 50.08

26 32,83 8 4,10 8 5,22 60.52

27 39,50 5 7,90 8 3,51 57.46

28 27,96 5 5,59 8 3,17 54.43

Total 1437.29 - - - 552,68 1741.21

Average 51.33 7.46 6.86 - 19,74 62.19



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Table VI.16 - Summary of the taxi tariff scheme for the convex demand scenario

Minibus number


Operation time


Minibus capacity


distance [km]

1 44,00 9 4,89 8 21,83 67.41

2 31,00 9 3,44 8 8,99 80.56

3 32,00 5 6,40 8 1,27 42.19

4 29,69 7 4,24 8 0,96 67.12

5 27,00 8 3,38 8 0,78 32.60

Total 163.69 - - - 33,82 289.87

Average 32.74 7.60 4.47

6,76 57.97

Figure VI.11 illustrates a typical route which results from this tariff scheme, where Lisbon

always plays a central role on the routes’ definition, although other municipalities as Almada,

Sintra and Vila Franca de Xira do also make part of this solution.

Figure VI.11- Example of a taxi tariff scheme route



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VI.3.4.3. Tariff Schemes Comparison and Summary

As it was stated, both tariff schemes are able to generate profitable routes and, excluding the

convex demand scenario, both of the others present a similar final operational balance.

One advantage of the taxi tariff scheme over the fixed one was the capability of generating

solutions with the convex scenario, which is mainly derived from the ability to charge for the extra

amounts imposed by a more disperse demand.

The taxi tariff scheme presented a different behaviour from the fixed tariff, where the

quantity of formed Minibuses with profit was substantially higher, although with less profit per

vehicle. This difference is mainly due to the specifications of each tariff, where the average

distance of the existing demand links may not compensate the difference to the full tariff scheme,

which can happen for smaller distances than the value used in the cost estimates.

After this brief comparison of both pricing schemes used, we should now analyse the impact

of the designed system on the overall travel demand during the morning peak. The most relevant

indicator will be number of passengers that might change from the private car to this new Express

Minibus service.

We can estimate this value based on the number of passengers obtained for the small

example of the LMA and try to extrapolate the results for the whole region. Table VI.17 and Table

VI.18 present the obtained estimates for the total number of passenger of the Express Minibus

service for the LMA on the different tariff schemes. The fixed fare system would generate,

considering a linear extrapolation from the model in a total market share of the morning peak, an

estimated market share which ranges from 0% in the convex scenario to 0.80% for the Concave

one, which is quite insignificant at metropolitan scale, but might contribute to improve the

system’s efficiency. Using a non-linear approach with a profit reduction of 20% the results are

significantly smaller than in the previous approach.

The results for the taxi fare system are approximately the double of the previous scenario.

These passengers would come mainly from the current bus system and private car users.

Although the main target of this service is the private vehicle users, the demand model estimated

suggested a greater acceptance of current bus users to this new service. This fact derives from the

actual low quality of service for long commuting trips between some municipalities of the LMA,



106

which are not able to afford currently the daily private cars costs, or are captive public transport

users.

We were able to estimate the impact of the proposed service over the actual private car

users. Considering the current mode choice distribution of the potential demand of the Express

Minibus service, which was estimated for the all LMA as 28.7%, we can estimate the reduction of

the number of car users that would change to this new service. This value would range from 2,695

to 5,246 car trip, depending on the tariff system and the extrapolation from the measured

demand. The expected reduction of number of cars is approximately 3,119 private cars for the

whole LMA, from a total of 404,256, considering a car occupancy level of 1.2, which would

produce a significant impact during the morning peak period (approximately 1% reduction).

Table VI.17 – Estimates of number of passengers of the Express Minibus service during the morning peak (Fixed Fare)

Demand Scenario

Number passengers estimated in the

simplified Routing model

Number of potential

passengers on the simplified version

of the Routing Phase

Number of potential

passengers of the entire study area

in the Routing Phase

Linear estimation of the remaining

O/D flow

Corrected estimation of the remaining

O/D flow

Linear 1,468.81 4,151.00 26,540.84 9,391.31 5,430.06

Convex - 1,011.00 3,319 0 0

Concave 1,591.16 4,467.00 27,521.75 9,803.34 5,697.25

Table VI.18 – Estimates of number of passengers of the Express Minibus service during the morning peak (Taxi Tariff)

Demand Scenario

Number passengers estimated in the

simplified Routing model

Number of potential

passengers on the simplified version

of the Routing Phase

Number of potential

passengers of the entire study area

in the Routing Phase

Linear estimation of the remaining

O/D flow

Corrected estimation of the remaining

O/D flow

Linear 2,833.17 4,151.00 26,540.84 18,108.45 10,470.31

Convex 848.96 1,011.00 3,319 2,787.77 1,818.36

Concave 2,967.06 4,467.00 27,521.75 18,280.41 10,623.73


Conclusions and Future Developments

107

VII Conclusions and Future

Developments

VII.1. Introduction

This dissertation has attempted to evaluate the viability of the implementation of a new

public transport mode in the LMA, which tries to assemble attributes from the private car, as

speed and flexibility, with the traditional public transport service, presenting fixed stops and

schedules. For this purpose we developed a systematic methodology that enables the complete

design of this new innovative demand responsive transport solution that we named “Express

Minibus Service”.

In order to develop the concept of this new public transport system, we performed a

thorough literature review of the current state of the art and state of the practice, focusing on the

public transport systems that are evolving towards more demand responsive solutions and less

supply intensive.

This literature review allowed us a more detailed design of the new service, being

complemented by an exhaustive characterisation and analysis of the study area. The final

specification of the system was obtained by the development of the business model for this

service, which entails a detailed characterisation of the value proposition of the service, the cost

structure and how the price system should be set. This analysis was complemented by valuable

information given by current public transport operators that presently operate similar services,

allowing a better definition of the cost structure of the business model.

After this comprehensive definition of the system, we tried to model the design of this new

service in an all inclusive approach, which encompassed the potential demand estimation, the

definition of the service’s stops and the main operational specifications, as routes and schedules.



108

The developed model was based on traditional Operations Research models, which were

reformulated and adapted to the current context. The model presents a high complexity level,

presenting a high number of decision variables that range from the definition of the stops location

to the routing process.

The model was then implemented in the LMA, where we identified a significant potential for

the implementation of this service. Nevertheless, the potential demand of the system is

significantly reduced by the consideration of spatial-temporal constraints of the trips.

The estimated configuration of the system proved to be profitable and with a considerable

size of volume of passenger transported, ranging from approximately 2,400 to 18,000 passengers

during the morning peak. This wide range of variation is due to the different demand scenarios

that were used, which could lead to very high demand for this system, or to a very spatial and

temporal constrained configuration.

The model allowed us to estimate the number of cars that would be reduced during the

morning peak period if this service was actually implemented, suggesting that this service would

significantly promote more efficient and sustainable transport solution in the LMA.

VII.2. Strengths and Shortcomings of the Research Presented

This current study was based on a well grounded methodology which encompassed a large

number of algorithms, linked under a common framework. The presented modelling framework

goes significantly beyond the current literature and practice on the design of a new public

transport service. Yet, the current model presents some limitations in terms of computational

capability, which led to several simplifications during the dissertation.

We should also acknowledge that the used input data might be, somewhat, outdated because

it was based on an original survey of 1994 which might bias the results, maybe not covering all the

current travel patterns that have emerged in the last decade. The use of a more updated mobility

survey and a greater computational capability could lead to a significant improvement of the

obtained estimates.



109

VII.3. Policy Implication of the Research and Future Developments

One of the main problems that emerged in the end of the complete run of the model was the

lack of computation capability. This problem was solved through the reduction of the problem

size, which, forcedly, led to a worse final solution.

This problem should be assessed and a possible solution might pass to move into a single

model formulation using more efficient meta-heuristics that would enable the possibility of

solving problems with this size and complexity. Not only should the general model formulation be

improved, but also some different approaches and simplification of the system operation should

be revised in order to improve the quality of the model and its ability to produce a holistic design

of this innovative public transport system.

Another form that should be pursued is a detailed analysis of the impacts of the introduction

of this new public transport service on the current mobility patterns of the LMA, paying a special

attention on how this new system may interplay and be integrated (physically, logically and

financially) with the conventional public transport options. A detailed analysis on how this

mobility option can complement and replace some intensive supply deficitary solutions in some

areas of the LMA might lead to a significant improvement of the region accessibility and more

efficient and sustainable mobility.

This integration may migrate into the creation of a new mobility tool which assembles all the

different transport solution under the same structure, which may allow a more flexible

identification of the trip chain requirement on a daily basis, and not introducing a penalty for that.

This concept may evolve in the current society to o new mobility paradigm of modal alternation.

This analysis should also identify all the legal barriers to the deployment of this system under

the current legal framework, which should evolve in order to integrate in the mobility system

other innovative and flexible transport solutions that might be a second best option for

individuals and the society.

We do also envisage an improvement to the business model of the system by defining more

accurately the activity of the vehicles during off-peak periods. The identification of new market

niches that could enhance the profitability of the operation of this system may be a decisive

factor on the scale that the system can reach at the LMA context.


References

111

VIII References Albalate, D & Bel, G (2009), 'What Local Policy Makers Should Know about Urban Road Charging: Lessons from Worldwide Experience', Public Administration Review, vol. 69, no. 5, pp. 962-74.

Allen, T (2006), 'Car Free Day 2006', Eurostat Press Office, no. STAT/06/125, p. 2.

Archetti, C, et al. (2007), 'Metaheuristics for the team orienteering problem', J Heuristics, vol. 13, pp. 49-76.

Armstrong, JS & Green, KC (2005), 'Demand Forecasting: Evidence-based Methods', in L Moutinho & G Southern (eds), Strategic Marketing Management: A Business Process Approach, Monash University, Department of Economics and Business Statistics.

Banister, DJ & Mackett, RL (1990), 'The minibus: theory and experience, and their implications', Transport Reviews, vol. 10:3, pp. 189-214.

Bertozzi, P (2009), 'Uma Abordagem Inovadora ao Planeamento de Transporte Colectivo: Aplicação num serviço com veículos de pequena e média dimensão na Área Metropolitana de Lisboa', Doctoral thesis, IST - Technical University of Lisbon.

Bland, RG & Shallcross, DF (1989), 'Large traveling salesman problems arising experiments in X-ray crystallography: A preliminary report on computation', Operations Research Letters, vol. 8, pp. 125-8.

Bontje, M & Burdack, J (2005), 'Edge Cities, European-style: Examples from Paris and the Randstad', Cities, vol. 22, no. 4, pp. 317-30.

Brög, W & Erl, E (1999), 'Systematic Erros in Mobility Surveys', in 23rd ATRF Conference, Perth, Australia.

Câmara Municipal de Lisboa (2005), Lisboa: o desafio da mobilidade, Câmara Municipal de Lisboa - Licenciamento Urbanístico e Planeamento Urbano, viewed May 15, 2010, <http://ulisses.cm-lisboa.pt/data/002/002/pdf/mobilidade.pdf>.


References

112

Casey, RF, et al. (2000), Advanced Public Transportation Systems the state of the art : update 2000, Federal Transit Administration, [Washington, D.C.].

Chandler, J (1993), 'Filling the Transit Gap', Nation's Business, January 1993, pp. 42-3.

Chao, I-M, et al. (1996), 'The Team Orienteering Problem', European Journal of Operational Research, vol. 88, no. 3, pp. 464-74.

CIVITAS (2010), CIVITAS - Cleaner and better transport in cities, viewed August 09, 2010, <http://www.civitas-initiative.org/main.phtml?lan=en>.

Correia, GH & Viegas, JM (2010), 'Applying a structured simulation-based methodology to assess carpooling time-space potential', Transportation Planning and Technology, vol. 33, no. 6, pp. 515-40.

Dantzig, GB & Ramser, JH (1959), 'The Truck Dispatching Problem', Management Science, vol. 6, no. 1, pp. 80-91.

Deakin, E (2002), 'Sustainable Transportation - U.S. Dilemmas and European Experiences', Transportation Research Record, no. 1792, pp. 1-11.

Dinh, TH & Mamun, AA (2004), The speedup of the cluster-based approach in the divide and conquer paradigm, Department of Electrical and Computer Engineering, National University of Singapore, Singapore.

Doerel, T, et al. (1993), 'Aufgaben und Organisation des Hamburger Verkchrsverbundes', Zoegu 16, pp. 105-16.

Eiselt, HA & Laporte, G (1991), 'A combinatorial optimization problem arising in dartboard design', Journal of the Operational Research Society, vol. 42, pp. 113-8.

Eliasson, J & Mattsson, L-G (2006), 'Equity Effects of Congestion Pricing: Quantitative Methodology and a Case Study for Stockholm', Transportation Research Part A 40(7), pp. 602-20.

European Commission (2007), 'GREEN PAPER - Towards a new culture for urban mobility'.

Fowkes, M & Watkins, I (1986), 'Design of small passenger vehicles: The passenger's needs.', paper presented to Community Transport Services Research Unit, 5th Annual Conference, Nottingham, June, 1986.


References

113

Garfinkel, RS (1977), 'Minimizing wallpaper waste, Part I: A class of travelin salesman problems', Operations Research, vol. 25, pp. 741-51.

Glaeser, E & Kohlhase, J (2003), 'Cities, regions and the decline of transport costs', Papers in Regional Science, vol. 83, no. 1, pp. 197-228.

Glaister, S & Graham, DJ (2005), 'An evaluation of national road user charging in England', Transportation Research Part A: Policy and Practice, vol. 39, no. 7-9, pp. 632-50.

Goodwill, JA & Carapella, H (2008), Creative ways to manage paratransit costs, University of South Florida. Center for Urban Transportation Research, National Center for Transit Research, Florida Dept. of Transportation, CUTR, [Tampa, Fla.].

Grubb, M, et al. (2006), Analysis of the Relationship between Growth in Carbon Dioxide Emissions and Growth in Income, Faculty of Economics, University of Cambridge.

Hair Jr., JF, et al. (2009), Multivariate Data Analysis, 7th edn, Prentice Hall.

Hawkins, R (1986), 'Developments in small bus operation in Britain.', paper presented to The Bus '86, Institution of Mechanical Engineers, London, September, 1986.

Hiscock, R, et al. (2002), 'Means of transport and ontological security: Do cars provide psycho-social benefits to their users?', Transportation Research Part D: Transport and Environment, vol. 7, no. 2, pp. 119-35.

Iles, R (2005), Public Transport in Developing Countries, El Sevier, Amsterdan.

INE (2003), Movimentos Pendulares e Organização do Território Metropolitano: Área Metropolitana de Lisboa e Área Metropolitana do Porto (1991/2001), Instituto Nacional de Estatística, Lisbon.

International Energy Agency (1997), Indicators of Energy Use and Efficiency - Understanding the link between energy and human activity.

International Energy Agency (2009), World Energy Outlook 2009, International Energy Agency (IEA), Paris.


References

114

Kariv, O & Hakimi, SL (1979), 'An algorithmic approach to network location problems, part 2. The p-Medians', S I A M Journal on Applied Mathematics, vol. 37, no. 3, pp. 539-60.

Kids Kab (2010), Kids Kab, viewed September 27, 2010, <http://www.kidskab.com/index.html>.

Kitamura, R, et al. (1997), 'A micro-analysis of land use and travel in five neighborhoods in the San Francisco Bay Area', Transportation, vol. 24, no. 2, pp. 125-58.

Kitsap Transit (2010), Kitsap Transit, viewed September 27, 2010, <http://www.kitsaptransit.org/>.

Knuth, DE (1998), The Art of Computer Programming: Volume 3, Sorting and Searching, 2nd edn, Addison-Wesley.

Land Transport Authority - Singapore Government (2010), Electronic Road Pricing, viewed August 05, 2010, <http://www.lta.gov.sg/motoring_matters/index_motoring_erp.htm>.

Laporte, G (1991), 'The Traveling Salesman Problem: An overview of exact and approximate algorithms', European Journal of Operational Research, vol. 59, pp. 231-47.

Lawler, EL, et al. (1985), The Traveling Salesman Problem. A Guided Tour of Combinatorial Optimization, Wiley-Interscience.

Lenstra, JK & Kan, AHGR (1975), 'Some simple applications of the travelling salesman problem', Operational Research Quarterly, vol. 26, pp. 717-33.

Light Pollution Science and Technology Institute (2000), The night sky in the World - Satellite monitoring of the artificial night sky brightness and the stellar visibility, Light Pollution Science and Technology Institute, viewed March 07 2010, <http://www.inquinamentoluminoso.it/worldatlas/pages/fig1.htm>.

Loo, B (2007), 'The role of paratransit: some reflections based on the experience of residents’ coach services in Hong Kong', Transportation, vol. 34, no. 4, pp. 471-86.

MacQueen, J (1967), 'Cluster Analysis: Basic Concepts and Algorithms', in P-N Tan, M Steinbach & V Kumar (eds), Introduction to Data Mining.

Mann, WW (1974), 'Auto Rapid Transit', Traffic Engineering, December.


References

115

Marsden, G (2006), 'The evidence base for parking policies - a review', Transport Policy, vol. 13, no. 6, pp. 447-57.

Martínez, L (2010), 'Financing Public Transport Infrastructure Using the Value Capture Concept', PhD thesis, Instituto Superior Técnico.

Martínez, L & Geraldes, R (2005), Sistema Minibus de Nova Geração, caso de Estudo: Massamá, Instituto Superior Técnico.

Martinez, LM & Viegas, JM (2009), Activities, Transportation Networks and Land Prices as Key Factors of Location Choices: An Agent-Based Model for Lisbon Metropolitan Area (LMA), TSI-SOTUR-09-04, MIT-Portugal Working Paper Series.

Menon, G (2002), Travel Demand Management in Singapore - Why did it work?, Singapore.

Metropolitano de Lisboa (2010), Diagramas e mapas, viewed August 6, 2010, <www.metrolisboa.pt/Default.aspx?tabid=540>.

Morlok, EK, et al. (1997), The Advanced Minibus Concept - A New ITS-Based Transit Service for Low Density Markets, Federal Transit Administration.

Mulder, SA & Wunsch, DC (2003), 'Million city traveling salesman problem solution by divide and conquer clustering with adaptive resonance neural networks', Neural Networks, vol. 16, no. 5-6, pp. 827-32.

Murray, AT & Estivill-Castro, V (1998), 'Cluster discovery techniques for exploratory spatial data anaylisis', International Journal of Geographical Information Science, vol. 12, no. 5, pp. 431-43.

Nelson\Nygaard Consulting Associates (2007), Toolkit for Integrating Non-Dedicated Vehicles in Paratransit Service, TCRP Report 121, Transit Cooperative Research Program - The Federal Transit Administration, Washington D.C.

Orski, CK (1975), 'Paratransit: The coming of age of a transportation concept', Transportation, vol. 4, no. 4, pp. 329-34.

Osterwalder, A, et al. (2005), 'Clarifying Business Models: origins, present, and future of the concept', Communications of the Association for Information Systems, vol. 15.


References

116

Pucher, J & Buehler, R (2008), 'Cycling for Everyone: Lessons from Europe', Transportation Research Record, no. 2074, pp. 58-65.

Pucher, J & Kurth, S (1996), 'Verkehrsverbund: the success of regional public transport in Germany, Austria and Switzerland', Elsevier Science, Transport Policy, vol. 2, no. 4, pp. 279-91.

Radin, S (2005), Advanced Public Transportation Systems Deployment in the United States - Year 2004 Update, John A. Volpe National Transportation Systems Center, U.S. Department of Transportation, Federal Transit Administration, viewed April 05, 2010, <http://www.itsdocs.fhwa.dot.gov/JPODOCS/REPTS_TE/14169_files/14169.pdf>.

Reimann, M, et al. (2004), 'D-ants: Savings based ants divide and conquer the vehicle routing problem', Computers and Operations Research, vol. 31, pp. 563-91.

Reinelt, G (1989), Fast heuristic for large geometric traveling salesman problems, Report No. 185, Institut für Mathematik, Universität Augsburg.

Rodriguez, J & Murtha, T (2009), Travel Demand Management - Strategy Paper.

Rouskas, GN (2009), 'The Directional p-Median Problem: Definition and Applications', in GN Rouskas (ed.), Internet Tiered Services

Theory, Economics and Quality of Service, pp. 1-9.

Rugina, R & Rinard, MC (2001), 'Recursion Unrolling for Divide and Conquer Programs', paper presented to Proceedings of the 13th International Workshop on Languages and Compilers for Parallel Computing-Revised Papers.

Shaheen, S, et al. (1999), 'Carsharing and Partnership Management: An International Perspective', Transportation Research Record: Journal of the Transportation Research Board, vol. 1666, no. -1, pp. 118-24.

Shephard, R (1966), 'Metric Structures in Ordinal Data', Journal of Mathematical Psychology, vol. 3, pp. 287-315.

Simon, RM (1998), Paratransit Contracting and Service Delivery Methods, TCRP Synthesis 31, Transit Cooperative Research Program - The Federal Transit Administration, Washington D.C.

Smith, DR (1985), 'The design of divide and conquer algorithms', Science of Computer Programming, vol. 5, pp. 37-58.


References

117

Solomon, MM (1987), 'Algorithms for the vehicle routing and scheduling problems with time window constraints', Oper. Res., vol. 35, no. 2, pp. 254-65.

Stockholmsforsöket (2006), 'Facts and Results from the Stockholm Trials: Final Report', Stockholm: Stockholmsforsöket.

SuperShuttle (2010), SuperShuttle - Need a lift?, viewed August 10, 2010, <http://www.supershuttle.com/>.

Taillard, ÉD (1993), 'Parallel iterative search methods for vehicle routing problems', Networks, vol. 23, pp. 661-73.

Tanaboriboon, Y (1992), 'An Overview and Future Direction of Transport Demand Management in Asian Metropolises', Regional Development Dialogue, vol. 13.

Taylor, C, et al. (1997), 'Selection and Evaluation of Travel Demand Management Measures', Transportation Research Record: Journal of the Transportation Research Board, vol. 1598, no. -1, pp. 49-60.

Teixeira, JC & Antunes, AP (2008), 'A hierarchical location model for public facility planning', European Journal of Operational Research, vol. 185, no. 1, pp. 92-104.

The World Bank (2010), Motor vehicles (per 1,000 people), viewed June 09, 2010, <http://data.worldbank.org/indicator/IS.VEH.PCAR.P3>.

Transit Cooperative Research, P (2001), Advanced Public Transportation Systems for rural areas where do we start? How far should we go?, National Research Council . Transportation Research, Board . TCRP web document, 20.

Transport for London (TfL) (2009), Congestion Charge Factsheet, July 07, 2010, <http://www.tfl.gov.uk/assets/downloads/corporate/congestion-charge-factsheetjuly-2009.pdf>.

Transport Select Committee (2003), Jam tomorrow? the multi modal study investmen plans third report of session 2002-03, vol. 1, Report and Proceedings of the Committee: House of Commons papers 2002–03 38–I, Stationery Office, London.

Tuppen, J (1979), 'New Towns in the Paris Region: An Appraisal', The Town Planning review, vol. 50, no. 1, pp. 55-70.


References

118

United Nations (2010a), World population Prospects: The 2008 Revision, viewed June 03, 2010, <http://esa.un.org/unpp/>.

United Nations (2010b), World Urbanization Prospects - The 2009 Revision, ESA/P/WP/215, New York.

Viegas, JM (2005), 'Organisation and Financing of Public Transport', in European Conference of Ministers of Transport (ECMT) 2005 - Sustainable Urban Travel.

Viegas, JM & Hansen, P (1985), 'Finding shortest paths in the plane in the presence of barriers to travel (for any lp-norm)', European Journal of Operational Research, vol. 20, pp. 373-81.

Viegas, JM & Martínez, LM (2010), 'Generating the universe of urban trips from a mobility survey sample with minimum recourse to behavioural assumptions', in Proceedings of the 12th World Conference on Transport Research, Lisbon.

Ward Jr., JH (1963), 'Hierarchical grouping to optimize an objective function', Journal of the American Statistical Association, vol. 56, pp. 236-44.

Watts, PF, et al. (1990), Urban Minibuses in Britain: Development, User Responses, Operations and Finances, Transport and Road Research Laboratory, Crowthorne, Berkshire, England.

Weiner, R (2008), Integration of Paratransit and Fixed-Route Transit Services, TCRP Synthesis 76, Transit Cooperative Research Program - The Federal Transit Administration, Washinghton D.C.

White, PR, et al. (1991), 'Cost benefit analysis of urban minibus operations', Transportation, vol. 19, pp. 59-74.

Work, DB & Bayen, AM (2008), 'Impacts of the Mobile Internet on Transportation Cyberphysical Systems: Traffic Monitoring using Smartphones', National Workshop for Research on High-Confidence Transportation Cyber Physical Systems: Automotive, Aviation and Rail.

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