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Design of a Car Sharing System
Matheus Silva Marreiros
Thesis to obtain the Master of Science Degree in
Energy Engineering and Management
Supervisor: Prof. João Pedro Bettencourt de Melo Mendes
Examination Committee
Chairperson: Prof. José Manuel Costa Dias de FigueiredoSupervisor: Prof. João Pedro Bettencourt de Melo Mendes
Member of the Committee: Prof. Gabriel César Ferreira Pestana
June 2018
Acknowledgments
I would like to start by acknowledging my dissertation supervisor Professor Joao Pedro Mendes for his
insight into the inner working of designing a model with SysML and support, without which this work
would not be possible.
I would also like to thank my family, whom I love dearly, for the unconditional love and support. They
may be across the ocean but will be here with me in spirit.
Lastly, I would like to thank all the friends that were made through these last 10 year. I would like to
give especial thanks to my elementary school friends, who I consider to be my Portuguese family.
iii
Resumo
A quota modal do uso do carro em Lisboa aumentou em 9.4% num perıodo de 10 anos, de 2001 a 2011,
e este e o problema que merece atencao para obter um sistema de transportes sustentavel. O mesmo
tem repercussoes, nomeadamente a escassez de estacionamento e o sub-desenvolvimento dos outros
modos de transporte. Apos analisar quais sao os fatores que influenciam a escolha modal de uma pes-
soa, um modelo do sistema foi criado utilizando Systems Modeling Language (SysML). Cada operador
de transporte foi modelado como uma entidade publica e como um ator do sistema, juntamente com a
autoridade de transporte do sistema, com a entidade responsavel pelo parqueamento e com o cliente.
O modelo construıdo tem 6 variaveis chave, 32 variaveis auxiliares e 5 contadores, 7 atores e 27 casos
de uso para descrever o problema. Este modelo fornece uma estrutura para alcancar uma solucao do
problema, que passa por ter uma rede que abrange toda a cidade, um operador de transporte publico
para cada modo de transporte, unificando-os fisicamente e atraves dum sistema unico de bilhetica, e
com uma plataforma unica de informacao. O sistema de partilha de carros desenhado e tratado como
um operador de transporte publico e tem como objetivo servir de substituto para o uso do veıculo pri-
vado, e como porta de entrada na utilizacao dos outros meios de transporte publico para quem ainda
nao os usa.
Palavras-chave: Systems Modeling Language, Mobilidade partilhada, Transporte publico,
Mobilidade sustentavel.
v
Abstract
The car modal share in Lisbon increased by 9.4% in a span of 10 years, from 2001 to 2011, and is
a problem that must be addressed in order to have a sustainable transport system. This problem has
consequences, namely parking shortage and underdevelopment of other modes of transport. After
analyzing which are the factors that influence a person in choosing a transport mode, a model of the
system was created using Systems Modeling Language (SysML). Each transport provider was modelled
as a public entity and as a system actor, along with the system’s transport authority, the entity responsible
for the parking and the customer. The constructed model has 6 key variables, 32 auxiliary variables and
5 counters, 7 actors, and 27 use cases used to describe the problem. The system model provides
a framework to achieve a solution to the problem, consisting in having a city-wide network, a public
transport provider for each of the modes of transport, unifying them physically, and through a unique
ticketing system and with a unique information platform. The designed car sharing system is treated as
a public transport provider and has the objective of serving as a replacement to the use of the private
vehicle and as a gateway to the other modes for the citizen that use the car as the only mode of transport.
Keywords: Systems Modeling Language, Shared mobility, Public transport, Sustainable mobil-
ity.
vii
Contents
Acknowledgments . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . iii
Resumo . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . v
Abstract . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . vii
List of Tables . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . xiii
List of Figures . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . xv
Nomenclature . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . xix
Glossary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . xxi
1 The Problem 1
1.1 Sustainable mobility paradigm . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2
1.2 Modal share . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2
1.3 Modal choice . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5
1.3.1 Socio-demographic factors . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6
1.3.2 Spatial characteristics . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6
1.3.3 Social factors . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10
2 System framework 12
2.1 Actors . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 13
2.1.1 Customer . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 14
2.1.2 Lisbon Municipal Hall (CML) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 14
2.1.3 EMEL . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 15
2.1.4 Carris . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 15
2.1.5 Metro . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 17
2.1.6 Bike Sharing Provider . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 18
2.1.7 Car Sharing Provider . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 20
2.2 Variables . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 21
2.2.1 K1 – Parking Easiness . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 21
2.2.2 K2 – Bike Lane Density . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 24
2.2.3 K3 – Information Utility . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 25
2.2.4 K4 – Systems Interconnectivity . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 27
2.2.5 K5 – System Coverage . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 29
ix
2.2.6 K6 – Services Capacity and Availability . . . . . . . . . . . . . . . . . . . . . . . . 31
3 System Interactions and Behaviours 39
3.1 Managing parking easiness . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 41
3.2 Infrastructure interactions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 41
3.2.1 Extending bike lanes network . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 41
3.2.2 Maintaining bike lanes network . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 42
3.2.3 Creating transport hubs . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 42
3.3 Handling information . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 43
3.4 Expanding systems’ coverage . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 44
3.4.1 Creating subway stations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 44
3.4.2 Creating bike sharing stations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 45
3.4.3 Expanding operational area . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 46
3.5 Integrating means of access . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 46
3.6 Managing systems’ capacity and availability . . . . . . . . . . . . . . . . . . . . . . . . . . 46
3.6.1 Managing bus system capacity . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 47
3.6.2 Managing subway system capacity . . . . . . . . . . . . . . . . . . . . . . . . . . . 47
3.6.3 Managing bike sharing system availability . . . . . . . . . . . . . . . . . . . . . . . 48
3.6.4 Managing car sharing system availability . . . . . . . . . . . . . . . . . . . . . . . 49
3.7 Usage interactions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 50
3.7.1 Using private vehicle . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 51
3.7.2 Using regular public transport . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 51
3.7.3 Using bike sharing system . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 51
3.7.4 Using car sharing system . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 54
4 Constraints and Analysis 55
4.1 Actor parametrics . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 55
4.1.1 EMEL’s parametrics . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 55
4.1.2 Customer parametrics . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 56
4.1.3 CML parametrics . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 58
4.1.4 Carris parametrics . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 58
4.1.5 Metro parametrics . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 60
4.1.6 BSP parametrics . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 62
4.1.7 CSP parametrics . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 63
4.2 Use case parametrics . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 64
4.3 Variable parametrics . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 65
4.3.1 Average variables . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 67
4.4 Analysis and proposed solution . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 70
4.4.1 Services accessibility . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 70
4.4.2 Information and reliability . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 71
x
4.4.3 Car sharing role . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 71
5 Conclusions 73
5.1 Achievements . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 73
5.2 Future work . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 74
xi
List of Tables
3.1 Actors, use cases and affected variables . . . . . . . . . . . . . . . . . . . . . . . . . . . . 40
4.1 Use cases parametric models. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 65
4.2 Variables and counters equations. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 66
xiii
List of Figures
1.1 Share of final energy consumed by sector in Portugal in 2014. . . . . . . . . . . . . . . . . 1
1.2 Modes of transport. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3
1.3 Modal share of commuting trips in the city of Lisbon, 2011. . . . . . . . . . . . . . . . . . 4
1.4 Modal share of commuting trips in the city of Lisbon, 2001. . . . . . . . . . . . . . . . . . 4
1.5 Modal choice definition. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5
2.1 System’s actors. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 13
2.2 Customer’s use cases. Each use case is an instance of modal choice. . . . . . . . . . . . 14
2.3 CML’s use cases. Being the transport authority, it’s responsible for integrating and han-
dling all the different services, in addition to managing the bike lanes network. . . . . . . . 15
2.4 EMEL’s use cases. In order to manage the parking utilization, the price and the quantity
of parking spaces can be altered. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 16
2.5 Bus system coverage. This service covers approximately 99% of the city’s area. . . . . . 16
2.6 Carris’ use cases. It only manages the service capacity and handles its information. . . . 17
2.7 Subway system coverage. This service covers approximately 57% of the city’s area. . . . 17
2.8 Metro’s use cases.It’s responsible for expanding the subway system, managing its capac-
ity and handling its information. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 18
2.9 Bike sharing system coverage. This is the system with the smallest coverage, covering
only approximately 16% of the city’s area. . . . . . . . . . . . . . . . . . . . . . . . . . . . 19
2.10 Bike sharing provider’s use cases. The system can be expanded and relocations can be
performed in order to always have bicycles available. . . . . . . . . . . . . . . . . . . . . . 19
2.11 Car sharing system coverage. Following the bus network, the car sharing service has the
biggest coverage with approximately 68%. . . . . . . . . . . . . . . . . . . . . . . . . . . . 20
2.12 CSP’s use cases. This actor may expand the system coverage, manage its capacity and
availability, and handles its information. . . . . . . . . . . . . . . . . . . . . . . . . . . . . 21
2.13 Key variable 1 - Parking Easiness . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 22
2.14 Effect of A01 on K1. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 23
2.15 Effect of A02 on K1. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 23
2.16 Effect of A03 on K1. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 23
2.17 Key variable 2 - Bike Lane Density . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 25
2.18 Key variable 3 - Information Utility . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 26
xv
2.19 Key variable 4 - Systems Interconnectivity . . . . . . . . . . . . . . . . . . . . . . . . . . . 28
2.20 Key variable 5 - System Coverage . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 30
2.21 Intersection of the systems coverage areas. K5 currently sits on a value of 0.14. . . . . . 30
2.22 Key variable 6 - Services Capacity and Availability . . . . . . . . . . . . . . . . . . . . . . 32
2.23 Auxiliary variable 16 - Bus System Capacity . . . . . . . . . . . . . . . . . . . . . . . . . . 33
2.24 Auxiliary variable 17 - Subway System Capacity . . . . . . . . . . . . . . . . . . . . . . . 33
2.25 Auxiliary variable 18 - Bike Sharing System Availability . . . . . . . . . . . . . . . . . . . . 34
2.26 Auxiliary variable 19 - Car Sharing System Availability . . . . . . . . . . . . . . . . . . . . 36
2.27 Auxiliary variable 20 - Required System Capacity . . . . . . . . . . . . . . . . . . . . . . . 37
3.1 Sequence diagram 00 – Managing parking easiness . . . . . . . . . . . . . . . . . . . . . 42
3.2 Sequence diagram 01 – Extending bike lanes network . . . . . . . . . . . . . . . . . . . . 42
3.3 Sequence diagram 02 – Maintaning bike lanes network . . . . . . . . . . . . . . . . . . . 43
3.4 Sequence diagram 03 – Creating transport hubs . . . . . . . . . . . . . . . . . . . . . . . 43
3.5 Sequence diagram 04 – Handling bus system information . . . . . . . . . . . . . . . . . . 44
3.6 Sequence diagram 09 – Creating subway stations . . . . . . . . . . . . . . . . . . . . . . 45
3.7 Sequence diagram 10 – Creating bike sharing stations . . . . . . . . . . . . . . . . . . . . 45
3.8 Sequence diagram 11 – Expanding operational area . . . . . . . . . . . . . . . . . . . . . 46
3.9 Sequence diagram 12 – Integrating means of access . . . . . . . . . . . . . . . . . . . . . 46
3.10 Sequence diagram 13 – Increasing bus service . . . . . . . . . . . . . . . . . . . . . . . . 47
3.11 Sequence diagram 14 – Decreasing bus service . . . . . . . . . . . . . . . . . . . . . . . 48
3.12 Sequence diagram 15 – Increasing subway service . . . . . . . . . . . . . . . . . . . . . . 48
3.13 Sequence diagram 16 – Decreasing subway service . . . . . . . . . . . . . . . . . . . . . 49
3.14 Sequence diagram 17 – Relocating bicycles . . . . . . . . . . . . . . . . . . . . . . . . . . 49
3.15 Sequence diagram 18 – Increasing car sharing capacity . . . . . . . . . . . . . . . . . . . 50
3.16 Sequence diagram 19 – Relocating cars . . . . . . . . . . . . . . . . . . . . . . . . . . . . 50
3.17 Sequence diagram 20 – Using private vehicle . . . . . . . . . . . . . . . . . . . . . . . . . 51
3.18 Sequence diagram 21 – Using regular public transport . . . . . . . . . . . . . . . . . . . . 51
3.19 Sequence diagram 22 – Using bike sharing system . . . . . . . . . . . . . . . . . . . . . . 53
3.20 Sequence diagram 23 – Using car sharing system . . . . . . . . . . . . . . . . . . . . . . 54
4.1 EMEL’s parametric diagram. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 56
4.2 Customer’s parametric diagram. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 57
4.3 CML’s parametric diagram. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 59
4.4 Carris’ parametric diagram. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 60
4.5 Metro’s parametric diagram. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 61
4.6 BSP’s parametric diagram. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 62
4.7 CSP’s parametric diagram. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 63
4.8 Creating bike sharing stations parametric diagram. . . . . . . . . . . . . . . . . . . . . . . 66
4.9 A21 – Average bus passage frequency parametric diagram. . . . . . . . . . . . . . . . . . 69
xvi
4.10 A31 – Average car trip time parametric diagram. . . . . . . . . . . . . . . . . . . . . . . . . 70
xvii
Nomenclature
Roman symbols
N Natural numbers.
R+ Positive real numbers.
K Key variable.
A Auxiliary variable.
C Counter.
Subscripts
i Computational index.
Superscripts
new New value.
old Previous value.
xix
Glossary
BSP Bike sharing provider is the entity responsible
for managing the bike sharing system.
CML Lisbon Municipal Hall (Camara Municipal de
Lisboa) is the transport authority of Lisbon’s
public transport system.
CSP Car sharing provider is the entity responsible
for managing the car sharing system.
EMEL Lisbon Municipal Mobility and Parking Com-
pany (Empresa Municipal de Mobilidade e
Estacionamento de Lisboa is responsible for
public parking management.
GHG Greenhouse gases are responsible for the
greenhouse effect which warms the planet’s
surface.
SysML Systems Modeling Language is a graphical
modeling language used for specifying, analyz-
ing, designing, and verifying complex systems,
as defined by the Object Management Group.
pkm Passenger-kilometre is a unit of measurement
that represents the number of passengers
transported in one kilometre by a certain mode.
xxi
Chapter 1
The Problem
Sustainability is a transversal trend that affects several areas of knowledge. Energy, environment, and
transportation are some examples. It has the goal of achieving more with fewer resources or with
renewable sources, to the point where future generations can have access to the same resources as
the present ones. The increasing shift to use renewable energy sources, especially wind and solar, in
electricity production is an example of the sustainable mindset [1].
The transportation sector is a major consumer of energy and emitter of greenhouse gases (GHG). In
2014, of the total 15.17 Mtoe of final energy consumed in Portugal, the transportation sector consumed
36.3%. Thus making it the activity sector with the biggest consumption of final energy, followed by the
industry sector with 34%, domestic sector with 16.9% and the services sector with 12.8%, as shown in
figure 1.1 [2]. During the same year, the Portuguese economy released 65 331.3 tonnes of CO2eq [3].
The transport sector was responsible for 36.7% of it, and road transport was dominant with a relative
share of 95.7% [4].
Figure 1.1: Share of final energy consumed by sector in Portugal in 2014.
1
In the city of Lisbon, the transport system isn’t sustainable due to the overuse of private transport.
Even with an extensive public transport network, almost half of the citizens in the city, 47.7%, choose to
use the private vehicle as a primary mode of transportation [5]. The dominance of the private vehicle
brings additional problems. Some are derivative from the sheer number of vehicles in circulation, such as
the occurrence of traffic jams and increasing levels of noise and environmental pollution. The remaining
problems are of a structural nature. Streets need to become larger in order to accommodate the vehicle
traffic and demand for parking spaces. One possible outcome is the reduction of soft modes’ mobility
(non-motorized modes of transport) since streets and sidewalks generally compete for the same space
[6].
1.1 Sustainable mobility paradigm
To solve this problem, it’s necessary to make the private vehicle a less attractive mode in relation to
others. However, the use of the private vehicle shouldn’t be banned. The car is widely viewed as a
symbol of personal freedom, and their prohibition could be considered a personal attack. Acceptability
is considered a cornerstone to achieve sustainable mobility, once without a certain degree of public
acceptance, change is impossible [6].
The objectives of a sustainable transport system are to provide high accessibility and environmental
quality to its users [6]. A high degree of mobility has already been reached, i.e. it’s possible to use public
transportation to reach almost any place within the city. However, in order to access public transport, the
user may have to walk a considerable distance and also needs to wait a considerable amount of time.
For these reasons, the current transport system hasn’t achieved a high degree of accessibility.
Accessibility represents the user’s capability to carry out his planned activities and there are two
distinct perspectives. Firstly, accessibility may be defined as the proximity of public transport access
points in relation to the user, both at origin and destination. It can also be defined as the facility of
movement, considering both the time and monetary costs, to reach the user’s destination [7].
High environmental quality is achieved through the increase of cleaner technologies, such as vehicles
powered by renewable and sustainable sources (renewable energy and biofuels [8]), and greater use
of walking, cycling, and public transport. These measures reduce the system’s environmental impact,
namely the GHG emissions and noise pollution, while also promoting active transport and increasing
personal health [9].
1.2 Modal share
Each citizen has a wide array of modes of transport available. The modes can be divided into motorized
and soft modes (non-motorized). Motorized modes of transport are further divided into private and public
transport. Private modes are cars and motorcycles, while public transport encompasses buses, light rail,
subway, trains, and boats. Soft modes are the bicycle and walk. Figure 1.2 shows all the different modes
and how they are divided.
2
Figure 1.2: Modes of transport.
In order to compare the utilization of each mode, the concept of modal share or modal split is utilized.
The modal share of a given transport mode is the ratio between a mode’s unit of measurement and the
sum of the same unit for all transport modes. All modes can be characterized by different units of
measurement, such as the number of trips, volume or weight of cargo transported, passenger-kilometre
or tonne-kilometre. Passenger-kilometre (pkm) is a unit of measurement that represents the number
of passengers transported in one kilometre by a certain mode. Tonne-kilometre (tkm) is analogous to
passenger-kilometre but measures the weight of cargo, in tonnes, transported in one kilometre by a
certain mode [10].
Modal share can be used as a gauge of a transport system sustainability [11]. High shares of public
transport or soft modes in a location shows that the citizens use more sustainable modes of transport.
In the city of Lisbon, the modal share of commuting trips is shown in figure 1.3. This data was
acquired during the 2011 national census and shows the share of Lisbon residents that use each mode
of transport during the daily commute to work. However, the data collected only feature the main mode
used, i.e. if there are more than one mode used, only the one used to cover the largest distance during
the trip is considered. For the residents that use different modes of transport for the round trip, the mode
3
considered is the one-way [5].
Figure 1.3: Modal share of commuting trips in the city of Lisbon, 2011.
Even though the modal share of private vehicles is higher for non-commuting trips [12] in compari-
son with commuting trips, the latter is responsible for peak demand on road networks [13]. Meaning that
commuting trips are accountable for most of the emissions and traffic generation during the day. Be-
cause of this, the commuting modal share is considered to be an acceptable indicator of the residents’
transportation habits.
In 2011, there were three main transport modes used, car, public transport and walking, with a
combined share of 98.2%. And as seen on figure 1.4, in 2001 the same three modes were the most
used, however, the car share increased from 38.3% to 47.7% to the detriment of public transport and
walk share.
Figure 1.4: Modal share of commuting trips in the city of Lisbon, 2001.
The increasing car modal share is the problem addressed in this work. The consequences re-
garding the transport system are the shortage of parking and underdevelopment of other modes. Thus
other modes aren’t accessible citywide, aren’t sufficiently interconnected, either physically or monetarily,
don’t have enough capacity to handle the required flow of users and aren’t reliable.
4
In order to solve this issue a model of Lisbon’s transport system is created. This model explores what
are the variables that affect the usage of different modes and how they interact with different entities,
namely the different public transport providers. The proposed solution revolves around having a public
car sharing service that replaces the usage of the private vehicle inside the city while also serving as a
gateway to more sustainable transport modes.
1.3 Modal choice
It’s necessary to comprehend the reasoning behind the user’s decisions to determine which are the
relevant system’s characteristics and how to best describe them.
The reasoning behind each user’s decision is generally viewed in accordance with the research’s
objectives. There are three main distinct approaches: the rationalist, the socio-geographical and the
socio-psychological.
In the rationalist approach, the user is treated as perfectly rational and with full awareness of all
available modes. They will choose the mode with lower costs and travel time regardless of other factors.
For the socio-geographical approach, the time and space are treated differently. The user now has an
agenda that must be fulfilled, and the chosen mode must abide by it. Thus, the mode has to be able
to take the user from a specific location and time to another. Lastly, the socio-psychological approach
introduces the individual’s attitudes and intentions towards each mode [14].
With the combination of the different approaches, it’s clear that a sensible framework of modal choice
must include economic, geographical and psychological factors. As such, the adopted definition of modal
choice is: “the decision process to choose between different transport alternatives, which is determined
by a combination of individual socio-demographic factors and spatial characteristics, and influenced by
social factors” adapted from [14, p. 331], as shown on figure 1.5.
Figure 1.5: Modal choice definition.
Some users are restrained to a given transport mode, be it by force or by choice. These users are
designated by captive users. Captivity by force exists when a user isn’t able to use any mode except
for a specific one, e.g. being a car captive because the public transport alternatives are too distant from
the origin or destination or because the travel time won’t allow the user to perform all of their activities;
being a public transport captive because the user doesn’t have a private vehicle available and can’t
perform their activities by soft modes. Captivity by choice exists when a user disregard all other viable
5
alternatives in relation to one specific mode, e.g. only using the car because of its flexibility or only using
public transport due to the possibility of engaging in different activities [7]. Captivity is one consequence
of a system that doesn’t allow the user to make the choice that best suits their needs.
Many researched factors are interdependent of each other and thus aren’t appropriate to be used
together. Factors such as age, gender, education, and income are manifested through the travel cost
and car availability [14]. This filtering of factors also serves to pick and chose factors that characterize
the system and not its actors. However, some redundancy is unavoidable because some factors are
interdependent but affect the modal choice in different ways.
Each mode chosen by the user can be considered to be independent of each other [13], thus each
mode has factors which are exclusive. For example, the public transport frequency only affects the
overall attractiveness of using public transport, it doesn’t affect how the user views the remaining modes.
This means that it’s possible to change specific aspects of the system that only affects one mode in such
a way that the whole system behaves differently.
1.3.1 Socio-demographic factors
Socio-demographic factors frame the user’s travel needs and social interactions. These factors are
household composition and car availability.
Household composition
Different household compositions create different mobility demands. A single person has different de-
mands than a person with a child. The latter has to care for the child and their needs, such as having
the responsibility of taking the child to school and back home. In this case, the user has a new restraint
that must be satisfied. If the additional restraints can’t be satisfied by a given mode, the user no longer
considers it to be a viable option [15]. A household with one or more children is correlated with increas-
ing uses of the car and decreasing use of public transport, due to the greater flexibility provided by the
car [13–15].
Car availability
Car availability plays a major role in modal choice. If the user doesn’t have a car available, this mode
simply isn’t an alternative. With increasing number of cars, its modal share also increases in prejudice
of public transport share [7, 13–15]. The number of cars per users in the system is an indicator of how
prevalent this mode is.
1.3.2 Spatial characteristics
Spacial characteristics describe the physical environment in which the journey takes place and also
describe the conditions in which a particular journey is made. The physical environment is composed
of the following factors: population density, land-use diversity, parking, accessibility, public transport
6
frequency, course impedance and supporting infrastructure. A particular journey is composed of the
following factors: travel motive, travel time, travel distance, travel cost, trip chaining, weather conditions,
interchange, and safety.
Population density
Population density, the number of inhabitants per area, is positively associated with higher shares of
public transport and soft modes. There are two reasons for these correlations: shorter distances in a
more congested section of the system and better public transport service. In zones of higher density, the
overall distance between points of interest is reduced and the system is more congested in relation to
lower density zones, thus public transport and soft modes become a more attractive option [16]. Higher
density zones generally have better public transport access than lower density zones, making public
transport a more attractive option [14].
Land-use diversity
Land-use diversity includes different activities in the same surroundings: residence, commerce, insti-
tutions, green space, industry and transport infrastructure. This mixture of land-use is related to travel
distances. In zones of higher diversity, the user has to travel smaller distances to reach the destination
since most activities are located near each other. A higher degree of land-use diversity is correlated with
lower uses of the car [14].
Parking
Parking is essential to the use of cars and, to some extent, of bicycles as well, thus parking availability
and price is strongly correlated with modal choice [7, 14, 17]. The system’s parking availability in relation
to its demand influences the user modal choice, higher availability makes the car and the bicycle more
attractive. There’s time spent finding a parking space and it adds to the total amount of travel time. The
bigger the parking demand, in relation to its availability, the higher the time needed to finish the trip and
the less attractive the mode becomes. The price also plays an important role, because it’s one of the
main variable costs when using a car, together with fuel costs [17] and because the availability of free
parking makes the car a more attractive choice regardless of travel time in relation to public transport
[14].
Accessibility
Using the definition of accessibility related to public transport, the proximity of public transport access
points in relation to the user, both at origin and destination, an increase in accessibility translates into a
shorter journey time wise. This makes it easier for the user to access the public transport system, and
since the user first chooses to use public transport if it has good access, it increases the modal share
[7]. Easy access and shorter travel times are associated with a higher modal share [16].
7
Public transport frequency
The inverse of the time between the same transport passing by the same location is defined as the
transport frequency. It’s directly associated with the total travel time of public transports, where higher
frequencies translate to lower waiting periods. A higher frequency also promotes flexibility since the user
doesn’t feel concerned having to wait too long for the next transport, encouraging its modal share [14].
Reliability is also improved along with increasing frequency, and this also makes the user more prone to
use public transport [13].
Course impedance
Course impedance affects soft modes and deals with the course slope, the quality of the pavement,
the size of the sidewalk and the existence of trees and obstacles to the circulation. The course slope
is regarded as significant to soft modes and reduced slopes increase their attractiveness. Slopes also
condition users carrying heavy objects, such as backpacks and shopping bags, decreasing the mode
attractiveness [17]. Pavement quality also has importance for both soft modes, since the journey quality
will depend heavily on it. The size of the sidewalk and the existence of trees and obstacles to the circula-
tion are related to walking. The user prefers courses with wider sidewalks, with trees that provide shade
and with few obstacles, making the course feel safer and more comfortable. The course impedance is
important because the user may choose longer routes if they have a lower impedance [17, 18].
Supporting infrastructure
A mode can only be used if there’s supporting infrastructure. The type of infrastructure varies with the
mode. Motorized modes require streets and parking spaces in order to be able to circulate. Public trans-
port requires stations to pick up and leave users. With the presence of mode’s supporting infrastructure,
its attractiveness increases because the mode becomes available and easier to use [13, 17, 18]. The
road network covers almost the entirety of the city. However, the same isn’t true for bike lanes and metro
stations, thus showing room available for expansion and increasing mode attractiveness.
Travel motive
Travel need is intimately related to the travel motive and it will dictate the user’s mobility demands. The
main travel motives are commute, business and leisure [14]. In the case of commute and business,
the demand for travel is mostly derived from the need to go from origin to the destination rather than
the pleasure of the trip itself, and thus the user will choose the mode which has the most utility for that
journey, composed of the best combination of travel time and comfort. For leisure activities, the user
may derive further utility from the journey itself, i.e. the enjoyment derived from the path chosen plays
an important role in choosing a mode. For example, the user may choose a slower or more costly mode
if it goes through a scenic route [19].
Travelling by car dominates when the motive is leisure or business. However, soft modes are note-
worthy for short leisure trips and public transport has higher shares for commuting trips [14].
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Travel time
The time needed to complete a trip is important while choosing a given mode. Different modes differ
in travel speed, possible paths, and requirements needed to use it. In order for a user to choose the
bicycle, the user must have access to it and the destination must be reachable while using it. If the user
were to use public transport, the user would have to afford the travel cost and both the origin and the
destination should have access to the public transport network. It’s thus important to account every step
needed for each mode. This includes the time spent waiting, transferring between different modes, while
in transit, parking the vehicle, moving to the system’s access points from the origin and from the access
points to the destination.
Depending on the travel motive, the user values travel time differently and is more sensitive to time
spent waiting in opposition to the time spent while in transit [14]. For commuting and business-related
travel, the user tends to dislike the journey, since it’s mostly seen as a means to an end, thus preferring
shorter trips time-wise. However, the optimal time desired by most users is different from zero. This im-
plies that the user finds some utility during the journey, such as the potential to use the time productively,
to experience the surroundings while travelling or to experience different non-home locations [19].
Travel distance
The distance between the origin and the destination has a heavy influence on the mode chosen. For
shorter journeys, soft modes have a substantial share. Bellow one kilometre, walking is usually the
preferred mode. Bicycle share rises with the distance before beginning to decrease. It reaches maximum
share for distances between 0.6km and 1.5km and for distances superior to 3km, the share is lower than
10% [20]. This indicates that there’s a maximum acceptable trip length for soft modes [18], probably due
to travel time or due to it being too tiresome. For motorized modes, the longer the journey, the higher
its share. However, public transport is weaker for interurban travels than for urban travels, thus its more
prolific inside the city and loses modal share to the car for interurban travels [20].
Travel cost
People mostly see travel as a means to an end, and as such try to minimize the inherent costs. Therefore
travel cost and mode attractiveness vary inversely [13, 14, 18].
What composes travel cost depends on the mode. Public transportation has a predetermined cost
that accounts for both fixed and variables costs in regards to the mode operation, whereas in private
vehicle transport, the user only accounts for the variable costs (fuel, parking, tolls) but not the fixed
cost (acquisition cost, insurance, yearly taxes). This distinction can set a disadvantage towards public
transportation because more costs are accounted for.
Trip chaining
A trip becomes increasingly complex with the additional stops between the origin and the final destina-
tion. The complexity of this trip chaining will also play a role in the mode chosen. In order to decrease the
9
effort required for a trip with stops, people choose the least complex mode available, which is usually the
car. Public transport, however, becomes progressively more complex with the number of intermediate
stops [14]. This can have a minor effect if the transition between different modes and within the same
mode is made easier.
Weather conditions
The weather can be a conditioner for how the modes are accessed [14]. Soft modes are especially
affected by adverse climate conditions becoming less attractive, while motorized modes are less affected
[17]. To the detriment of soft modes, motorized modes have an increased use during adverse climate
conditions. The interest in utilizing public transportation increases only if the respective infrastructure is
adequate for the weather in question, otherwise, it may decrease [13].
Interchanges
Interchanges are changes between different modes or within the same mode but between different
operators [14]. They exist in order to complement different systems, yet can also increase the journey
time and complexity. When a user changes between modes, there are extra waiting times that don’t exist
in a direct trip [18]. This phenomenon only influences public transports and makes them less attractive,
especially in comparison with the car, that is able to make a journey without interruptions between the
origin and destination [7, 14].
Safety
Safety is a primary concern of the user. A mode that isn’t safe has a very low utility and becomes
unavailable to the user. Thus, it’s important to provide an infrastructure that makes the trip safer for the
user, specifically for soft modes. Bike lanes and parking, crosswalks and large sidewalks are crucial in
order to make soft modes attractive [15, 18]
1.3.3 Social factors
The social factors are the filter between the physical system and what the user considers to be suitable
for their needs. They are subjective and vary from person to person, although they are also shaped by
the encompassing society. However, they are important to consider, since they act as a mediator.
Experiences and perceptions
All experiences with a given mode shape the user’s perception of it and of the remaining modes [14].
For public transports, this implies that it’s important to provide a positive image towards the users. The
system not only has to reach every person but also has to be reliable and comfortable. Should a provider
have the image of unreliable service, e.g. not following the established timetable, the user may choose
to not use it even if theoretically it would be the best option.
10
The perception towards a mode also comes from how the society views it. If a given mode is viewed
favourably, the general public is more inclined to use it instead of another mode [15].
Mode use habit
Strong habits with a specific mode reduce the cognitive load necessary to use it effectively and are a
strong indicator of modal choice. Using a given mode and gaining a stronger habit of doing so positively
reinforce each other, making the mode in question more attractive and easier to use with the passage
of time [14, 15].
%section•
11
Chapter 2
System framework
The problem affects Lisbon’s transport system and as such it’s necessary to describe its surroundings
and how the system works. The system is bound by the city’s limit, not only because of the physical
boundaries but also because the majority of the commutes made by the population of the surrounding
cities is to Lisbon [21]. Consequently, the transport system of Lisbon, not only has to deal with the local
population, but it also has to deal with the daily commuters coming from surrounding counties.
Lisbon Municipal Hall (Camara Municipal de Lisboa, CML) is the transport authority for the system
and is responsible for the management of the different parts of the system organization and for how the
exploration takes place. This work will focus only on public service operators within the city of Lisbon,
therefore operators such as Comboios de Portugal (CP), Fertagus, Transtejo and Soflusa, Rodoviaria de
Lisboa (RL) and Transportes do Sul do Tejo (TST), that are mainly inter-municipal, will not be modelled.
There are four distinct public service operators, which provide a municipal passenger transport public
service:
• Companhia de Carris de Ferro de Lisboa (Carris): Responsible for bus and light rail service.
• Metropolitano de Lisboa (Metro): Responsible for the subway service.
• Bike sharing Provider (BSP): Responsible for the bike sharing service.
• Car sharing Provider (CSP): Responsible for the car sharing service.
Along with the public service operators, others entities are responsible for the infrastructure which
isn’t dedicated to a particular service. Lisbon Municipal Mobility and Parking Company (Empresa Munic-
ipal de Mobilidade e Estacionamento de Lisboa, EMEL) is responsible for public parking management
and CML is responsible for the roads, sidewalks and bike lanes.
Model restrictions and assumptions
There were a few considerations made while building the model, some restrictions and some assump-
tions. In one hand, the restrictions relate to known information related to or parts of the transport system
12
that weren’t modelled. On the other hand, the assumptions were made due to lack of knowledge of how
the system’s parts interact with each other. As such, the model restrictions are:
• No mainly or exclusively inter-municipal public transport operator is modelled.
• Private parking wasn’t considered and only parking in public spaces was.
• There’s no temporal distinction or seasonality. Every day is considered to be a working day.
• Since travel distances aren’t considered, the emissions derived from the system aren’t modelled.
Finally, the model assumptions are:
• Inter-modal trips aren’t considered as a whole and are broken up in single mode sections.
• The customer only has access to information regarding their next trip at their destination.
2.1 Actors
Every entity that actively interacts with the system is considered an actor. This definition doesn’t require
the actor to be a physical person or system, it can be a company. The system’s boundary dictates what
is considered an actor and what is considered part of the system itself.
Figure 2.1: System’s actors.
The system has seven distinct actors, as shown in figure 2.1, comprised of the system’s costumer;
the transport authority, CML, which is responsible for the organization of the other actors, roads and
bike lanes; the company responsible for the parking infrastructure, EMEL; two distinct regular public
transport operators, Carris which is responsible for the bus network, and Metro which is responsible for
the subway network; and two distinct flexible public transport operators, BSP which is responsible for
the bike sharing system and CSP which is responsible for the car sharing system. Even though Carris is
13
also responsible for the light rail network, this service is aimed primarily at tourists and not commuters,
therefore it’s not included.
Actors interact with the system through use cases. These describe actions performed by an actor
and dictate how the variables change. They can increase, decrease or converge the value of a given
variable.
2.1.1 Customer
A customer is a person who uses the transport system. Given this fact, it’s this actor who dictates the
required system capacity. More customers require a system with greater capacity and availability, how-
ever, each provider can’t simply provide full capacity at all times due to economic constraints. Therefore
the providers have to follow the costumers daily travel patterns and provide an adequate service. Fur-
thermore, it’s not sustainable to have a provider with a fully deployed vehicle fleet if those vehicles are
nearly empty.
The use cases performed by the costumer are shown in figure 2.2. This actor takes the part in using
the system, and as such, all the use cases are instances of usage. Depending on the mode chosen
for the journey, a different use case will be triggered. Since walking doesn’t require a public transport
service to exist, no use case is modelled after it.
Figure 2.2: Customer’s use cases. Each use case is an instance of modal choice.
2.1.2 Lisbon Municipal Hall (CML)
Lisbon Municipal Hall is the transport authority of Lisbon’s transport system and as such is responsible
for the macro management of the system, i.e., it’s responsible for each transport provider and their
respective information. Additionally, it’s responsible for building and maintaining bike lanes. CML is also
14
responsible for the road network, but this is considered to be constant and as a result, there are no use
cases regarding its state. Use cases performed by CML are shown in figure 2.3.
Figure 2.3: CML’s use cases. Being the transport authority, it’s responsible for integrating and handlingall the different services, in addition to managing the bike lanes network.
As stated before, CML is responsible for expanding and maintaining the bike lanes network. Being
in charge of the system as an authority implies that it’s responsible for handling (collecting, processing
and displaying) the systems’ information as a whole. It must always be knowledgeable in regards to the
current system state and how they are interacting with each other. CML creates transport hub. These
are locations where all the systems are connected physically and where interchanges are expected and
simplified. Lastly, it oversees and integrates the means of access to different systems, i.e. it creates
different public transport passes that integrates different operators depending on the customers’ needs.
2.1.3 EMEL
Currently, EMEL is overseen by CML but since it’s in charge of a different part of the system, namely
the parking, it’s treated as a separate entity. In order to manage the parking, EMEL can increase or
decrease the parking prices as well as providing more parking spaces or cutting them back. These
managerial actions are shown as use cases in figure 2.4.
2.1.4 Carris
Bus service is provided by Carris. For that reason, it’s responsible to manage the bus service capacity,
increasing and decreasing as necessary.
As seen in figure 2.5, the bus system already covers most of Lisbon. Of the 70.93 km2 considered
(this excludes the area covered by the airport and by the Monsanto forest park), the bus system covers
69.92 km2. This means that approximately 99% of the city’s area is within a 5 minutes walking distance
15
Figure 2.4: EMEL’s use cases. In order to manage the parking utilization, the price and the quantity ofparking spaces can be altered.
from the nearest bus station, assuming an average walking speed of 1.29 ms−1 [24]. Therefore this actor
doesn’t have the need to expand its transport network, and as such, there’s no use case for creating
new bus stations.
Figure 2.5: Bus system coverage. This service covers approximately 99% of the city’s area.
Figure 2.6 shows the use cases performed by Carris. In order to manage the bus system’s capacity,
Carris can deploy more buses if they wish to increase the service or recall buses if they wish to decrease
the service. Finally, in order to supply the customer with the relevant information, it handles (collects,
16
process and displays) information regarding the bus service.
Figure 2.6: Carris’ use cases. It only manages the service capacity and handles its information.
2.1.5 Metro
The subway network is managed by the Metropolitano de Lisboa (Metro), meaning that it’s in control of
the daily service variations and how the network expands or contracts. Differently, from the bus network,
the subway network is very limited and not present in a considerable part of the city, as shown in figure
2.7.
Figure 2.7: Subway system coverage. This service covers approximately 57% of the city’s area.
The subway system covers an area of approximately 40.36 km2 considering a 10 minutes walking
distance from the nearest subway station, meaning that 43% of the city area isn’t serviced.
17
Metro’s use cases are shown in figure 2.8.
Figure 2.8: Metro’s use cases.It’s responsible for expanding the subway system, managing its capacity
and handling its information.
Considering that the subway is the preferred mean of transport for greater distances within the city,
the whole transport system suffers and isn’t fully accessible for a non-negligible amount of the population.
Metro can expand the subway network by creating subway stations. In order to manage the service
capacity, the number of circulating trains can be altered by deploying more trains or by recalling trains.
For the service to be efficient, the customer must be able to have as much useful information as possible
in regards to the service. Therefore, the Metro must handle its information.
2.1.6 Bike Sharing Provider
At the present, there are two bike sharing operators in Lisbon, Gira - Bicicletas de Lisboa [25] and oBike
[26]. Gira is a one-way bike sharing system, where the customer can rent a bicycle, make their journey
and leave it in a dedicated station, thus ending the renting. On the other hand, oBike is a free-floating
bike sharing system, where the customer can rent a bicycle and end the journey anywhere within the
operational area. Gira is part of EMEL and oBike is a private company, however, in the model the bike
sharing provider (BSP) is distinct from these two and is considered to be a public service operator. Being
a public service operator implies that the BSP may have to fulfil public service obligations, that will be
compensated by the transport authority. These obligations are specific elements that are quantifiable.
Gira is used as the base for the model bike sharing provider, and as such its coverage is shown in
figure 2.9. The system currently has 55 stations [26] and covers an area of 11.25 km2, considering a 5
minutes walking distance of the nearest station. Therefore this system only covers approximately 16%
of the city’s area.
18
Figure 2.9: Bike sharing system coverage. This is the system with the smallest coverage, covering onlyapproximately 16% of the city’s area.
The bike sharing provider manages a one-way bike sharing system, it’s responsible to manage the
bicycle fleet, the creation of bike sharing stations and the handling of relevant system information.
Use case performed by the bike sharing provider are shown in figure 2.10. The BSP can expand the
network by creating bike sharing stations. In order to ensure that the stations are neither full nor empty,
the bicycles must be moved between stations, this action is referred to as relocation. Following the need
for an efficient system, the customer must be provided with up to date information about the service and
as such, the BSP must handle information of the system.
Figure 2.10: Bike sharing provider’s use cases. The system can be expanded and relocations can beperformed in order to always have bicycles available.
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2.1.7 Car Sharing Provider
There are currently four distinct car sharing companies operating inside Lisbon, namely Hertz 24/7TMCar
Sharing [27], Citydrive [28], DriveNow [29] and emov [30]. All of these companies utilize a free-floating
car sharing system, where the customer can pick up and leave the car anywhere within the operational
area, but none of them is considered to be a public service operator. Therefore in order to have a cen-
tralized authority that oversees all the transport inside the city, the car sharing provider will be modelled
as a public service operator. With this change, CML will be able to combine and juggle all parts of the
transport system in a more effective manner.
The operational area of the car sharing system is the area in which the customer can start or end a
trip. The operational area for the car sharing provider is based upon DriveNow’s and is shown in figure
2.11. With a coverage of 48.19 km2, the service covers 68% of the city area.
Figure 2.11: Car sharing system coverage. Following the bus network, the car sharing service has thebiggest coverage with approximately 68%.
The car sharing operator commands a free-floating car sharing system, it is its responsibility to
manage the car fleet, the service operational area and to collect, process and display the relevant
system information.
All use cases performed by the car sharing operator are displayed on figure 2.12. It can expand the
operational area in order to change the service’s coverage. The car fleet is managed by deploying more
cars and by relocating cars. The relocation is used in order to grant that there are cars where there
are customers. This increases the system’s availability because the vehicle itself is the system’s access
point. Finally, the customer must be provided with up to date information about the service and as such,
the CSP must handle the system’s information.
20
Figure 2.12: CSP’s use cases. This actor may expand the system coverage, manage its capacity andavailability, and handles its information.
2.2 Variables
Given the consequences of the problem at hand and the factors that influence the general public modal
choice, there are six variables used to describe it. These variables are key variables and are the main
descriptors of the problem, they quantify it and create its boundaries. However, it’s necessary to resort
to auxiliary variables in order to fully describe the problem.
A system’s variable is described by its name, how it’s measured or observed, appropriated units of
measurement or quantification scales, the previous and present behaviour over time (BOT), the desired
BOT, the way the variable is calculated and how it’s affected by the interactions with the system’s actors
[22].
Auxiliary variables are described in the same manner as key variables, however, the desired BOT
may not necessary. This stems from the fact that usually, the future state of an auxiliary variable isn’t
relevant for the problem [22].
2.2.1 K1 – Parking Easiness
Parking shortage is a consequence of having a system where the citizens use their cars for most of their
daily dislocations since parking is imperative for using the car. The spatial characteristics of the route
taken also contribute to the parking issue. When a person uses the car to go to a business centre or to
a location with a high population density, the available parking spaces are reduced in comparison with
journeys towards locations with more residences or less population density.
The easiness in finding a parking spot decreases with the number of cars in circulation, the higher
the number of cars circulating, the higher difficulty in locating an available parking spot. It also varies
with the number of parking spots that exist. More parking spaces reduce the difficulty of finding one
that’s available, and vice-versa.
Travel time and cost are also related to parking availability. Having fewer vacancies makes the journey
21
longer and more costly since more fuel is spent searching for a parking spot. Places with higher traffic
also have higher parking prices, what can lead to a situation where finding a parking place is difficult
and the cost of remaining there is also high in comparison with other places [31].
Parking easiness is thus defined as the probability of a car driver finding an empty public parking
sport, as shown in figure 2.13. It has a quantification scale between 0 and 1, where 0 means that there’s
no parking spot available to the customer and 1 means that the customer finds a vacant parking sport
immediately whenever desired. The current BOT is to decrease and the desired BOT is to remain stable
at a value of 0.2.
Figure 2.13: Key variable 1 - Parking Easiness
As seen on fig. 2.13, this variable is derived from three auxiliary variables: A01 – “Average Parking
Price”, A02 – “Quantity of Parking Spaces” and A03 – “Quantity of Cars”. The relationship between these
variables is given by equation 2.1.
K1(A01, A02, A03) =A01
(A01 + 1)(e
−A02a +b + 1
)(e
A03c +d + 1
) (2.1)
Where a, b, c and d are parameters to adjust how the function behaves. This relationship is based
on the assumptions that the parking easiness varies with the inverse of the average ticketing price, as
shown on figure 2.14. When the ticketing price is 0, K1 it’s considered to be 0. This shows that when
the park is free of charge, it’ll be in constant use and thus no parking space will be available for a
considerable amount of time.
The effects of the amount of parking spaces and number of cars in circulation are modelled as a
sigmoid function. They follow the expression of equation 2.2. The effects are shown on figures 2.15
and 2.16 for the quantity of parking spaces and the quantity of cars, respectively. This type of curve
22
0 2 4 6 8 10A01
0.2
0.4
0.6
0.8
1.0Effect of A01 on K1
Figure 2.14: Effect of A01 on K1.
was chosen because parking is a local action, i.e. the driver needs to park his car near the destination.
When there is a big influx of drivers to a given location, the parking easiness starts to slowly drop until
it reaches a point where it rapidly becomes difficult to find an available parking space. This is better
described with an “s” shaped function.
f(x) =1
e−xa +b + 1
(2.2)
For the quantity of parking spaces (A02), K1 is 0 when there are no parking spaces and tends to 1
when the amount of parking spaces is high enough. The opposite happens with the quantity of cars.
When there are no cars, K1 is 1 since all parking spaces are available.
0 100000 200000 300000 400000 500000A02
0.2
0.4
0.6
0.8
1.0Effect of A02 on K1
Figure 2.15: Effect of A02 on K1.
0 100000 200000 300000 400000 500000A03
0.2
0.4
0.6
0.8
1.0Effect of A03 on K1
Figure 2.16: Effect of A03 on K1.
A01 – Average Parking Price
It’s defined as the average cost of parking a car inside the city during one hour. It’s measured in EUR/h
and has a domain of R+.
EMEL is responsible for the parking system as a whole, and as such manages the parking prices
and parking spots. It can decrease the average parking price, thus reducing the travel cost and making
the car more attractive, and can also increase the average parking prices, thus making people become
less prone to use their personal vehicle, resulting in more empty spaces available.
23
A02 – Quantity of Parking Spaces
It’s defined as the number of public parking spaces. It’s measured in park and has a domain of N.
EMEL can increase or decrease the number of parking sports, increasing or decreasing the variable,
respectively.
A03 – Quantity of Cars
It’s defined as the number of cars that require a public parking space to finish the trip. It’s measured in
car and has a domain of N.
When the CSP deploys more cars, the system as a whole has to deal with more vehicles, therefore
the quantity of cars increases. Finally, when a customer uses their private vehicle they will occupy a
parking space, so the more customers using their cars, the more difficult it is to park it.
2.2.2 K2 – Bike Lane Density
Cycling can be done along with motorized vehicles on the roads but for safety and to not disturb the traf-
fic, it’s easier to segregate motorized modes and cycling. This calls for bike lanes, which are dedicated
infrastructures for cycling. These infrastructures are underdeveloped, not only due to the usage of cars
but also because Lisbon isn’t a flat city. The town’s topography puts an extra barrier to this mode since
the citizens must often climb uphill. This issue can be resolved by providing the adequate infrastruc-
ture while also proving motorized bicycles. The bike sharing system considered is composed of electric
bicycles, the main reason for the need for fixed stations.
Having an extensive bike lane network serves to increase the bicycle mode attractiveness by also
reducing the travel time and distance for cyclists. In order to characterize the extent to which the city
is shaped to handle exclusive bike traffic, the variable “Bike Lanes Density” is used. It’s defined as
the usable bike lanes’ length divided by the useful city’s area (road area), as shown in figure 2.17. To
compare the extension of the usable bike lanes in relation to the total road area available, this variable
is measured in length divided by area and has units of km−1.
The current BOT is to increase the variable’s value with the creation of new bike lanes as seem on
the Lisbon’s Urban Sustainable Mobility Action Plan (PAMUSLx) [23]. And the desired BOT is to remain
stable at or above the road density. Road density is considered to be a constant in the system.
As shown in figure 2.17 and in equation 2.3, this variable is calculated using two auxiliary variables:
A04 – “Total Bike Lanes Length” and A05 – “Share of Usable Bike Lanes”.
K2(A04, A05) =A04A05
ra(2.3)
Given the definition of the variable, the relationship between the different variables means that K2
varies directly with both of them. The road area is considered to be constant and as such, isn’t a
variable.
24
Figure 2.17: Key variable 2 - Bike Lane Density
A04 – Total Bike Lanes Length
It’s defined as the total length of the bike lane network. It’s measured in kilometre and has a domain of
R+.
In order to increase this variable, it’s necessary to build more bike lanes where they don’t exist. CML
is the only entity able to do so.
A05 – Share of Usable Bike Lanes
It’s defined as the share of bike lanes that are in good conservation state and can be used divided by
the total number of bike lanes. Where 0 means that all the bike lanes are unusable and 1 means that all
the bike lanes are usable. It’s dimensionless and has a domain of [0,1].
With the passage of time, the infrastructure degrades and becomes effectively useless, decreasing
the variable’s value. Since the lanes degrade over time, it’s necessary to perform maintenance works in
order to sustain the actual level. This action is also performed by the CML. Lastly, the degradation of the
bike lanes is accentuated by the customers use.
2.2.3 K3 – Information Utility
When a service is underdeveloped and isn’t able to provide reliable information to its customers, it
creates an unreliable image and eventually becomes less attractive. This issue is key to an efficient
service and to capture more costumers. The customers should be able to know with ease what’s the
best route to their destination in accordance with their individual preferences, e.g. fastest route, the route
with the least amount of changes. To be able to reduce the travel time, the customer should also know
when a certain regular transport will stop near their location.
25
The transport system is an extensive system, where different operators provide distinct services.
Each operator has their own network of stations and lines, possibly providing different services and
accesses. This means that the system has a lot of information that must be made accessible to the
user. However, not all information is useful. Better information quality translates into increased utility,
e.g. having a display with the waiting time for the next bus is more useful than having a timetable with
the waiting time between buses and the hour that the first bus passes that location.
Information utility is then defined as the average level of information quantity, quality, and placement
regarding the public transport system, as shown in figure 2.18. It has a quantification scale between
0 and 4, where 0 means that there’s no information available to the customer and 4 means that all the
information that the customer may need is available, that it’s placed in an easy to access location and
has the highest level of detail without being cumbersome.
The desired BOT is to remain stable at a level higher than 3.25, meaning that the customer, most of
the times, has the information needed at hand.
Figure 2.18: Key variable 3 - Information Utility
This variable is computed by the sum of four auxiliary variables multiplied by another, as shown in
figure 2.18 and equation 2.4. Variables A06 to A09 deals with the information of a specific system while
A10 deals with information regarding how the systems interact as one.
K3(A06, A07, A08, A09, A10) = (A06 +A07 +A08 +A09)A10 (2.4)
The information coming from the different services are summed and then multiplied by how the
transport authority handles them. This is to show that it’s not only enough that each transport provider
handles their own information, but that it all must be available in the same location for the customer.
26
A06 – Bus System Information
It’s defined as how much information regarding the bus service has been collected, then processed and
displayed to the customer. When it’s equal to 0, no information was collected, processed and displayed.
When it’s equal to 1, all relevant information was collected, processed and displayed to the customer.
It’s dimensionless and has a domain of [0,1].
Carris handles the information regarding the bus system and doing so converges the variable to a
value of 1 minus the frequency of error.
A07 – Subway System Information
A07 is likewise defined as A06 but for the subway system. Metro handles the information regarding the
subway system and doing so converges the variable to a value of 1 minus the frequency of error.
A08 – Bike Sharing System Information
A08 is likewise defined as A06 but for the bike sharing system. BSP handles the information regarding
the bike sharing system and doing so converges the variable to a value of 1 minus the frequency of error.
A09 – Car Sharing System Information
A09 is likewise defined as A06 but for the car sharing system. CSP handles the information regarding the
car sharing system and doing so converges the variable to a value of 1 minus the frequency of error.
A10 – Systems Information
It’s defined as how much information regarding how the different systems connect and interact have
been collected, then processed and displayed to the customer. When it’s equal to 0, no information
was collected, processed and displayed. When it’s equal to 1, all relevant information was collected,
processed and displayed to the user. It’s dimensionless and has a domain of [0,1].
CML is responsible for the handling of this kind information and the variable converges to a value of
1 minus the frequency of error by doing so.
2.2.4 K4 – Systems Interconnectivity
How the different systems are organized is important for the system as a whole. In the end, the system
must be more than just the sum of its parts, it cannot feel as though it’s an aggregate of independent
systems. With an underdeveloped network, the result is exactly what must be avoided, a system that
doesn’t integrate well its parts.
Interconnecting the systems must be done both physically by the means of transport hubs, with
stations of different services very near each other, but also by way of having public transport passes
that can be used in all services. This interconnection has the objective of providing a better service and
making the customer experience the whole system as one, and not a collection of independent systems.
27
Along with the overlaid networks comes a facility to the customer to switch modes as deemed fit to
achieve their best route. Lastly, the system robustness increases with interconnected networks. If one
particular service isn’t available for whatever reason, the remaining services should be able to absolve
their workload without substantial setbacks. Currently, all the different transport providers have distinct
ticketing systems.
Key variable four describes the systems interconnectivity and is defined as the number of hubs
(overlapping access points of different subsystems) multiplied by the normalized number of services
that use the same ticketing systems, as shown in figure 2.19. It’s dimensionless and has a domain of
R+, where 0 means that no subsystem have overlapping access points or every provider has their own
ticketing system.
Figure 2.19: Key variable 4 - Systems Interconnectivity
As seen on figure 2.19 and shown in equation 2.5, K4 requires two auxiliary variables: A11 – “Quantity
of Hubs” and A12 – “Quantity of Ticketing Systems”. It varies linearly with both variables. Since there are
4 distinct systems, if A12 is subtracted from 5 and then divided by 4, the result is the normalized number
of services that use the same ticketing system.
K4(A11, A12) = A115−A12
4(2.5)
A11 – Quantity of Hubs
It’s defined as the number of hubs where there’s an overlapping of all the subsystems access points. It’s
dimensionless and has a domain of N.
Creating new transport hubs is carried out by the transport authority, CML.
28
A12 – Quantity of Ticketing Systems
Defined as the number of distinct ticketing systems used by the public transport providers. It’s dimen-
sionless and has a domain of N.
In order to decrease the quantity of different ticketing systems and to create inter-modal transport
passes CML can integrate the means of access of different systems.
2.2.5 K5 – System Coverage
As discussed earlier, the systems underdevelopment can also be assessed by how extensive their net-
works are. It’s important to have all the services reaching the whole city in order to provide choice for
the customers since they can’t use a service if they can’t access it. This also decreases the travel time
and increases attractiveness. If the customer doesn’t have to walk long distances to reach an access
point, the travel time is reduced. In the limit, expanding the system’s network also breaks the captivity of
some customers that only had one mode that fulfilled their travel needs.
It’s necessary to build supporting infrastructure to expand the system coverage. The built infrastruc-
ture is important to attract more costumers because they provide shelter in adverse climate conditions,
in addition to serving as an access point. This will reinforce the mode use habit and increases the
attractiveness.
System coverage is defined as the maximum city’s area share within 5 minutes walking distance from
the nearest bike sharing and bus access points, within 10 minutes walking distance from the nearest
subway access point and inside the car sharing service operational area, as shown in figure 2.20. It has
a quantification scale between 0 and 1, where 0 means that there’s no area within the city that’s in a 5
minutes walk from all the different system’s access points and 1 means that the whole city is covered by
all the systems.
As seen on figure 2.20 and on equation 2.6, K5 is obtained from the intersection of the coverage
zones of the different systems. This ensures an accurate representation of the zones where all the
services overlap. The final result is shown in figure 2.21, with a coverage of 9.9 km2.
K5(A13, A14, A15) = bsc ∩A13 ∩A14 ∩A15 (2.6)
A13 – Subway System Coverage
Defined as the area within 10 minutes walking distance from the nearest subway access point. It’s
measured in km2 and has a domain of [0,70.93].
The subway coverage is increased with the addition of new subway stations. This action is performed
by the Metro.
29
Figure 2.20: Key variable 5 - System Coverage
Figure 2.21: Intersection of the systems coverage areas. K5 currently sits on a value of 0.14.
A14 – Bike Sharing System Coverage
Defined as the area within 5 minutes walking distance from the nearest bike sharing station. It’s mea-
sured in km2 and has a domain of [0,70.93].
Creating new bike sharing stations increases its service coverage.
30
A15 – Car Sharing System Coverage
It’s defined as the area in which the customer is able to start and end their journey (operational area).
It’s measured in km2 and has a domain of [0,70.93].
Expanding the operational area increases the car sharing system coverage.
2.2.6 K6 – Services Capacity and Availability
The last problem consequence tackled is the public transports capacity and availability deficiency. The
current system doesn’t have a large enough capacity to handle the workload at any given time. This is
especially noticeable during rush hours when the workload is significantly higher.
The purpose of a transport system is to move its costumers from their origin to their destination
when the system doesn’t have enough capacity to do so, it fails at their main objective. This issue isn’t
simple because the required workload is dynamic and has peaks during rush hours. The services can’t
operate at their maximum capacity at all times, doing so would not be economically and environmentally
sustainable.
Others factors such as land-use diversity and population density also influence how the required
workload varies during the day. Places with more homogeneous land-use, e.g. business and industrial
neighbourhoods and higher population density have higher peaks during the day than places with a
more heterogeneous land-use or lower population density.
How the customer experiences the system also rely on its capacity. Having to wait for the next vehicle
because the desired is full or feeling crammed create bad experiences and perceptions towards public
transports. This, in turn, reduces the services attractiveness and pushes away the customers that have
the choice of using a different mode. Most of the citizens that use car have a bad perception of the public
transport system [15].
Services capacity and availability is defined as the system’s capacity to manage the required work-
load at any given time, as shown in figure 2.22. It has a domain of R+, where 0 means that no system
is working at the moment and can’t transport any costumer, 1 means that the system has the exact
capacity to transport all the customers at the moment and above 1 means that the system has higher
capacity than that required.
As shown in figure 2.22 and equation 2.7, this variable is calculated by adding all the different services
capacity and availability, and dividing by the required system capacity.
K6(A16, A17, A18, A19, A20) =A16 +A17 +A18 +A19
A20(2.7)
A16 – Bus System Capacity
The capacity of a regular transport system is given by equation 2.8.
Cap =
nL∑i
= 1miSi
δti(2.8)
31
Figure 2.22: Key variable 6 - Services Capacity and Availability
where Cap is the system capacity, nL is the number of lines, mi is the number of vehicles in line i, Si
is the number of seats in line i and δti is the time necessary to travel the whole line.
Assuming that Si is constant and equal for all lines and that the frequency of passage is given by the
number of vehicles diving by the line travel time, the result is eq. 2.9.
Cap = SL
nL∑i
= 1fi (2.9)
where fi is the frequency of passage of line i. Lastly, using the average value of the frequency of
passage in all lines, we have eq. 2.10. This is the equation used for the capacity of the regular transport
systems.
Cap = SLnLf (2.10)
where f is the average passage frequency in the whole system.
The bus system capacity is defined as the number of persons that the bus system is able to transport
in an hour. It’s measured in passenger/hour and has domain of R+, as seen in figure 2.23.
A16 is calculated using eq. 2.11. Due to the extensiveness of the bus network, the quantity of
bus lines (bl) is considered to be constant. The average number of passengers per bus (bc) is also
considered to be a constant. Thus, in order to change its capacity, Carris must change the bus passage
frequency (A21).
A16 = A21bcbl (2.11)
A21 – “Average Bus Passage Frequency” is defined as the inverse of the average time interval be-
tween two consecutive buses. It’s measured in 1/h and has a domain of R+. Carris can increase or
decrease it by deploying or recalling buses. If there are more vehicles in circulation, the average waiting
time is reduced and thus increases the service capacity, and vice versa.
32
Figure 2.23: Auxiliary variable 16 - Bus System Capacity
A17 – Subway System Capacity
Defined as the number of persons that the subway system is able to transport in an hour. It’s measured
in passenger/hour and has domain of R+, as seen in figure 2.24.
Figure 2.24: Auxiliary variable 17 - Subway System Capacity
The subway system capacity is calculated in the same manner as the bus’, with the exception that
the quantity of subway lines is a variable, as shown in eq. 2.12. To alter its capacity, Metro can change
A22 – “Average Train Passage Frequency” or A23 – “Quantity of Subway Lines”. The Metro has the same
mechanisms of service maintenance as Carris, however, the subway network isn’t as extensive and as
such, it can be expanded with the creation of new subway lines.
33
A17 = A22A23tc (2.12)
A22 – “Average Train Passage Frequency” is defined as the inverse of the average time interval
between two consecutive trains. It’s measured in 1/h and has a domain of R+.
A23 – “Quantity of Subway Lines” is defined as the number of subway lines. It’s measured in subway
lines and has a domain of N.
A18 – Bike Sharing System Availability
The bike sharing system has a limited availability since it’s not usable if there are no available bicycles.
It’s defined as the number of persons that the bike sharing system is able to transport in an hour. It’s
measured in passenger/hour and has domain of R+, as seen in figure 2.25.
Figure 2.25: Auxiliary variable 18 - Bike Sharing System Availability
Its availability is given by equation 2.13. This definition requires three auxiliary variables: A24 – “True
Capacity Factor”, A25 – “Bicycle Fleet Size” and A26 – “Average Bicycle Trip Time”.
A18 =A24A25
A26(2.13)
A25 – “Bicycle Fleet Size” is defined as the total number of bicycles in the bike sharing system. It’s
measured in quantity of bicycles and its domain is N. To increase the fleet size, it’s necessary to create
new bike sharing stations that come with a set number of bicycles.
A26 – “Average Bicycle Trip Time” is defined as the average time interval during a trip by the users
when using the bike sharing system. It’s measured in hour and its domain is R+. This variable converges
with the customer’s use of the system.
A24 – “True Capacity Factor” is defined as the ratio between effective stations and the total number
34
of stations. Effective stations are neither full nor empty. When it’s 0, all stations are either completely
empty or full and when it’s 1, no stations are either completely empty or full. It’s dimensionless and
has a domain of [0,1]. A24 arises from the fact that stations are considered to be the system access
points, but each access point has a limited amount of bicycles. The bike sharing stations can become
full or empty, and unusable if the costumers wish to terminate or start a trip, respectively. This variable
requires the definition of three additional auxiliary variables: A27 – “Quantity of Bike Sharing Stations”,
A28 – “Quantity of Full Bike Sharing Stations” and A29 – “Quantity of Empty Bike Sharing Stations”. Their
relationship is given by equation 2.14.
A24 = 1− A28 +A29
A27(2.14)
A27 – “Quantity of Bike Sharing Stations” is defined as the number of bike sharing stations. It’s
measured in quantity of bike sharing stations and has a domain of N. It can be increased by creating
more stations.
A28 – “Quantity of Full Bike Sharing Stations” is defined as the quantity of bike sharing stations with
an occupancy rate equal or above 75%. It’s measured in quantity of bike sharing stations and has a
domain of N. A station is considered to be full at an occupancy rate equal or superior to 75% due to
the time constraints of the relocation action. Since it’s not instantaneous, it must be triggered before the
occupancy rate reaches 100% to guarantee the maximum availability.
A29 – “Quantity of Empty Bike Sharing Stations” is defined as the quantity of bike sharing stations
with an occupancy rate equal or below 25%. It’s measured in quantity of bike sharing stations and has
a domain of N. A station is considered to be empty at an occupancy rate equal or inferior to 25% due to
the time constraints of the relocation action. Since it’s not instantaneous, it must be triggered before the
occupancy rate reaches 0% to guarantee the maximum availability.
A19 – Car Sharing System Availability
Similarly to the bike sharing system, the car sharing system has an upper limit in its availability. It’s
defined as the number of persons that the car sharing system is able to transport in an hour. It’s
measured in passenger/hour and has domain of R+, as seen in figure 2.26.
The car sharing system availability is given by equation 2.15. This equation has two constants: cc –
“Average car capacity” and paramCDG – “Car density gradient reference value”; and it has three auxiliary
variables: A30 – “Car Fleet Size”, A31 – “Average Car Trip Time” and A32 – “Car Density Gradient”. The
system’s availability increases linearly with the amount of cars in its fleet and varies inversely with the
average time that the customer expends using the system.
A19 =ccA30
A31MIN
(1,paramCDG
A32
)(2.15)
A30 – “Car Fleet Size” is defined as the number of cars in the car sharing system fleet. It’s measured
in quantity of cars and has a domain of N. It can be increased by the car sharing provider by deploying
more cars.
35
Figure 2.26: Auxiliary variable 19 - Car Sharing System Availability
A31 – “Average Car Trip Time” is defined as the average time interval during a trip by the users when
using the car sharing system. It’s measured in hour and its domain is R+. This variable converges with
the customer’s use of the system.
A32 – “Car Density Gradient” is defined as the maximum spatial variation of the car area density
within the city. It’s measured in car/km3 and has a domain of R+. Similarly to the true capacity factor for
the bike sharing system, the car density gradient is used to ensure that the car distribution within the city
is adequate to the customers use patterns. If there are too many or too few cars in a given location, the
customer may not be able to use the system as desired. The constant parameter, paramCDG, exists as a
reference value. If A32 is higher than the accepted value, the system availability decreases accordingly.
However, if A32 is lower than the accepted value, it’s not considered that the availability has increased
since it’s limited by choosing the minimum value between 1 and the ratio paramCDG/A32. The CSP can
relocate its cars from zones with a high car density and low demand to zones with a low car density and
high demand.
A20 – Required System Capacity
It’s defined as the number of passengers kilometre that the whole transport system is required to trans-
port in an hour. It’s measured in passenger/hour and has domain of R+, as seen in figure 2.27.
This variable increases whenever a customer utilizes any of the public transport services and de-
creases when it chooses to walk to their destination. If the customer chooses to use their private vehicle,
it has no impact on the required system capacity.
36
Figure 2.27: Auxiliary variable 20 - Required System Capacity
37
Chapter 3
System Interactions and Behaviours
Once all the problems variables, actors and use cases are defined, it’s necessary to lay out how these
interact with each other and how the system behaves. Table 3.1 shows all the actors, use cases and
which variables are affected when they are executed.
Sequence diagrams are used in order to represent interactions between the different actors and vari-
ables through the execution of use cases. The dynamic behaviour of the system is explored qualitatively.
An actor uses the value of one or more variables and then trigger an use case. The value being used by
the actor is represented by a data flow arrow and is labelled as “value”.
To trigger an use case, the actor sends a create arrow labelled “Create()”. The use case can have
one or more effects. If the execution result is then used by another use case, actor or variable, it’s
represented by a data flow arrow labelled as “output”. To indicate that the use case execution changed
a variable value, it’s used an event arrow. It can be labelled as “increase()”, “decrease()” or “converge()”,
depending on how the variable changes with the use case execution.
Lastly, some variables can change their value without a use case execution. In this case, the alter-
ation is displayed on the diagram with an action block on the respective variable timeline.
The interactions of the system are divided into groups as:
• Managing parking easiness – describes how EMEL manages parking easiness.
• Infrastructure interactions – describes how CML create and maintain infrastructure, namely bike
lanes and transport hubs.
• Handling information – depicts how all transport providers and CML handles their respective infor-
mation.
• Expanding systems’ coverage – describes how Metro, BSP and CSP expand their respective net-
works and coverage.
• Integrating means of access – shows how CML integrates the different means of access for the
providers.
39
• Managing systems’ capacity and availability – describes how the different transport providers man-
age their respective services.
• Usage interactions – shows how the customer uses the different modes available.
Table 3.1: Actors, use cases and affected variables
Triggering Actor Use Case Affected Variable
EMEL Increasing parking prices A01 Average Parking Price
Decreasing parking prices A01 Average Parking Price
Creating parking spaces A02 Quantity of Parking spaces
Decreasing parking spaces A02 Quantity of Parking spaces
Customer Using private vehicle A03 Quantity of Cars
Walking A20 Required System Capacity
Using regular public transport A20 Required System Capacity
Using bike sharing system A20 Required System Capacity
A26 Average Bicycle Trip Time
A28 Quantity of Full Bike Sharing Stations
A29 Quantity of Empty Bike Sharing Stations
Using car sharing system A20 Required System Capacity
A31 Average Car Trip Time
A32 Car Density Gradient
CML Building bike lanes A04 Total bike lanes extension
Maintaining bike lanes A05 Share of usable bike lanes
Handling systems information A10 Systems information
Creating transport hubs A11 Quantity of hubs
Integrating means of access A12 Quantity of Ticketing Systems
Carris Handling bus information A06 Bus System Information
Deploying buses A21 Average Bus Passage Frequency
Recalling buses A21 Average Bus Passage Frequency
Metro Handling subway information A07 Subway System Information
Creating subway stations A13 Subway System Coverage
A23 Quantity of Subway Lines
Deploying trains A22 Average Trains Passage Frequency
Recalling trains A22 Average Trains Passage Frequency
Continued on next page
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Table 3.1 – Continued from previous page
Triggering Actors Use Case Affected Variable
BSP Handling bike sharing information A08 Bike Sharing System Information
Create bike sharing station A14 Bike Sharing System Coverage
A25 Bicycle Fleet Size
A27 Quantity of Bike Sharing Stations
Relocating bicycles A28 Quantity of Full Bike Sharing Stations
A29 Quantity of Empty Bike Sharing Stations
CSP Deploying cars A03 Quantity of Cars
A30 Car Fleet Size
Handling car sharing information A09 Car Sharing System Information
Expanding operational area A15 Car Sharing System Coverage
Relocating cars A32 Car Density Gradient
3.1 Managing parking easiness
EMEL is the actor in charge of managing the parking system. As shown in table 3.1, it can increase or
decrease parking prices and can create or decrease parking spaces. Knowing that the desired BOT of
K1 is to be stable at 0.2 and that there are different ways to change the variable’s value, the actor uses
the value of K1 to decide what to do. This is represented as an interaction occurrence where there is a
condition at the top and inside shows what will happen should the condition be met, as shown in figure
3.1.
If K1 > 0.3, EMEL will decrease the parking spaces, thus decreasing A02, the quantity of parking
spaces. If 0.3 ≥ K1 > 0.2, then the increasing parking prices use case will be triggered and A01 will
increase. When the value of K1 is bellow 0.2, EMEL must take action in order to increase the easiness
of parking. If 0.2 > K1 ≥ 0.05, then the decreasing parking prices use case will be triggered and A01 will
decrease. Lastly, when K1 < 0.05, EMEL will create new parking spaces and A02 will increase.
3.2 Infrastructure interactions
There are three infrastructure interactions. All of them are performed by CML. These shows how this
actor creates and maintains the bike lanes and also how it creates new transport hubs.
3.2.1 Extending bike lanes network
As shown in figure 3.2, the actor uses the value of K2 in order to build new bike lanes. The result is an
increase in the total bike lanes extension, A04. The value of A04 is then used to recalculate K2.
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Figure 3.1: Sequence diagram 00 – Managing parking easiness
Figure 3.2: Sequence diagram 01 – Extending bike lanes network
3.2.2 Maintaining bike lanes network
As shown in figure 3.3, the actor uses the value of A05 in order to make the maintenance of the bike
lanes. It’s noteworthy that the bike lanes deteriorate with time and as such the value of the share of
usable bike lanes decreases. The triggering of the “maintain bike lanes” use case is an increase in A05.
Its value is then used to recalculate K2.
3.2.3 Creating transport hubs
CML uses the value of K4 to determine if it will trigger the “building transport hubs” use case. By doing
so, the value of the quantity of transport hubs (A11) will increase accordingly and K4 will be updated with
this new value. This interaction is shown on figure 3.4.
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Figure 3.3: Sequence diagram 02 – Maintaning bike lanes network
Figure 3.4: Sequence diagram 03 – Creating transport hubs
3.3 Handling information
Each transport provider and the transport authority have the same type of interaction for while handling
information. The actor will receive their respective information value, trigger the appropriate handling
use case which will, in turn, converge the value of the information. This value will then be used to
calculate the new information utility, K3.
• Handling bus system information
For the bus system, Carris uses the value of A06, bus system information, to trigger the use case
“handling bus information”. The result is an alteration of A06 value. The value converges to 1 minus
the frequency of error, since the process isn’t perfect. The new value of is used to recalculate K3,
as shown in figure 3.5.
• Handling subway system information
Metro utilizes the value of A07 subway system information and triggers the use case “handling
subway information”. The value of A07 then converges to 1 minus the frequency of error and is
next used to recalculate K3. Its sequence follow the same pattern as figure 3.5.
• Handling bike sharing system information
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Figure 3.5: Sequence diagram 04 – Handling bus system information
The BSP uses the value of the bike sharing information, A08, to trigger the handling of the bike
sharing information. This results in an alteration of A08 to 1 minus the frequency of error. Lastly,
K3 uses this new value, its sequence follows the same pattern as figure 3.5.
• Handling car sharing system information
For the car sharing system, CSP uses the value of A09, car sharing system information, to trigger
the use case “handling car sharing information”. The result is an alteration of A09 value. The
value converges to 1 minus the frequency of error. The new value of is used to recalculate K3. Its
sequence follows the same pattern as figure 3.5.
• Handling systems information
Finally, the last interaction regarding the systems’ information is performed by CML. It uses the
value of A10, systems information, and triggers the use “handling systems information”. The out-
come is a variation of the value of A10, that is then used to recalculate K3. Its sequence follows the
same pattern as figure 3.5.
3.4 Expanding systems’ coverage
Off the four transport operators, Carris is the only one that doesn’t have the need to expand its system
coverage. The remaining do so by creating new stations or by expanding the operational area.
3.4.1 Creating subway stations
In order to increases the subway system coverage, Metro utilizes the value of A13 to trigger the use case
“creating subway stations”. The outcome may change two variables, A13 and A23 (quantity of subway
lines), as shown in figure 3.6.
Whenever a new subway station is created, the subway system coverage increases, unless it’s cre-
ated inside the coverage area. Once A13 changes, the whole system coverage, K5, also changes.
When creating a new subway station, Metro may want to create a new subway line. Should this
happen, the value of A23, quantity of subway lines, increases. Using the new value of A23, the subway
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system capacity (A17) changes and subsequently K6 also changes.
Figure 3.6: Sequence diagram 09 – Creating subway stations
3.4.2 Creating bike sharing stations
The BSP uses the value of A14 to trigger the use case “creating bike sharing stations”. Once triggered,
the bike sharing system coverage increases and the value of K5 is recalculated, as seen in figure 3.7.
With the creation of a new bike sharing station, two other variables increase, A25 – “Bicycle Fleet
Size” and A27 – “Quantity of Bike Sharing Stations”. The value of A25 is directly used to calculate A18,
but the value of A27 is used to recalculate the value of the true capacity factor, and then the bike sharing
system availability is recalculated. Once A18 has been set, K6, the services capacity and availability,
uses A18 to be recalculated.
Figure 3.7: Sequence diagram 10 – Creating bike sharing stations
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3.4.3 Expanding operational area
The operational area of the car sharing service is equal to the system’s coverage, therefore CSP uses
the value of the car sharing system coverage, A15, in order to trigger the use case “expanding operational
area”. The result is an increase of A15 that is then used to recalculate K5.
Figure 3.8: Sequence diagram 11 – Expanding operational area
3.5 Integrating means of access
The integration of means of access means that the CML is unifying the different ticketing systems in
order to facilitate mode changing. To do so, the value of A12 is used by CML to trigger the use case
“integrating means of access”, as shown in figure 3.9. The outcome is a reduction of A12 that is then
used to calculate K4, the systems interconnectivity.
Figure 3.9: Sequence diagram 12 – Integrating means of access
3.6 Managing systems’ capacity and availability
Each transport provider is responsible to manage their own service. For regular transport services, such
as the bus and the subway, this means that the provider will deploy or recall vehicles depending if the
capacity is below or above the required, respectively. For flexible transport services, such as the bike
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sharing and the car sharing, this means relocating vehicles to a zone where it’s needed or deploying
more vehicles to increase the total fleet size.
3.6.1 Managing bus system capacity
Carris is responsible for the management of the bus system capacity. It can do two things, increase or
decrease the service.
Increasing bus service
To increase the bus service, Carris utilizes the values of A16 and A20, respectively, bus system capacity
and required system capacity. Then the use case “deploying buses” is triggered. With the increase
of buses in service, the average bus passage frequency (A21) increases. The value of A21 is used to
redetermine A16, which is then used to recalculate K6, services capacity and availability, as seen in
figure 3.10.
Figure 3.10: Sequence diagram 13 – Increasing bus service
Decreasing bus service
To decrease the bus service, Carris utilizes the values of A16 and A20, respectively, bus system capacity
and required system capacity. Then the use case “recalling buses” is triggered. With the decrease of
buses in service, the average bus passage frequency (A21) decreases. The value of A21 is used to
redetermine A16, which is then used to recalculate K6, services capacity and availability, as seen in
figure 3.10.
3.6.2 Managing subway system capacity
The management of the subway system capacity is done by Metro and in the same way that is done for
the bus system.
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Figure 3.11: Sequence diagram 14 – Decreasing bus service
Increasing subway service
Increasing the subway service requires the usage of A17 and A20, respectively, subway system capacity
and required system capacity, by Metro. The use case execution results in an increase of A22. The new
value of A22 is then used to adjust A17, which is subsequently used to calculate K6, services capacity
and availability, as seen in figure 3.12.
Figure 3.12: Sequence diagram 15 – Increasing subway service
Decreasing subway service
Decreasing the subway service requires the usage of A17 and A20, respectively, subway system capacity
and required system capacity, by Metro. The use case execution results in a decrease of A22. The new
value of A22 is then used to adjust A17, which is subsequently used to calculate K6, services capacity
and availability, as seen in figure 3.12.
3.6.3 Managing bike sharing system availability
For the BSP to manage the bike sharing system availability, it can increase the bicycle fleet size or can
increase the value of the true capacity factor. Increasing the bicycle fleet is done by creating new bike
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Figure 3.13: Sequence diagram 16 – Decreasing subway service
sharing stations, as shown in figure 3.7. The interactions needed to increase the true capacity factor,
A24, are shown in figure 3.14.
Figure 3.14: Sequence diagram 17 – Relocating bicycles
The BSP uses the value of A24 to trigger the use case “relocating bicycles”. The outcome is a
reduction in the number of bike sharing stations that are full and that are empty, respectively, A28 and
A29. These values are then used to redetermine A24, which is then used to adjust the bike sharing
system availability, A18, and finally, K6 is adjusted.
3.6.4 Managing car sharing system availability
To manage the car sharing system availability, the CSP can either increase the size of the car fleet or
decrease the car density gradient, by deploying cars or relocating cars, respectively.
Deploying cars
The CSP uses the values of K6 and A30, respectively, services capacity and availability and car fleet
size, to trigger the use case “deploying cars”. This results in an increase of A30 and A03, quantity of cars,
as seen in figure 3.15.
The increase of A30 is taken into account when determining the value of A19, car sharing system
availability. K6 then uses the value of A19 to be adjusted.
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Figure 3.15: Sequence diagram 18 – Increasing car sharing capacity
The increase of A03 is taken into account to adjust the value of K1, parking easiness.
Relocating cars
Car relocation serves the purpose of diminishing the car density gradient and guaranteeing that the cars
are appropriately distributed inside the operational area.
The value of A32, car density gradient, is used by CSP to trigger the use case “relocating cars”. This
will, in turn, decrease the value of A32, thus increasing the value of the car sharing system availability,
A19, and finally the value of K6 will be adjusted, as seen on figure 3.16.
Figure 3.16: Sequence diagram 19 – Relocating cars
3.7 Usage interactions
Usage interactions refer to all the interactions of the customer with the system. Whenever the customer
chooses to use a service, the required system capacity will increase, and in the case of the flexible
modes, their availability will also change.
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3.7.1 Using private vehicle
If the customer chooses to not engage in the public transport system, then they trigger the use case “us-
ing private vehicle”. This will increase the quantity of cars, A03, and the value of K1 will be recalculated,
as seen in figure 3.17.
Figure 3.17: Sequence diagram 20 – Using private vehicle
3.7.2 Using regular public transport
To use a regular public transport, the bus or the subway service, the customer uses the value of K3 to
trigger the use case “using regular public transports”. Once triggered, the value of A20, required system
capacity, increases and the value of K6, services capacity and availability, is recalculated.
Figure 3.18: Sequence diagram 21 – Using regular public transport
3.7.3 Using bike sharing system
When using a flexible system, not only will the required system capacity, A20, change, but also the
own system availability. Using the value of K3, the customer triggers the use case “using bike sharing
system”. The outcome is a change in several variables, as shown in figure 3.19. The value of A20,
required system capacity, increases. The values of A26, average bicycle trip time, A28, quantity of full
bike sharing stations, and A29, quantity of empty bike sharing stations. And based on the assumption
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that the customer always uses the bike lanes network when using the bike sharing system, the value of
A05, share of usable bike lanes, decreases.
The average bicycle trip time converges with each instance of use since some customers use the
service for a longer amount of time and others for a shorter amount of time than the average. The value
of A26 is the used to calculate A18, bike sharing system availability.
The convergence of A28 and A29, are due to the fact that when a customer uses the system, the
number of bicycles in the station where they start and end the trip changes. Therefore when starting
a trip the number of full stations can decrease and the number of empty stations can increase. The
opposite may happen when ending the trip. The values of A28 and A29 are used to recalculate the true
capacity factor, A24, which is then used to calculate A18.
With the new values of A20 and A18, the services capacity and availability, K6 can be adjusted. Finally,
with the decrease of A05, K2, bike lanes density, is adjusted.
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Figure 3.19: Sequence diagram 22 – Using bike sharing system
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3.7.4 Using car sharing system
Using the value of K3, the customer triggers the use case “using car sharing system”. The outcome
is a change in several variables, as shown in figure 3.20. The value of A20, required system capacity,
increases. The values of A31, average car trip time,e and A32, car density gradient, converge.
The average car trip time converges with each instance of use since some customers use the service
for a longer amount of time and others for a shorter amount of time than the average. The value of A31
is the used to calculate A19, car sharing system availability.
A32 converges because the customer can end the trip in a zone with a lower car density, thus de-
creasing the gradient, or can end the trip in a zone with a high car density and thus increasing the
gradient. A19 receives the value of A32 and is updated.
With the new values of A20 and A19, the services capacity and availability, K6 can be adjusted.
Figure 3.20: Sequence diagram 23 – Using car sharing system
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Chapter 4
Constraints and Analysis
After the behaviour of the system has been laid out with sequence diagrams, it can be modelled with
parametric diagrams. This type of diagram is used to explore the constraints of the system, when and/or
how extensively the use cases are triggered.
Each actor is governed by a set of equations. These are symbolic and needed in order to model a
given problem since no person is actually ruled by a set of immutable equations. The same is applicable
to use cases.
The constraints are modelled using constraint blocks. These blocks have ports, for input and output
of information, and also constraints. These are the equations that determine behaviour.
4.1 Actor parametrics
4.1.1 EMEL’s parametrics
Since all the use cases of EMEL are related to managing the parking system, all the constraints use the
value of K1, as seen in figure 4.1.
With the value of K1, that is depicted as a dashed rectangle because it’s part of another structure of
the model, namely the block used to define K1. As seen before in the sequence diagram for managing
parking easiness, there are four different conditions with four different outcomes. These conditions are
the constraints shown in equation 4.1a to 4.1d.
EMEL’s constraint equations:
DPSpace = if(K1 > 0.3) then DDPS else 0 (4.1a)
IPPrice = if(0.3 ≥ K1 > 0.2) then DIPP else 0 (4.1b)
DPPrice = if(0.2 > K1 ≥ 0.05) then DDPP else 0 (4.1c)
CPSpace = if(0.05 > K1) then DCPS else 0 (4.1d)
Following EMEL’s constraint equations, there is:
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Figure 4.1: EMEL’s parametric diagram.
4.1a triggers “decreasing parking spaces” with a value decided by the actor, labelled as DDPS. This
value is the number of parking spaces that will become unavailable for any driver inside the system.
4.1b triggers “increasing parking prices” with a value of DIPP. This value is the increase of the average
parking price.
4.1c triggers “decreasing parking prices” with a value of DDPP. This value is the decrease of the average
parking price.
4.1d triggers “increasing parking spaces” with a value decided by the actor, labelled as DCPS. This
value is the number of parking spaces that will be added to the total.
4.1.2 Customer parametrics
The only type of action possible for the customer is to use a given transport mode, and as such, there’s
only one constraint block regarding the customer’s mode choice, as seen in figure 4.2. To make this
decision the customer uses several internal parameters, aside from K3:
paramDist trip distance. To use the bike sharing system, the trip distance must be between 774m (10
minutes walk distance) and 6.25km (15 minutes trips at 25km/h, the maximum bicycle speed
[25]). The other modes have only a lower limit of 774m.
paramBSA bike sharing service attractiveness. The customer will only choose a mode if its attractive-
ness is higher than the other modes.
paramCSA car sharing service attractiveness.
paramPVA private vehicle attractiveness.
paramRPTA regular public transport attractiveness.
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paramCA car availability. The customer can only use a private vehicle if it’s available.
paramPTP public transport pass. The customer only uses the regular transport services if they possess
a pass.
paramInfo relates to the amount of information regarded as necessary for the customer to choose a
mode.
Figure 4.2: Customer’s parametric diagram.
There are as many constraint equations as there are modes, considering the bus and subway as one
under the label of regular transport. These equations are shown from 4.2a to 4.2d.
Customer’s constraint equations:
UseBS = if [0.774 < parD < 6.25 ∧K3 > parI ∧ parBSA = MAX(parBSA, parCSA, parPV A, parRPTA)] then 1 else 0
(4.2a)
UseCS = if [parD > 0.774 ∧K3 > parI ∧ parCSA = MAX(parBSA, parCSA, parPV A, parRPTA)] then 1 else 0
(4.2b)
UsePV = if [parD > 0.774 ∧ parCA = 1 ∧ parPV A = MAX(parBSA, parCSA, parPV A, parRPTA)] then 1 else 0
(4.2c)
UseRPT = if [parD > 0.774 ∧ parRTP = 1 ∧K3 > parI ∧ parPV A = MAX(parBSA, parCSA, parPV A, parRPTA)] then 1 else 0
(4.2d)
Following the customer’s constraint equations, there is:
4.2a triggers “using bike sharing system” with a value of 1 indicating there’s one more passenger for the
system to handle.
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4.2b triggers “using car sharing system” with a value of 1 indicating there’s one more passenger for the
system to handle.
4.2c triggers “using private” with a value of 1 indicating there’s one more car inside the city.
4.2d triggers “using regular public transport” with a value of 1 indicating there’s one more passenger for
the system to handle.
4.1.3 CML parametrics
CML may perform several actions that are related to different parts of the system, thus it has five con-
straint blocks. Each constraint block refers to one specific use case and shares the same name. The
parametric diagram of CML is shown in figure 4.3.
It uses one parameter, paramRD, that is the road density. This parameter is used to assess if CML
should build more bike lanes or not. As seen in the sequence diagrams before, each block requires a
specific variable input related to the respective use case.
There are five constraint equations, shown in eqs. 4.3a to 4.3e. One for each constraint block.
CML’s constraint equations:
BuildBL = if(K2 < parRD) then DBL else 0 (4.3a)
MaintainBL = if(A05 < 1) then 1 else 0 (4.3b)
CreateTH = if(A11 < 10) then DTH else 0 (4.3c)
IntegrateMoA = if(A12 6= 1) then DTS else 0 (4.3d)
HandSsI = if(A10 < 0.9) then 1 else 0 (4.3e)
Following CML’s constraint equations:
4.3a triggers “building bike lanes” with a value of DBL. This value is the extension of the new bike lanes
that will be built.
4.3b triggers “maintaining bike lanes” with a value of 1. This value signifies that the use case is triggered.
4.3c triggers “creating transport hubs” with a value of DTH. This value is the number of new transport
hubs that will be created.
4.3d triggers “integrating means of access” with a value of DTS. This value is the number of ticketing
systems that will be put out of commission.
4.3e triggers “handling systems information” with a value of 1. This means that the use case is triggered.
4.1.4 Carris parametrics
There are two blocks that represent the actions of Carris, managing bus service capacity and handling
bus information, as shown in figure 4.4.
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Figure 4.3: CML’s parametric diagram.
To manage the service’s capacity, it’s necessary to use a parameter along with the bus system
capacity and the required system capacity. The parameter paramBS serves to determine the share of
the required capacity that the bus service should handle.
To handle the service’s information, Carris needs only of the value of the bus system information.
There are three constraint equations for Carris, these are shown in eqs. 4.4a to 4.4c.
Carris’ constraint equations:
DeployB = if(A16 < parBSA20) then DBus else 0 (4.4a)
RecallB = if(A16 > parBSA20) then RBus else 0 (4.4b)
HandBI = if(A06 < 0.9) then 1 else 0 (4.4c)
Following Carris’ constraint equations:
4.4a triggers “deploying buses” with a value of DBus. This value is the number of buses that will be
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Figure 4.4: Carris’ parametric diagram.
added to the current working bus fleet.
4.4b triggers “recalling buses” with a value of DBus. This value is the number of buses that will be
removed to the current working bus fleet.
4.4c triggers “handling bus system information” with a value of 1. This means that the use case is
triggered.
4.1.5 Metro parametrics
There are three blocks that represent Metro’s actions, managing subway service capacity, creating sub-
way stations and handling subway information, as shown in figure 4.5.
To manage the service’s capacity, it’s necessary to use a parameter along with the subway system
capacity and the required system capacity. The parameter paramSS serves to determine the share of
the required capacity that the subway service should handle.
To create subway stations, the current subway system coverage must be lower than 67.39 km2, i.e.
95% of the city’s area. When creating new subway stations, Metro can choose to create a new subway
line as well. This is given by the parameter paramNL, that if its equal to 1, then there’ll be new lines
created.
To handle the service’s information, Metro needs only of the value of the subway system information.
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Figure 4.5: Metro’s parametric diagram.
There are five constraint equations for Metro, these are shown in eqs. 4.5a to 4.5e.
Metro’s constraint equations:
DeployT = if(A17 < parSSA20) then DTrains else 0 (4.5a)
RecallT = if(A17 > parSSA20) then RTrains else 0 (4.5b)
CreateSS = if(A13 < 67.39) then DSS else 0 (4.5c)
NewSL = if(parNL = 1) then DSL else 0 (4.5d)
HandSI = if(A07 < 0.9) then 1 else 0 (4.5e)
Following Metro’s constraint equations:
4.5a triggers “deploying trains” with a value of DTrain. This value is the number of trains that will be
added to the current working train fleet.
4.5b triggers “recalling trains” with a value of RTrain. This value is the number of trains that will be
removed to the current working train fleet.
4.5c triggers “creating subway stations” with a value of DSS. This value is the number of subway stations
that will be created in result.
4.5d is a component of “creating subway stations”. If triggered, DSL new subway lines will be created.
4.5e triggers “handling subway system information” with a value of 1. This means that the use case is
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triggered.
4.1.6 BSP parametrics
There are three blocks that represent BSP’s actions, creating bike sharing stations, relocating bicycles
and handling bike sharing information, as shown in figure 4.4.
To create bike sharing stations, the current bike sharing system coverage must be lower than 67.39
km2, i.e. 95% of the city’s area.
In order to relocate bicycles, the true capacity factor must be different than one. This indicates that
there are stations that are either full or empty.
To handle the service’s information, BSP needs only of the value of the bike sharing system informa-
tion.
Figure 4.6: BSP’s parametric diagram.
BSP has three constraint equations and these are shown in eqs. 4.6a to 4.6c.
BSP’s constraint equations:
CreateBSS = if(A14 < 67.39) then DBSS else 0 (4.6a)
RelocBi = if(A24 6= 1) then DRB else 0 (4.6b)
HandBSI = if(A08 < 0.9) then 1 else 0 (4.6c)
Following BSP’s constraint equations:
4.6a triggers “creating bike sharing stations” with a value of DBSS. This value is the number of bike
sharing stations that will be created in result.
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4.6b triggers “relocating bicycles” with a value of DRB. This indicates the number of bicycles that will be
relocated.
4.6c triggers “handling bike sharing system information” with a value of 1. This means that the use case
is triggered.
4.1.7 CSP parametrics
The CSP actions are represented by four blocks, deploying cars, expanding operational area, relocating
cars and handling car sharing information, as shown in figure 4.7.
To deploy more cars, CSP uses two variables and a counter. C5 is the counter for the quantity of busy
cars of the car sharing service, i.e. the number of cars being used by a customer. CSP will only deploy
more vehicles if the required system capacity is greater than all the systems capacity and availability, i.e.
if K6 < 1, and if all of the car fleet is being used.
If the car sharing system coverage is lower than 67.39 km2, i.e. 95% of the city’s area, CSP will
expand the operational area.
In order to relocate cars, the car density gradient must be greater than parCDG. The parameter
parCDG is used as a reference value to indicate if relocation is needed or not.
To handle the service’s information, CSP needs only of the value of the car sharing system informa-
tion.
Figure 4.7: CSP’s parametric diagram.
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There are four constraint equations for CSP, these are shown in eqs. 4.7a to 4.7d.
CSP’s constraint equations:
DeployC = if(K6 < 1 ∧A30 = C5) then DC else 0 (4.7a)
ExpandOA = if(A15 < 67.39) then DOA else 0 (4.7b)
RelocC = if(A32 ≥ parCDG) then DRC else 0 (4.7c)
HandCSI = if(A09 < 0.9) then 1 else 0 (4.7d)
Following CSP’s constraint equations:
4.7a triggers “deploying cars” with a value of DC. This value is the number of cars that will be added to
the car sharing service car fleet.
4.7b triggers “expanding operational area” with a value of DOA, indicating the increase in coverage
area.
4.7c triggers “relocating cars” with a value of DRC. This indicates the number of cars that will be relo-
cated.
4.7d triggers “handling car sharing system information” with a value of 1. This means that the use case
is triggered.
4.2 Use case parametrics
Once a use case is triggered, it is its parametric diagram that shows what is the outcome. Most of the
outputs in this model are equal to the input that triggered the use case and is represented by “Create”,
as displayed in table 4.1. In the cases where the input has different units than the output, there’s a
condition to be met. When the condition is fulfilled, the output is different from 0.
The outputs are named using the initials after the quantity that the respective use case changes, and
are prefixed with a d, to signify difference. If there are two use cases that change the same quantity or
quantities that have the same initials, the outcomes are prefixed with the first letter of the respective use
case.
As an example, the parametric diagram for creating bike sharing stations is shown in figure 4.8. It’s
represented by a constraint block that belongs to the use case. There’s one input, CreateBSS, that
comes from the bike sharing provider, as seen in its parametric diagram (fig. 4.6). Since the input is
the number of bike sharing stations that will be created, the output that represents the variation in the
number of bike sharing stations, dBSSS, is equal to the input.
The other two outputs check if the use case is triggered with the condition CreateBSS6=0. With the
creation of bike stations, the system coverage increases by a given amount of DBSC. This increase is
represented by the output dBSC. Finally, the size of the bicycle fleet increases by CB and is represented
64
Table 4.1: Use cases parametric models.Use Case Output EquationIncreasing parking prices iPP CreateDecreasing parking prices dPP CreateCreating parking spaces cPS CreateDecreasing parking spaces dPS CreateUsing private vehicle dCU if (UsePV=1) then 1 else 0Using regular public transport uRPT if (UseRPT=1) then 1 else 0Using bike sharing system uBS if (UseBS=1) then 1 else 0
uTBS if (UseBS=1) then DTBS else 0uF if (UseBS=1) then DFBSS else 0uE if (UseBS=1) then DEBSS else 0uB if (UseBS=1) then 1 else 0
Using car sharing system uCS if (UseCS=1) then 1 else 0uTCS if (UseBS=1) then DTCS else 0uGrad if (UseBS=1) then UGrad else 0uC if (UseCS=1) then 1 else 0
Building bike lanes dL CreateMaintaining bike lanes dLm if (MaintainBL6=0) then DMBL else 0Handling systems information dISs if (HandSsI=1) the DISs else 0Creating transport hubs dTH CreateIntegrating means of access dTS CreateHandling bus information dIB if (HandBI=1) the DIB else 0Deploying buses dB CreateRecalling buses rB CreateHandling subway information dIS if (HandSI=1) the DIS else 0Creating subway stations dSC CreateSS
dNsl NewSLDeploying trains dT CreateRecalling trains rT CreateHandling bike sharing information dIBS if (HandBSI=1) the DIBS else 0Create bike sharing station dBSC if (CreateBSS6=0) then DBSC else 0
cB if (CreateBSS6=0) then CB else 0dBSS Create
Relocating bicycles dF if (RelocBi 6=0) then DF else 0dE if (RelocBi 6=0) then DE else 0
Deploying cars dC CreateHandling car sharing information dICS if (HandCSI=1) the DICS else 0Expanding operational area dA CreateRelocating cars rGrad Create
by the output named cB. Since the change is of a quantity with the same initial as another, namely
bicycle and bus, the output has a prefix of c, the initial of the use case, instead of d.
4.3 Variable parametrics
After a use case is finished, its outcome will change the value of one or more variables. This is rep-
resented by a parametric diagram. Every variable has one parametric diagram and one equation to
determine its new value. Table 4.2 displays the equations used for each key variable, auxiliary variable
and counter. Most of the variables are calculated by adding or subtracting one or more outputs that
come from the use cases. However, some variables are averages and their equations are different.
65
Figure 4.8: Creating bike sharing stations parametric diagram.
Table 4.2: Variables and counters equations.
Variable Equation
K1 Parking EasinessA01
(A01 + 1)(e
−A02a +b + 1
)(e
A03c +d + 1
)K2 Bike Lanes Density
A04A05
ra
K3 Information Utility (A06 +A07 +A08 +A09)A10
K4 Systems Interconnectivity A115−A12
4
K5 System Coverage bsc ∩A13 ∩A14 ∩A15
K6 Services Capacity and AvailabilityA16 +A17 +A18 +A19
A10
A01 Average Parking Price Anew01 = Aold
01 + iPP − dPP
A02 Quantity of Parking spaces Anew02 = Aold
02 + cPS − dPS
A03 Quantity of Cars Anew03 = Aold
03 + dC + dCU
A04 Total bike lanes extension Anew04 = Aold
04 + dL
A05 Share of usable bike lanes Anew05 = Aold
05 + dLm
A04
A06 Bus System Information Anew06 = Aold
06 + dIB
A07 Subway System Information Anew07 = Aold
07 + dIS
A08 Bike Sharing System Information Anew08 = Aold
08 + dIBS
A09 Car Sharing System Information Anew09 = Aold
09 + dICS
Continued on next page
66
Table 4.2 – Continued from previous page
Variable Equation
A10 Systems information Anew10 = Aold
10 + dISs
A11 Quantity of hubs Anew11 = Aold
11 + dTH
A12 Quantity of Ticketing Systems Anew12 = Aold
12 − dTS
A13 Subway System Coverage Anew13 = Aold
13 + dSC
A14 Bike Sharing System Coverage Anew14 = Aold
14 + dBSC
A15 Car Sharing System Coverage Anew15 = Aold
15 + dA
A16 Bus System Capacity A16 = A21bcnl
A17 Subway System Capacity A17 = A22A23tc
A18 Bike Sharing System Availability A18 =A24A25
A26
A19 Car Sharing System Availability A19 =ccA30
A31MIN
(1,parCDG
A32
)A20 Required System Capacity Anew
20 = Aold20 + uBS + uCS + uRPT
A21 Average Bus Passage Frequency Anew21 = Aold
21
(1 +
dB − rBC1
)C1 Quantity of Circulating Buses Cnew
1 = Cold1 + dBD − rB
A22 Average Trains Passage Frequency Anew22 = Aold
22
(1 +
dT − rTC2
)C2 Quantity of Circulating Trains Cnew
2 = Cold2 + dT − rT
A23 Quantity of Subway Lines Anew23 = Aold
23 + dNsl
A24 True Capacity Factor A24 = 1− A28 +A29
A27
A25 Bicycle Fleet Size Anew25 = Aold
25 + dB
A26 Average Bicycle Trip Time Anew26 = if(uB = 1) then Aold
26 +uTBS −Aold
26
C3 + 1else Aold
26
C3 Bike Sharing Trips Counter Cnew3 = if(uB = 1) then Cold
3 + 1 else Cold3
A27 Quantity of Bike Sharing Stations Anew27 = Aold
27 + dBSS
A28 Quantity of Full Bike Sharing Stations Anew28 = Aold
28 − dF + uF
A29 Quantity of Empty Bike Sharing Stations Anew29 = Aold
29 − dE + uE
A30 Car Fleet Size Anew30 = Aold
30 + dC
A31 Average Car Trip Time Anew31 = if(uC = 1) then Aold
31 +uTCS −Aold
31
C4 + 1else Aold
31
C4 Car Sharing Trip Counter Cnew4 = if(uC = 1) then Cold
4 + 1 else Cold4
A32 Car Density Gradient Anew32 = Aold
32 + rGrad+ uGrad
C5 Quantity of Busy Cars Cnew5 = Cold
5 + uC
4.3.1 Average variables
There are four average variables and each requires a counter:
A21 requires a counter for the quantity of buses that are currently in circulation. C1 is used for this
67
purpose.
A22 requires a counter for the quantity of trains that are currently in circulation. C2 is used for this
purpose.
A26 requires a counter for the number of trips made using the bike sharing system. C3 is used for this
purpose.
A31 requires a counter for the number of trips made using the car sharing system. C4 is used for this
purpose.
The counters are updated and determined in the same diagrams as the auxiliary variable for which
they were created.
Average frequencies
The average frequency for a service takes into account the frequency of passage of all the lines in that
service. To change the frequency of a line, it’s necessary to change the number of vehicles circulating
in that particular line. This variation of frequency is represented in equation 4.8.
f(m+ dm)− f(m) =dmf(m)
m(4.8)
where f is the frequency, m is the number of circulating vehicles and dm is the variation in the number
of vehicles.
Since A21 and A22 are the average frequencies of the whole service, a variation of the number of
circulating vehicles is given by equation 4.9.
f ′ = f +1
nL
nL∑i=1
dmifimi
(4.9)
where f ′ is the new average frequency, f is the previous average frequency, nL is the number of
lines, fi is the frequency of line i, mi is the number of circulating vehicles in line i and dmi is the variation
in number of vehicles in line i.
Since the lines weren’t modelled individually, it’s not possible to use equation 4.9 for the parametric
diagrams. Assuming that the quantity of circulating vehicles and the variation of vehicles is the same for
all lines, it’s possible to then use equation 4.10 for the parametric diagrams.
f ′ = f
(1 +
dm
m
)(4.10)
where f ′ is the new average frequency, f is the previous average frequency, is the number of circu-
lating vehicles and dm is the variation in the number of vehicles in line i.
68
Finally, equations 4.11a and 4.11b show the parametric equations for A21 and A22, respectively.
Anew21 = Aold
21
(1 +
dB − rBC1
)(4.11a)
Anew22 = Aold
22
(1 +
dT − rTC2
)(4.11b)
As an example, figure 4.9 shows the parametric diagram of A21. Due to software limitations, it’s
necessary to use two constraint blocks to change the value of a variable that receives itself as an input.
The first block adjusts the new values of the variables with the inputs received. The second block updates
the values of the variables and of the counter.
Figure 4.9: A21 – Average bus passage frequency parametric diagram.
Average trip times
The average trip time is a simpler variable to calculate, it follows the structure of equation 4.12.
x′ = x+
∑n+di=n xi − dxn+ d
(4.12)
where x′ is the new average, x is the previous average, n is the number of entries used for the
previous average, d is the number of new entries and xi is the new entry i.
Since the values of A26 and A31 are determined every time there’s an instance of system use, d=1,
69
as seen in equations 4.13a and 4.13b.
Anew26 = Aold
26 +uTBS −Aold
26
C3 + 1(4.13a)
Anew31 = Aold
31 +uTCS −Aold
31
C4 + 1(4.13b)
As an example, figure 4.10 shows the parametric diagram of A31. Likewise, A21’s parametric diagram,
the values of the variable and of its counter are adjusted and then updated together.
Figure 4.10: A31 – Average car trip time parametric diagram.
4.4 Analysis and proposed solution
Once all the problem’s parts are modelled using parametric diagrams, it’s possible to analyse the system
and propose a solution.
4.4.1 Services accessibility
The transport system should cater to the customer, however, due to insufficient coverage, a large amount
of the city’s area isn’t covered by more than one public transport. Currently, only the subway and the
bus service are considered public transport, and as such, approximately, only 57% of the total city area
is covered with all public transport services. This leaves 43% of city area that isn’t accessible for the
customer to use both modes.
Being able to use all the modes at your service becomes increasingly important as the trip distance
70
increases because the customer wants to minimize the trip time and having more options means that
the optimal path can always be chosen. Therefore the model only has options to increase the coverage
of the different system. It’s not fruitful to also model use cases that will decrease the coverage, because
it’s currently insufficient. Once all the different services have reached most of the city area, then it’s
advisable to decommission some stations that are being underused in relation to what’s expected.
The bike sharing and the car sharing services aren’t currently considered as public transport, thus
their expansion is motivated only by self-interest and the transport authority, CML, can’t impose public
service obligations.
Apart from physical integration, each system has its own ticketing system. The regular transports
have VIVA [32], the bike sharing service and each car sharing provider have different means of access.
Since the systems are currently segregated, it’s difficult for the customer to use different services while
making a journey, i.e. the optimal path may require different the use of different services and the cus-
tomer may not be able to access all of them. This, in turn, can make the journeys longer, since the public
transport system isn’t interconnected.
System unification also leads towards system robustness, i.e. even if one subsystem has a pertur-
bation or is inoperable, the system as a whole is able to adjust and handle the required service capacity.
Expanding each service coverage and unifying their ticketing system will improve their overall attrac-
tiveness to the customer. Once a public transport mode has a higher attractiveness than the private
vehicle, the former will be used instead of the latter, thus reducing the problem in question.
4.4.2 Information and reliability
The information was modelled to represent another threshold to use a service. If the information is
deemed insufficient by the customer, they will not choose that mode as the information isn’t reliable or
simply doesn’t provide enough for the customer to make an informed decision.
Having multiples car sharing systems works in detriment to the unification of the transport system.
The nearest car may not belong to the specific provider that the customer uses, this limits the customer
options and adds a mental burden to the customer, who now must sift through the different providers in
order to find the nearest vehicle.
Nowadays, there’s one multimodal information platform, TRANSPORLIS [33], that has information
regarding the regular transport services within the city. This platform has also developed a mobile
application, Lisboa Viagem, with the same information. With one information system that integrates all
the different modes, the customer would be able to choose the most convenient to their needs.
4.4.3 Car sharing role
The intended role of the car sharing service is to replace the private vehicle use and at the same time
serve as a gateway to the other public transport systems. If the car sharing system is integrated with
the other modes of transport, the customer will become aware of the other options and may be able to
use them. As discussed before, a mode attractiveness increases with the user’s familiarity with it. The
71
shift to treat the car sharing system as a flexible public transport is necessary in order to the transport
authority to be able to impose public transport obligations.
72
Chapter 5
Conclusions
The identified problem was the increasing car modal share for commute trips in the city of Lisbon. It in-
creased 9.4% in a span of 10 years, from 2001 to 2011. This problem entails two major consequences,
a parking system overloading and a underdevelopment of other modes of transport. The underdevelop-
ment can be broken down in parts regarding the public transport system coverage, interconnectivity and
capacity.
To characterize the problem a model was constructed using SysML. The model is restricted to the city
of Lisbon and its internal transport providers. No inter-municipal public transport provider was modelled.
After analysing the different factors that influence a citizen to choose a transport mode a simple was
constructed with 6 key variables, 32 auxiliary variables and 5 counters, 7 actors, and 27 use cases.
Due to software limitations and the nature of the work, most of the system’s variables deal with average
values.
The system model provides a framework to achieve a solution to the problem. This solution consists
in having a public transport provider for each of the modes of transport, unifying them physically, and
through a unique ticketing system and with a unique information platform. A car sharing system that is
treated as a public transport provider would serve as a replacement to the use of the private vehicle and
as a gateway to the other modes for the citizen that use the car as the only mode of transport.
5.1 Achievements
A simple model using Systems Modelling Language of the public transport system of the city of Lisbon
was achieved in this work. This model characterizes the behaviour of the system through sequence
diagrams that show how the actors interact with each other and with parts of the system. 24 different
sequence diagrams were created and explored.
To analyse the constraints under which the system operates, 74 parametric diagrams and 103 con-
straint equations were created. There’s one parametric diagram for each actor, use case and variable.
The constraint equations dictate how the actors trigger each use case, how the use case produce an
output based on an actor input and how these outputs change the system’s variables.
73
5.2 Future work
First and foremost, data must be gathered in order to test the model and validate it. While in the process
of validation, the model restrictions and assumptions will be put to test. This will prove or disprove them
in order to make the model more authentic.
Once the model has been validated more future work would rely on adding more detail and depth to
the model. Some quantities, such as the number of full bike sharing stations or the car density gradient,
can’t be directly calculated with this model. In order to do this, it would be necessary to cooperate with
the different service providers. Only them can relay how their service actually operates to fine-tune the
model.
More detail could also entail the use of less average variables, through the modelling of each individ-
ual line and having a variable vehicle capacity function of the deployed vehicles. The number of vehicles
that can be deployed is, in reality, limited by the current service fleet.
Adding the different inter-municipal transport services and how the systems interact geographically
would also be a good extension of the model. With its current format, the customers’ origins are consid-
ered to start and end the journey inside Lisbon.
The different modes attractiveness could also be modelled as a systems variable, thus providing
more information to the decision makers of how the system could be modified in order to attract a wider
array of customers.
Finally, the car sharing system coverage is considered to be equal to its operational area. This
doesn’t always correspond to the actual coverage because some zones may not have any vehicles and
as such, the system isn’t accessible. A dynamic coverage that takes into account the position of the
each parked vehicle could be a more precise way of depicting the system’s coverage.
74
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