Modelling the Demand Evolution of New Shared Mobility Title Services( Dissertation_全文 )
Author(s) Zhang, Cen
Citation 京都大学
Issue Date 2019-03-25
URL https://doi.org/10.14989/doctor.k21747
Right
Type Thesis or Dissertation
Textversion ETD
Kyoto University
Modelling the Demand Evolution of New Shared Mobility Services
ZHANG CEN
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Acknowledgments
The writing of this dissertation has been one of the most significant academic challenges
I have ever had to face. A great many people have contributed to its production. Without their supports and guidance, this study would not have been completed.
First of all, I would like to thank my sincere gratitude and deep regards to my supervisor,
Associate Prof. Jan-Dirk Schmöcker, in Kyoto University for his patience, motivation, and immense knowledge. His guidance helped me in all the time of research and writing of this thesis.
Besides my advisor, I would like to thank the rest of my thesis committee and co- supervisors: Prof. Yamata and Associate Prof. Uno in the Kyoto University, for their insightful comments and encouragements, but also for the questions which inspired me to widen my research from various perspectives.
Also my sincere thanks also goes to Prof Fuji in the Kyoto University, Asscoiate Prof.
Nakamura in Nagoya University who advised me at several stages. Without their precious support it would not be possible to conduct this research.
Regards the assistance of administration process, I hope to give this opportunity to express a deep sense of gratitude to thanks to the secretaries, Mrs. Nagata, Mrs. Nishimura and Mrs. Ichihashi, their various helps have made me concentrate on my research.
Above all, I would like to thank members of ITS laboratory and all friends who have a great time and willing to share their thoughts and ideas with me in Japan. Last but not the least, I would like to thank my family for supporting me spiritually throughout writing this thesis and my life in general.
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Abstract
Recently, shared mobility, including car-sharing, bicycle-sharing, microtransit and on demand ride service, has emerged as popular forms of alternative transport. This form of collaborative consumption, which promotes the sharing of access to transport service, rather than having individual ownership, will largely save the cost as well as space and of course, reduce carbon emissions.
With the emergence of these and other new transport modes, our transport systems are undergoing major changes and behavioural responses are expected (and desired).
Understanding long term demand dynamics remains an important challenge for new transport systems. To achieve this, this dissertation contains two parts: One is the adoption process of potential users, that leads a person from initial recognising the scheme and then starting to use it. The other part is the change in behaviour over usage life-time, that is variation of usage frequency from initial usage to finally dropping out/quitting the system.
In the first part of this dissertation, our objective is to be able to forecast the number of new adopters and the potential market with facility extension, including when new stations/service areas are added to the system. In order to do so, potential users are divided into two types: Fast and Hesitant adopters. Stations are classified into four groups according to their location: Residential area, Business area, Public service area and Transit Hub. We formulate the adoption model of fast-adopters integrated with an information diffusion model to capture the initial changes. The adoption model for the Hesitant-adopters considers both a follower effect and a hesitant effect. Further, to estimate spatial differences in adoption rates and interconnectedness of stations, location specific parameters and a redistribution model are established. The purpose of the latter is to recognize that despite initial usage being carried
v out at a specific station, the new user might be attracted to join the system due to the existence of several stations.
The least square method and gradient descent optimization algorithms are used to estimate the parameters. The methodology is applied to data from the Ha:mo RIDE car share system in Toyota city. We observe two peaks in the new user curve which can be explained by our model, the initial peak may be caused by information diffusion whereas the later peak can be explained by market saturation. A comparison between a range of models for estimation and forecasting are made.
In the second part of this dissertation, the focus is on describing the individual behaviour changes over time and then forecasting the demand dynamics of system. At first, to describe the stochastic behaviour changes over time by using panel data, an approach based on stochastic state equations (Markov model) is proposed. Transition functions determine the likely change in behaviour from one time period to another. To overcome the problem of a dynamic population and explain seasonal irregularities, we introduce “life-cycle”, “potential demand” and “willingness to use” into our models. With this we discuss time-homogeneity issues, possibilities to identify usage states and calibrate the transition function. The life-cycle model is applied to panel data from Kyoto University’s bicycle share system. The errors between actual and estimated values are analysed to evaluate two model specifications. The findings help us understanding adaptation, “recovery” and drop-out behaviour.
Later, by introducing some latent “Life Stages” into the lifecycle models, the model can deal better with time-heterogeneity in transition, leading to an improved description on user behaviour changes. Therefore, a total of five individual life-cycle stages are define; Birth,
Growing, Maturity, Recession and Death. As the current stage of users can change over time, transition functions in different stages will further decide the state transitions within each stage. The model can be considered as a special case of Hierarchical Hidden Markov Model
(HHMM). To estimate the latent variables and the transition functions, the Expectation- vi maximization (EM) algorithm is used. The extended lifecycle model is applied to panel data from Montreal`s Free Floating Car Sharing Service (FFcs). The results show that the model can fit the observed demand distribution curve in lifetime and real-time well. At the same time, an impact of facility extension (new service areas) on user behaviour is noticed, in that a higher drop out ratio but increased usage frequency at all stages is observed. It is also found that differences in behaviour exist between users with experience of using the prior existing station-based car sharing service (SBcs) and users without such experience. Experienced users have longer lifetime but also slower adaptation and lower usage frequency at the beginning.
These findings help understanding impacts of other factors, such as previous experience and facility extension on initial trials, adaptation, maintaining, decline and drop-out behaviour.
Finally, to further explore the usefulness and limitations of our methodologies, a combination of the adoption model and the user life-cycle model is conducted to forecast the demand dynamics of new transport system with the facility extension in case study Ha:mo.
Keywords: Shared Mobility; Demand Evolution; Adoption and Diffusion; Stochastic Process; Lifecycle Model;
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viii Preface
Papers published or submitted related to this thesis are listed in the following:
I. Zhang, C.,Schmöcker, J.-D (2017). Modelling User Adaptation to a Campus Bicycle Share System. 96th TRB Annual Meeting, Washington DC, USA. (Chapter 5) II. Zhang, C.,Schmöcker, J. D. (2017). A Markovian model of user adaptation with case study of a shared bicycle scheme. Transportmetrica B: Transport Dynamics, 1-14. (Chapter 5) III. Zhang, C., Schmöcker, J.-D (2019). Stochastic process based life-cycle modelling for user behavior changes. 98th TRB Annual Meeting, Washington DC, USA. (Chapter 6) IV. Zhang, C., Schmöcker, J.-D, Toshiyuki Nakamura, Masahiro Kuwahara. (2017), Modeling adoption and diffusion of new transportation system in station level, Autumn Conference of Committee of Infrastructure Planning and Management, Morioka, Japan. (Chapter 4) V. Zhang, C., Schmöcker, J.-D, Toshiyuki Nakamura, Nobuhiro Uno, Masahiro Kuwahara (2018). Modeling temporal and spatial differences in the adoption of new transport systems, Transportation Research Part C: Emerging Technologies (under review) (Chapter 4)
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x Table of Contents
_Toc534923292 Acknowledgments ...... iii Abstract ...... v Preface ...... ix Table of Contents ...... xi List of Tables...... xv List of Figures ...... xvii CHAPTER 1. INTRODUCTION ...... 1 1.1. Background ...... 1 1.2. Research Objective ...... 2 1.3. Outline and Structure of the Dissertation ...... 4 CHAPTER 2. OVERVIEW OF SHARED MOBILITY ...... 7 2.1. Introduction ...... 7 2.2. Bikesharing ...... 7 2.3. Carsharing...... 10 2.4. Other forms of Sharing ...... 13 2.4.1. On-demand Ride Service ...... 13 2.4.2. Ridersharing ...... 14 2.4.3. Alternative Transit ...... 15 2.5. Summary ...... 16 CHAPTER 3. LITERATU REREVIEW ...... 19 3.1. Introduction ...... 19 3.2. Demand Modelling for New schemes ...... 19 3.2.1. Factors for demand analysis in shared mobility ...... 19 3.2.2. Demand modelling for estimation and forecasting ...... 22 3.2.3. Comparison ...... 23 3.3. Adoption and Diffusion for New Schemes...... 24 3.3.1. Two extremes: Econometric (Macro) versus ABM models (Micro) 24 3.3.2. Mathematical modelling of innovation diffusion ...... 26 3.3.3. Individual heterogeneity ...... 28 3.3.4. Space heterogeneity ...... 30 3.3.5. Time Granularity ...... 30 3.3.6. Comparison and Summary ...... 31
xi 3.4. Data Analysis Methods on User behavior change ...... 32 3.4.1. Stochastic Process Modelling ...... 32 3.4.2. Marketing concepts adapted in this research ...... 34 3.5. Summary ...... 36 CHAPTER 4. ADOPTION AND DIFFUSION OF NEW SERVICE ..... 39 4.1. Introduction ...... 39 4.2. Individual Adoption Process ...... 39 4.3. Individual adoption Classification ...... 41 4.4. Methodology ...... 42 4.4.1. Information Diffusion Model ...... 42 4.4.2. Adoption Model ...... 43 4.4.3. Station Demand Attraction Model ...... 44 4.4.4. Reduced Model ...... 48 4.5. Illustration and Comparison ...... 48 4.6. Parameters Estimation ...... 51 4.7. Case Study...... 52 4.7.1. Ha:mo RIDE car sharing system...... 52 4.7.2. Full and Reduced Model Specification ...... 53 4.7.3. Estimation and Forecasting of New Adopters ...... 54 4.7.4. Parameter analysis ...... 56 4.8. Summary ...... 59 CHAPTER 5. BEHAVIOR DYNAMICS: LIFECYCLE MODEL ...... 61 5.1. Introduction ...... 61 5.2. Model Conceptualization ...... 62 5.2.1. Notations ...... 62 5.2.2. Life-Cycle Model ...... 63 5.3. Estimation of parameters ...... 67 5.3.1. Overview ...... 67 5.3.2. Identifying States ...... 67 5.3.3. Estimation for transition function ...... 69 5.3.4. Revision of Willingness Matrix ...... 71 5.3.5. Estimation of potential demand ...... 71 5.4. Case study ...... 72 5.4.1. The COGOO System ...... 72 5.4.2. Aggregate Data Analysis ...... 73 5.4.3. Estimated Parameters ...... 74 5.4.4. Results based on Transition probabilities...... 75 5.4.5. Estimation results of different models ...... 76
xii 5.5. Summary ...... 77 CHAPTER 6. EXTENSION OF LIFECYCLE MODEL ...... 81 6.1. Introduction ...... 81 6.2. Extension of Life-cycle Models ...... 81 6.2.1. Notations ...... 81 6.2.2. Formulations of the Models ...... 83 6.3. Estimation of parameters ...... 85 6.4. Case study ...... 88 6.4.1. The Communauto Car-sharing System ...... 88 6.4.2. Estimation Results ...... 90 6.4.3. Impact of Previous Experience ...... 96 6.4.4. Facility Extension ...... 101 6.4.5. Model Comparison ...... 107 6.5. Summary ...... 108 CHAPTER 7. FRAMEWORK OF DEMAND EVOLUTION ...... 111 7.1. Introduction ...... 111 7.2. Framework of demand dynamics modelling ...... 111 7.3. Case study ...... 114 7.3.1. Ha:mo RIDE car sharing system...... 114 7.3.2. Estimated parameters ...... 115 7.3.3. Data Analysis ...... 117 7.3.4. Forecasting ...... 119 7.4. Summary ...... 121 CHAPTER 8. CONCLUSIONS ...... 123 8.1. Summary of Research ...... 123 8.2. Contributions to knowledge ...... 124 8.3. Limitations of the study and opportunities for further works 126 Reference ...... 128
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xiv List of Tables
Table 2.1 Aggregated Shift in Public Transit and Non-Motorized Modes Due to Carsharing Use. Taken from: Martin and Shaheen (2010) ..... 13 Table 3.1 Innovation Diffusion Models/Methods ...... 32 Table 4.1 Parameters of models ...... 49 Table 5.1. Notations in Lifecycle Modeling ...... 62 Table 5.2 State divisions ...... 73 Table 6.1 Transition Matrix π for Life Cycle ...... 84 Table 6.2 State Divisions ...... 90 Table 6.3 Transition Matrix in stages for 5-stages and 3-stages model .... 91 Table 6.4 Transition Matrix in states for 5-stages and 3-stages model ..... 92 Table 6.5 Estimated Parameters for Stage Transition ...... 97 Table 6.6 Estimated Parameters for State Transition ...... 98 Table 6.7 Service Areas extension of FFcs in Montreal ...... 101 Table 6.8 Transition Matrix in stage for time before and after facility extension ...... 103 Table 6.9 Transition Matrices of States for time before and after facility extension ...... 104 Table 6.10 Performance of models in life time and real time ...... 108 Table 7.1 Parameter estimates and standard errors for the Reduced Model (M6). Significant of parameters at the 5% level of confidence...... 115 Table 7.2 Stage Transition Matrix ...... 116 Table 7.3 State Transition Matrices ...... 116
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xvi List of Figures
Figure 1.1 Dissertation structure ...... 6 Figure 2.1 Overview of Shared mobility ...... 17 Figure 4.1 The adoption process ...... 40 Figure 4.2 Illustration of the station attraction model ...... 45 Figure 4.3 Relationship of attracted and observed new users in one station ...... 47 Figure 4.4 Comparison of models with focus on long-term trends ...... 50 Figure 4.5 Comparison of models with focus on initial time periods ...... 51 Figure 4.6 Location of Ha:mo stations ...... 52 Figure 4.7 Estimated New adopters of system ...... 54 Figure 4.8 Prediction of new adopters ...... 56 Figure 4.9 Estimated time coefficient ...... 57 Figure 4.10 Boxplot of parameters a, p, I, M ...... 58 Figure 5.1 User life cycle ...... 64 Figure 5.2 Distinguishing temporarily inactive and drop-out users ...... 68 Figure 5.3 Location of stations in COGOO of Kyoto University ...... 72 Figure 5.4 Number of users for different states ...... 74 Figure 5.5 Users entering and exiting COGOO ...... 75 Figure 5.6 Estimated potential demand for users in the system ...... 76 Figure 5.7 MAPE errors of the two models ...... 77 Figure 6.1 Life Cycle of Individuals...... 83 Figure 6.2 Introduce of FFcs service in Montreal ...... 89 Figure 6.3 New users and usage of system overtime ...... 90 Figure 6.4 Estimation and observation of two models in lifetime ...... 93 Figure 6.5 Dropping Out Users ...... 94 Figure 6.6 Active Users in System ...... 95 Figure 6.7 Estimation of active users states in real time ...... 95 Figure 6.8 Estimated and Observed State Distribution ...... 99 Figure 6.9 Lifetime and Stage Distribution ...... 101 Figure 6.10 Map of Facility extension in May 2015 ...... 102 Figure 6.11 Estimation of states in lifetime ...... 106 Figure 6.12 Estimated lifetime and stages distribution ...... 107 Figure 6.13 Estimation of states in real time for models ...... 107 Figure 7.1 Structure of Framework in Demand Evolution ...... 113
xvii Figure 7.2 Ha:mo Stations in Toyota City ...... 114 Figure 7.3 Observation and Estimation of new adopter ...... 117 Figure 7.4 Estimation of users states in lifetime ...... 119 Figure 7.5 Prediction of In and Out of Ha:mo System without Facility Extension ...... 120 Figure 7.6 Prediction of Users in the system ...... 120 Figure 7.7 Prediction of Users in states ...... 122
xviii CHAPTER 1. INTRODUCTION
1.1. Background
Due to advancements in social networking, location-based services, the Internet, and mobile technologies, the sharing economy, a developing phenomenon based on renting and borrowing goods and services rather than owning them, are becoming more and more popular over the world. This sharing economy, occurs among peers or through businesses, can improve efficiency, provide cost savings, monetize underused resources, and offer social and environmental benefits.
Driven by the Internet, the origins of the sharing economy can be traced back to the dot- com boom of the late 1990s. Marketplaces of websites, such as eBay, PayPal, and Ali, made it possible for individual entrepreneurs to have access to the global clientele. At the early 2000s,
P2P(peer-to-peer) file sharing, such as Napster, one of the most prominent sharing models, let more and more people accept the sharing model and benefit from it. Technological advancements facilitated changes in consumption and financial transactions and also more broadly promoted sociological transformations regarding how people view shared resources.
During the late 2000s, numerous further sharing models, such as P2P marketplaces (e.g.,
Airbnb), P2P carsharing (e.g.Getaround) and crowdfunding (e.g., Kickstarter), emerged and were accepted by people quickly. Among them, Shared mobility, the shared use of a motor vehicle, bicycle, or other low-speed transportation mode, is one key facet of the sharing economy related to everyone’s daily life. Usually, it includes carsharing, bikesharing, microtransit, and on-demand ride services.
Due to advances in technology, evolving social and economic perspectives toward transportation and urban lifestyles, shared mobility has developed rapidly especially in the
1 last decade. Recently, it has been widely regarded as popular forms of alternative transport, especially in space-constrained cities where the cost of transport is high. This form of collaborative consumption, which promotes the sharing of access to transport service, rather than having individual ownership, will largely save the cost as well as space and of course, reduce carbon emissions.
With the emergence of new transport modes, especially shared mobility, our transport systems are undergoing major changes and behavioural responses are expected (and desired).
In china, High speed railway and free-floating bikesharing have already solved the traffic problems of long distance travelling and last-mile, and totally changed everyone's daily life.
As discussed in the example Li and Schmöcker (2016) for the case of High Speed Rail, it highlights the need to revisit demand modelling for both new and existing modes.
Over the last decades, various studies focus on the Demand Forecasting, which is a key issue for transport planning. However, understanding long term demand dynamics remains an challenge for new transport systems. Traditional “equilibrium models” are suitable to forecast demand in relatively stable markets. Otherwise, if the transport system is undergoing rapid expansion, the prediction accuracy of traditional methods drops quickly in the longer the planning horizon. In some cases demand estimations have been found to be very far from predictions. The limitations of such models for new systems are apparent which motivates this research.
1.2. Research Objective
As explained in previous section, demand forecasting for developing transport systems would be challenging. The initial idea of this dissertation is to break down this difficult problem into several small ones, then solve them with suitable methodologies, and finally combine them together to achieve our goal.
2 In specific, there are two parts what we interested in, one is the “Adoption Process”, how and why potential users are attracted by new service and finally accept it and begin the initial usage. It involves with initial perceptions, past experiences, expectations, potential demand, as well as diffusion of innovation (consumer behaviour). The others is “Behaviour Changes”, the process that users begin the initial usage and then increase, maintain, decrease frequency and finally drop out/quit the system over time. The process is related to potential demand and willingness or attitude to new service.
In more details, to solve the problem, there are some questions we need to answer in this research:
Adoption process:
Individual level
How can a person adopt to a new service?
What factors decide whether a person accepts the new transport service or not?
Are there any adoption patterns for different potential users?
System level
What is effect of facility extension on adoption?
How many people will adopt to the new transport service in the future?
Behaviour changes
Individual level
What affect user behaviour changes in the new service?
How will users change their behaviours in the future?
System level
What is total usage and demand distribution of the system in the future?
How many users will stop using the service in the future?
3 What is development trend for new transport system?
Capturing adoption of new system and the dynamics in travel behaviour may be of fundamental importance for the analysis and prediction of travel demand. Moreover, the objectives in this thesis are to discover those perception factors that might influence user adoption and behaviour changes during the development of new transport system, and forecast the demand dynamics. To summarize in this dissertation the objectives are:
1.Discovering the determining factors that might influence user adoption for shared mobility system.
2.To estimate the potential markets for new shared mobility system
3.To quantify adoption in spatial level in shared mobility system, especially considering effect of facility extension.
4.Forecasting the number of new adopters and dropping out users for shared mobility system.
5.Formulate approach to describe and explains the different changes of behavior over time by using panel data.
6.Predicting the demand dynamics for shared mobility system in the future.
1.3. Outline and Structure of the Dissertation
The dissertation is organized by seven chapters. The introduction chapter explains the motivation and the background and objectives of the study, and research outline of the dissertation.
In Chapter 2, the development of various forms of Shared mobility are reviewed, such as carsharing, bikesharing, ridesharing (carpooling and vanpooling),alternative transit, on-
4 demand ride services around the world and the impacts on travellers, transport system and environment.
Chapter 3 will review research regarding demand modelling in shared mobility and found that we still need better understanding of demand dynamics in new transport system, which may related two parts, adoption and user behaviour changes. Firstly, adoption and diffusion models/methods are introduced and compared. To apply diffusion models into transport system, spatial heterogeneity needs to be considered. This is followed by a description of models/methods that reflect the demand dynamics for new schemes, especially
Markov models. The chapter concludes by introducing some concepts related to our models from marketing, such as lifecycle, potential demand and what will be referred to as
“willingness”.
In Chapter 4, we offer a description of our methodological framework and details of the models in adoption, including the adoption process, information diffusion model, adoption model and redistribution model in spatial level. Specifically, to reduce the number of parameters and avoid overfitting we analyse correlations and simplify the model accordingly.
As an example for adaptation to Ha:mo RIDE, a one-way electric car sharing system, data from Toyota city are used to illustrate how well new adopters can be estimated and forecasted over time.
In Chapter 5, a description of the stochastic process of discrete behaviour observed at discrete time periods is offered. This process can be calibrated by observations from a panel study using the maximum likelihood estimation together with Newton’s iteration method.
Panel data obtained from Kyoto University’s bicycle share system are used to illustrate the approach.
In Chapter 6, by introducing additional “Life Stages” we can deal with a dynamic population and time-heterogeneity in transitions. To estimate the latent variables and the
5 transition functions, the Expectation-maximization (EM) algorithm is used. The extension model is applied to panel data from Montreal’s Carsharing Service (FFcs). Some additional factors，such as previous experience, facility extension and seasonal effects are considered to improve the models compared to a base version.
Chapter 7 combine the adoption model and lifecycle model together to form the structure of demand dynamics forecasting for new shared mobility service. A case study of Ha:mo in
Toyota City is made to prove feasibility of our framework in application.
Chapter 8 concludes this study by summarizing and converging the central findings of this study from both adoption and behaviour changes. Implication for policy and planning are derived, shortcomings of the study, recommendations for future work, as well as an assessment of the overall contribution of this study.
The structure of this dissertation and the main concepts that are introduced are shown in
Figure 1.1.
Figure 1.1 Dissertation structure
6 CHAPTER 2. OVERVIEW OF SHARED MOBILITY
2.1. Introduction
Shared mobility, the shared use of a vehicle, bicycle, or other mode is an innovative transportation strategy that enables users to gain short-term access to transportation modes based on their needs. It includes various forms of service, carsharing, bikesharing, ridesharing
(carpooling and vanpooling), on-demand ride services, and also alternative transit services, including paratransit, shuttles, and microtransit, which may supplement fixed route bus and rail services. With more and more options for mobility, smartphone apps that aggregate most possible travel choices and optimize routes for travellers are becoming popular. In addition to these innovative travel modes, new ways of transporting and transporting goods have emerged, eg. courier network services (CNS). These new services have the potential to change not only the nature of the package delivery industry, but also the broader transportation network. Shared mobility is having a transformative impact on cities over the world by enhancing transportation accessibility, while simultaneously reducing personal vehicle ownership and driving willingness.
In this chapter, we aim to provide an overview of this emerging field and current understanding—in the next few years shared mobility will continue to evolve and develop.
The sections in this chapter are organized by the forms of shared mobility service.
2.2. Bikesharing
Bikesharing was first launched in Europe in 1965. After that，bikesharing programs have grown exponentially over the word. At present, it exists in Europe, Asia, and North and
7 South America. In China alone, by August 2017 there were more than 20 million shared bikes from 50 companies over 170 cities.
Bike-sharing has already gone through four generations with operational and logistical development over the past 53 years since inception. First generation bikesharing, such as
“White Bicycles, a free bike systems started in the summer of 1965 in Amsterdam, consisted of bicycles haphazardly placed throughout a city center. These bikes were supposed to unlocked and free for public use. However, bicycles in these systems can be easily damaged or stolen.
Second generation systems, such as “Copenhagen City Bikes” a coin deposit systems launched in 1995,”are an improved version by incorporating a lock that required users to insert a refundable deposit to unlock (Shaheen et al., 2010). Though bicycle locks and user deposits provided protection, they were not enough. In addition, these systems would not limit bike-usage times. Thus, users often kept bicycles for extended time periods.
The third-generation bike sharing systems, such as “Vélos à la carte” an “IT-Based
Systems” launched in Rennes, France in 1998, employ designated docking stations for security, kiosks for user interface, advanced technology for bicycle distinguishing and tracking (i.e., radiofrequency identification, RFID) and check-in/checkout (i.e., smart cards or mobile phones) (Shaheen et al., 2010). The use of a smart card/mobile phone answered the need for real-time information for the operator, and started the use of technology to assist in re-balancing the bikes between different stations. Tough it prevents theft and encourage bicycles to return to some extension, there have still limitations on convenience of usage due to the fixed stations.
Lessons from previous bike sharing systems have prompted the rise of fourth-generation systems, Free-floating bike sharing (FFBS), also known as station-less bike sharing. It is a new generation of bike sharing systems (BSS) that allows bikes to be locked to ordinary bike
8 racks (or any solid frame or standalone), eliminating the need for specific stations. It saves on start-up cost by avoiding the construction of expensive docking stations and kiosk machines required for station-based bike sharing (SBBS). With built-in GPS, customers can find and reserve bikes via a smart phone or a web app, and operators can track the usage of the bikes in real-time. The success of FFBS is attributed to at least two points. For users, the ease of use, with advanced technology renting and returning bikes become extremely convenient, makes user satisfaction levels increase. For operators, with advanced technology high efficiency smart management greatly reduce cost in large-scale systems and then provide low service price to attract more users. ( DeMaio and Pal; Zhang)
Bike-sharing service provides a low-carbon option for the first-and-last mile of a short distance trip, providing a link for trips between home and public transit and/or transit stations and the workplace that are too far to walk, as well as a many-mile alternative. Evidence reviewed in the following suggests that it has been significantly changing daily travel behavior.
Shaheen (2012b and 2014) conducted a two-part study of bikesharing programs in North
America to determine the program impacts on modal split. The results suggest that bikesharing in larger cities takes riders off of crowded buses, while bikesharing in smaller cities improves access/egress from bus lines. Moreover, 5.5% of bikesharing members sold or postponed a vehicle purchase and about 50% of respondents reduce both their personal automobile use and rail usage in larger cities due to faster travel speeds and cost savings from bikesharing.
In addition, several studies have demonstrated a modal shift toward bicycle use which may lead to educed CO2 emissions. Evaluations indicate an increased public awareness of bikesharing as aviable transportation mode. A study which surveyed 2008 bike sharing users found that 89 percent of users said the program made it easier to travel through the city
9 (Vélib’, 2012). 59% of Nice Ride Minnesota bikesharing users said that the convenience of bikesharing is what they care most in the programe (SurveyGizmo, 2010). In 2011, Denver
BCycle achieved a 30% increase in riders and a 97 % increase in number of rides over the previous year (Denver BCycle, 2011). These studies suggest that public bikesharing programs have a positive impact on bicycle using as a transportation mode.
The potential bikesharing benefits can be concluded as: 1) increased mobility; 2) cost savings from modal shifts; 3) low implementation and operational costs (e.g., in contrast to shuttle services); 4) reduced traffic congestion; 5) reduced fuel use; 6) increased use of public transit and alternative modes (e.g., rail, buses, taxis, carsharing, ridesharing); 7) increased health benefits; 8) greater environmental awareness; 9) economic development.
Despite obstacles remain currently, as limited supportive infrastructure (i.e., docking stations, bike lanes), numerous lost and damaged bicycles, high costs in new technologies, and new emerged problems in management and safety, we still believe that it has great future.
The ultimate goal of bike-sharing is to expand and integrate cycling into transportation systems so that it can more readily become an important part in daily transportation mode (for commuting, personal trips, and recreation).
2.3. Carsharing
Carsharing launched in Canada in 1994, and later numerous car sharing programs throughout the United States started in 1998. Individuals can gain the benefits of private vehicle use without the costs and responsibilities of ownership. Rather than owning vehicles, a household or business accesses a fleet of shared vehicles as needed. According to operational mode, Carsharing services can be divided into two categories: B2C (Business to
Customer) Carsharing and P2P (Peer to Peer) Carsharing.
10 B2C Carsharing Service models can include roundtrip carsharing (vehicle returned to its origin), oneway stationed-based carsharing (vehicle returned to different designated carsharing location), and one-way free-floating (vehicle returned anywhere within service areas).
Roundtrip carsharing, the earliest carsharing service model, allows members access to shared vehicles at a specific location，which means users must return vehicles to the same location from where they were picked up. One-way carsharing (point-to-point carsharing) allows members to pick up a vehicle at one location and drop it off at another. Ideas for one- way, open-end car sharing service date back to the 1990s. One-way carsharing experienced a rapid worldwide expansion during 2012, operating in seven countries, especially the U.S. and
Canada (Shaheen and Cohen, 2012). Compared to roundtrip carsharing, one-way carsharing can allow increased flexibility and has the potential to further enhance last-mile connectivity.
For a long time, carsharing has been primarily set up as a station-based (SBcs) service.
Recently, free-floating carsharing (FFcs) have seen a significant rise in popularity since the introduction of car2go (2008) and Drive-Now (2011). Usually, this system uses GPS technology to track the location of each vehicle. Since that vehicles could be picked up or dropped off anywhere within the operating area and driven outside of the area in rental period is also allowed. FFcs services allow greater flexibility than traditional SBcs service, as the users do not need to return the vehicle to certain points. This flexibility is the key point leading to the huge growth of the services, along with a worldwide focus on increased sustainability of transport systems and variety of travel options.
Peer-to-peer (P2P) carsharing or Personal vehicle sharing (PVS) is another carsharing service model characterized by short-term access to privately-owned vehicles. PVS companies provide the organizational resources needed, such as an online platform, customer support, automobile insurance, and vehicle technology, to make the transactions among car
11 owners and renters possible. To enable unattended access, members access vehicles through a direct key transfer from the owner to the renter or through operator-installed in-vehicle technology.
Numerous studies have documented that carsharing that carsharing reduces the number of vehicles on the road, Vehicle Miles Traveled (VMT), Greenhouse Gas (GHG) emissions, and transportation costs for individuals. A study of City Car Share members found that 30% of members largely reduced their own personal cars usage, and two-thirds chose to postpone the purchase of vehicles after 2 years’ usage of the service (Cervero and Tsai, 2004). An aggregate-level study in the US and Canada documented these impacts 25 percent of members sold a vehicle due to carsharing, and another 25 percent postponed purchasing a vehicle. According to that, one carsharing vehicle can replace 9 to 13 private vehicles among carsharing members. It also documented reductions in VMT (Vehicle Miles Travelled, 27 to
43 percent decline) and in GHG emissions (Greenhouse Gas, 34 to 41 percent decline or an average reduction of 0.58 to 0.84 metric ton/household) (Martin and Shaheen, 2011). Another notable impact of carsharing is modal shift. Martin and Shaheen (2011) studied the impact of carsharing on public transit and non-motorized travel. While a slight overall decline in public transit use, a significant increase in alternative modes, such as walking, bicycling, and carpooling (Table 1) were observed. Furthermore, more studies found that carsharing can reduce transportation costs. It was reported that carsharing saved an average of $154 to $435 per month per carsharing household compared to their private vehicle-use expenses in North
America. (Shaheen et al., 2012a)
12 Table 2.1 Aggregated Shift in Public Transit and Non-Motorized Modes Due to Carsharing Use. Taken from: Martin and Shaheen (2010)
AVERAGE HOURS PER WEEK BY SURVEY RESPONDENTS ROUND TRIPS PER WEEK BY SURVEY RESPONDENTS MODE Wilcoxon Sign No Wilcoxon Sign Decreased No Change Increased Decreased Increased Rank Test Change Rank Test RAIL 589 (9%) 5198 494 (8%) 0.001946a 571 (9%) 5226 484 (8%) 0.007395a
BUS 828 (13%) 4721 732 (12%) 0.007537 a 783 (12%) 4794 704 (11%) 0.02025 b
WALK 568 (9%) 4957 756 (12%) 1.19 × 10-7 c 559 (9%) 5046 676 (11%) 4.35 × 10-4 c
BIKE 235 (4%) 5418 628 (10%) <2.20 × 10-16 c 219 (3%) 5480 582 (9%) <2.20 × 10-16 c
CARPOOL 99 (2%) 5893 289 (5%) <2.20 × 10-16 c 86 (1%) 5932 263 (4%) <2.20 × 10-16 c FERRY 13 (0%) 6262 6 (0%) 0.05415 14 (0%) 6259 8 (0%) 0.1004
a. One-tailed Wilcoxon Signed Rank Test, Decline Statistically Significant at 99%; b. One-tailed Wilcoxon Signed Rank Test, Decline Statistically
Significant at 95%; c. One-tailed Wilcoxon Signed Rank Test, Increase Statistically Significant at 99%.
Overall, carsharing leads to a reduction in vehicle ownership, GHG emissions and parking needs. In addition, it increases mobility for those that could not access a vehicle before, reduces household transportation costs, and increases modal share of transit and active modes such as cycling and walking.
2.4. Other forms of Sharing
2.4.1. On-demand Ride Service
On-demand rides, including ridesourcing, ridesplitting, and e-Hail services for taxis, have experienced significant growth over the past few years, but they face an uncertain situation in regulatory and policy.
Ridesourcing companies or TNCs (transportation network companies) provide prearranged and on-demand transportation services by using smartphone apps to connect community drivers who have personal vehicles with passengers. With only a smartphone app, booking, ratings (for both drivers and passengers), electronic payment and other functions make ridesourcing convenient.
Ridesourcing also includes “ridesplitting,” which involves splitting a ridesourcing/TNC- provided ride with someone else taking a similar route. Service providers (such as, Lyft, Uber,
Didi) match riders with similar OD (origins and destinations) together, and they split the ride
13 and the cost. These shared services allow for dynamic routes changes in real time as passengers request pickups.
With the rising in ridesourcing/TNCs, the taxi industry has also been modernizing. Taxis can now be reserved by an “e-Hail” Internet or mobile application maintained either by the taxi company or a third-party provider. There has been a dramatic increase in taxi use of e-
Hail services,
Since ridesourcing/TNCs and e-Hail solutions are relatively new service models, few studies document their travel behaviour impacts. Rayle et al. (2014) conducted an early exploratory study of 380 ridesourcing/TNC users in San Francisco, California. 92% of user would still have made these trips if on-demand Ride Service were not available, which means that only 8% of people were impacted on travel demand. Besides, only 4% named transit station as O/D, suggesting use ridesourcing to access transit. However, 40% of ridesourcing/TNC users who owned a car stated that they had reduced their driving due to the service. To sum up, on demand service would not reduce travel demand or promote the use of transit, but replace some parts of private cars usage with ridesourcing.
2.4.2. Ridersharing
Ridesharing, including vanpooling and carpooling, provide the shared rides between drivers and passengers with similar origin-destination pairings. Vanpooling is classified as a grouping of seven to 15 persons commuting together in one van, whereas carpooling involves groups smaller than seven traveling together in one car. Ridesharing has several categories: 1) acquaintance-based, 2) organization-based, and 3) ad hoc. Acquaintance-based ridesharing are consist of a group of people that everyone knows each other before. Organization-based carpools require participants to join the service through membership or by visiting the site. Ad hoc ridesharing involves more unique forms of ridesharing, including casual carpooling
(Chan and Shaheen, 2012).
14 Carpooling and vanpooling have the added benefit of reducing driver costs as well as
VMT and GHG reduction. A vanpool could cost between $100 and $300 per person per month, although this varies considerably depending on gas prices, local market conditions, and government subsidies. For flexible carpoolers, it can save two-thirds the cost of commuting compare to the one by a single-occupancy vehicle (Dorinson et al., 2009). Besides, the report CTP 2040 points out that if by 2040 there is a five percent increase in the adoption rates of carpooling, there would be a 2.9 percent reduction in VMT in California. (Caltrans,
2015)
2.4.3. Alternative Transit
Alternative transit services existed in parallel to established public transit networks and target special populations. Many alternative transit services can include fixed route or flexible route services, as well as fixed schedules or on-demand service. Some shuttles service, generally subsidized by transportation demand management agencies or employers, can be free or low cost for user. Other services, such as microtransit, are paid in full by users.
Shuttles are shared vehicles that can connect passengers to public transit stations or to workplace. They can also act as replacement services for public transit lines that are undergoing adjustment or maintenance, which focus on solving the “first and last mile” problem, and ferrying people to/from suburban residences or workplace from/to public transit stations. One example of a shuttle service is a distributer/circulator service, which can connect to core areas in urban city that are relatively close but too far away from walking distance. Due to the subsidy of government or employers, these services can be free or low cost for the user.
Compared to shuttles, microtransit is a privately owned and operated shared transportation system that can have fixed routes and schedules, as well as flexible routes and on-demand scheduling. Microtransit operators target commuters, primarily connecting
15 residential areas with downtown job centers. The use of advanced technology, like using smartphone to avoid traditional and costly methods of booking rides, has the potential to lower operating costs for services that target special populations, such as disabled, older adults, and low-income groups.
It was found that alternative transit service can not only save time and cost for commuters, but also contribute to a job-housing imbalance by enabling commuters to live farther from their workplace. Additionally, private employer shuttles may divert ridership from public transportation (Dai and Weizimmer,2014). Besides, A 2011 San Francisco
County Transportation Authority (SFCTA) survey found that 63 percent of shuttle passengers would choose to drive alone, if the these services were not provided. Moreover, these shuttles produce only 20 percent of the emissions that would have been emitted by the vehicles they take off the road (SFCTA, 2011). To sum up, alternative transit can save time and cost for users, especially commuters, reduce the usage of transit and private cars at same time and contribute to job-housing imbalance and GHG emissions reduction.
2.5. Summary
Shared mobility is an innovative transportation strategy that enables users to gain short- term access to transportation modes on an as-needed basis for passenger trips. The advent of carsharing, bikesharing, ridesourcing/TNCs, and other innovative mobility services is changing how urban travelers, in particular, access transportation. In the future, these options could spread more to suburban and rural locations, particularly with the arrival of connected and automated vehicle technology. Numerous studies of shared mobility have documented a number of environmental, social, and transportation-related impacts, such as the reduction of vehicle use, ownership, and vehicle miles travelled. Cost savings and convenience are frequently cited as popular reasons for shifting to a shared mode.
16
Figure 2.1 Overview of Shared mobility
Additionally, shared mobility could extend the catchment area of public transit, potentially playing a key role in bridging gaps in existing transportation networks and encouraging multi-modality by addressing first-and-last mile issues relating to public transit access. Finally, shared mobility could provide economic benefits, such as increased economic activity near multimodal hubs and cost savings to users. Since these benefits, the shared mobility service is accepted by the public and under the rapid development. While shared mobility holds promise for addressing a number of social and environmental goals, it is important to note that challenges remain in mainstreaming services and ensuring public safety, adequate insurance in the shared service model. More studies, particularly shared mobility
17 strategies, are needed. To do that, we need more understanding on user behavior and demand features of shared mobility service, which motivates us to do this research.
18 CHAPTER 3. LITERATU REREVIEW
3.1. Introduction
In this chapter, a number of literature relating to user adoption was reviewed and discussed. The following Section 3.2, contains and overview of demand analytics of shared mobility, including describing the demand trend and forecasting the future demand. Then in
Section 3.3, we briefly introduce development of diffusion models, and then make a comparison. Moreover, the Bass Model，related to our research in Chapter 4， regarding its advantage and drawbacks is highlighted and discussed. Section 3.4 will focus on methodologies for modelling behaviour changes. Different from traditional methods, the focus is on stochastic process models. We also introduce some concepts, like life-cycle, ability and “willingness” related to the subsequent research in Chapter 5. Finally, the literature is summarized.
3.2. Demand Modelling for New schemes
A larger body of literature related to demand analytics of shared mobility service can be can be found. Broadly, these studies can be classified into two categories, based on their research contents: 1) the factors of demand 2) estimation and forecasting for demand.
3.2.1. Factors for demand analysis in shared mobility
Factors for adoption and potential demand
One of the most productive streams of research on shared mobility service has been the study of the characteristics of its users. Most works report on the mean value of population characteristics using a sample of members. Existing shared mobility users appear to be younger and more educated (Burkhardt and Millard-Ball, 2006; Zheng et al,2009; Efthymiou et al., 2013). Shaheen and Schwartz (2004) found that users were often students and belong to
19 low income households. Besides, some studies suggest that members are more environmentally conscious (Costain et al.,2012; Clewlow,2016; Zheng et al,2009). Coll et al.
(2014) summarized that the socio-economic profiles, education, income, family structure, and nonmotorized mode use, are strong predictors of shared mobility membership.
Recent several studies focus on evolution with the adoption of shared mobility service by introducing the Rogers' technology diffusion theory. Several key factors influencing early adoption are analysed. Shaheen (1999) conducted a longitudinal survey of individuals interested in joining a carsharing program and found that sociodemographic (e.g., age, gender, income, auto ownership) and psychographic characteristics (i.e. attitudes toward current modes, vehicles, congestion, environment, and experimentation) influence an individual’s decision to participate. Meijkamp (2000) categorized the possible determinants of carsharing adoption as 1) personal attributes (e.g., car ownership, auto use frequency); 2) service oriented (e.g., carsharing availability near home); 3) context oriented (e.g., rising vehicle costs, fuel price). Zheng et al. (2009) studied the potential carsharing market at the University of Wisconsin, Madison performing a stated-preference survey about transportation habits and carsharing preferences, namely travel habits (primary mode of travel and trip purpose), attitudes on transportation and the environment, and familiarity with carsharing, in the university community. To sum up, identified common factors to behavioural adoption can be categorized into three aspects: demographics, attitudes, and innovation perception.
Factors for Usage
Prior research has identified a variety of determinants2 for the usage of shared mobility systems. Stillwater et al. (2008) compared the use of carsharing vehicles over a period of 16 months with the built environment and demographic factors for an urban US carsharing operator. They concluded that the most significant variables were: street width, the provision of a railway service, the percentage of drive-alone commuters, the percentage of households
20 with one vehicle, and the average age of the stations. Lorimier and El-Geneidy (2011) studied the factors affecting vehicle usage and availability in the carsharing stations from
“Communauto” in Montreal. They found that larger stations offered more vehicle options and had a larger catchment basin than smaller stations. Moreover, the showed the seasonal impacts of both availability and usage with more usage in summer. Vehicle age was also considered as a key factor. “old” vehicles decreased usage since members tend to prefer newer vehicles. Morency et al. (2011) also analysed the carsharing transaction dataset of the
Communauto and found huge difference of distance travelled, and trip frequency between weekday and weekends. Faghih-Imani et al. (2014) examined the influence of meteorological data, temporal characteristics, bicycle infrastructure, land use and built environment attributes on arrival and departure flows at the station level using a multilevel approach to statistical model. Zhang et al. (2016) explore the impact of the expansion of a bicycle-sharing system on the usage of the system in Zhanghzou (China) and concluded that expanding the system not only extends the original users usage in new areas but also attracts new users to the service.
The most common factors considered in the literature are (Faghih-Imani et al. 2017,
FaghihImani and Eluru 2016. Caulfield et al. 2017, Wagner et al 2014, Zhang et al. 2016):
1.Temporal factors (season, month, day of week, working day / holiday, time of day)
2.Meteorological factors (weather, temperature, relative humidity, wind speed, etc)
3.Socio-demographic factors (social norms, service costs, costs of alternatives, safety, media, etc)
4. Physical Infrastructure (Urban form, Road, Parking space, Vehicles, Operating area,
System infrastructure)
5. Individual characteristics (Gender, age, income, Employment status, Household structure, Car ownership, Level of education, Attitudes, Environmental beliefs, Habits)
6. Development of system (extension of stations and service areas)
21 3.2.2. Demand modelling for estimation and forecasting
Measure the performance of system
New technological improvements have resulted in fast and widespread adoption of some shared mobility services meaning that the evaluation of the effectiveness of different shared mobility systems becomes important. A few broader studies have been carried out by making quantitative evaluations of a selection of BSS based on system size, connectivity, shape, flows and temporality of concurrent vehicle use as well as trips per day per vehicle (Fishman, 2015; O’Brien et al., 2014; Parkes et al., 2013; Fishman et al.,
2013; Zaltz, Austwick et al., 2013). The difficulty in obtaining data and infrequency of publicly published equivalent metrics are the main causes making the comparison difficult. Therefore Chardon and Caruso (2015) and Chardon et al. (2017) propose metrics to measure the quality and performance of a shared mobility system only based on publicly available data without using daily trip data.
Demand Estimation
Other research focused on describing demand development only. Ciari et al. (2013), recognizing these special characteristics of carsharing systems, applied an activity-based microsimulation approach (MATsim) to estimate more accurately the demand for carsharing systems, taking into consideration all transport modes, such as public transport, car, bicycle, walking and carsharing, and the characteristics of each traveller. The same authors later evolved their model to consider station-based and free-floating carsharing in both their demand and supply side (Ciari, Bock, & Balmer, 2014). Morency et al. (2012) took a two- stage approach to study the behaviour of carsharing users. In the first stage, the probability of each member being active in a given month was studied using a binary probit model. In the second stage, the probability of an active member using the service multiple times per month
(monthly frequency of use) was determined by a random utility-based model. Parikh and
22 Ukkusuri (2014) proposed a model to predict the demand at each station of the Antwerpen
(Belgium) system. For their approach, they used a Markov process to determine the demand, in combination with a mixed-integer program (MIP) to balance the number of bikes. Martínez et al (2017) proposed a detailed agent-based model that was developed to simulate one-way carsharing systems with the perspective both of the operators and users. The simulation incorporates a stochastic demand model discretized in time and space and a detailed environment characterization with realistic travel times.
Demand Forecasting
Shared mobility service companies have the collective goal of meeting the needs of the final customer, by providing service at the right place, time and price (Helms, Ettkin, and
Chapman 2000). Accurate and effective forecasting of future demand is essential for making supply chain decisions. Yet, the complexity and uncertainty existing around demand makes forecasting a challenge. As reviewed above, demand is influenced by a variety of factors, understanding relationships between these factors and demand would enable companies to improve the forecasts. It is interesting to note that, papers focused on predicting future demand almost always rely on non-parametric statistical methods, like neural networks (Cheu et al. 2006), gradient boosted machines (Regue and Recker,2014), non-homogeneous Poisson process (Alvarez-Valdes et al.,2016) or Markov Models (Lee, Wang, and Wong, 2014).
3.2.3. Comparison
It is interesting that most works which mainly focus on demand factors, use linear regression model, while the majority of research on demand estimation based on combined simulation model, such as Agent-Based Model with Decision Choice Model, Probit Model with Utility Model and Microsimulation with Activity-Based approach. Besides, papers
23 focused on predicting future demand almost always rely on non-parametric statistical methods, like Neural Networks, Gradient Boosted Machines, Decision forest, etc.
Among all the research axes cited, there is widespread interest in understanding the role, use, impacts and adoption of shared mobility services, but very limited knowledge about the temporal evolution of the system and users with the rapid development of system, such as facility extension. Besides, existing studies have tried to characterize travel behaviour are almost always based on surveys of users due to a lack of accurate trip datasets over long periods and suitable methods for new transport system. This is the reason why in this research a new approach with a different methodology to have a better understanding on adoption and demand dynamics under the temporal and spatial angle is developed.
3.3. Adoption and Diffusion for New Schemes
Adoption occurs in at least two stages. Initially a population might be sceptical or not aware of the system. The first adoption will then be to accept the system and register to participate. A second adoption will be to gradually use the system more until one possibly relies on its existence. Here to forecast first adoption towards new technologies and transport service/system a range of methodologies focusing on different aspects are introduced. In this section we aim to group and review the main approaches and aim to position our approach within this set of literature.
3.3.1. Two extremes: Econometric (Macro) versus ABM models (Micro)
Econometric time series analysis has been applied extensively for demand forecasting at a macroscopic, aggregate level. For example, Li et al. (2015) focused on defining variables that influence ridership during the first years of Taiwan’s high speed rail system by using monthly ridership data. Seasonal autoregressive and moving average models were used to
24 explore the influence of socio-economic variables. The results showed that considering the seasonal effects can significantly improve the model when forecasting the potential demand at specific regular short-time intervals (less than one year, such as monthly, or quarterly). A weakness of econometric time series models is though that market saturation levels and system capacities cannot be explicitly modelled.
In contrast to econometric time series analysis, agent-based modelling (ABM) and simulation methods have become more popular in forecasting the adopters or market shares of new technologies since they operate at the individual level and can capture (and explain) complex emergent phenomena relevant in the diffusion research. Consumers’ heterogeneity, social interactions, decision making processes and effectiveness of strategies, such as advertisement, promotional strategies can be modelled explicitly.
Examples for research that use ABM to model adaptation to new transport systems are
Plötz et al (2014) who capture heterogeneity among decision-makers in the diffusion process of electric vehicles by using real-world driving data (Plötz et al, 2014) and Gnann et al (2015) who forecast market penetration of plug-in electric vehicles (PEVs) in Germany. Further examples for ABM approaches dealing with adaption to new systems and integrated with discrete choice modelling of the agents can be found in Eppstein et al. (2011); Zhang et al.
(2011) and Brown (2013).
ABMs often focus on how macro dynamics emerge from the individual decisions of many individuals and how the resulting macro dynamics feedback to individual decision- making (Kiesling et al., 2012). Given that ABMs are “much more concerned with theoretical development and explanation than with prediction” (Gilbert 1997), it is not surprising that the majority of contributions aim to obtain theoretical insights about diffusion processes on a highly abstract level. Recently, attempts are made to demonstrate their potential as a practical tool for tackling real-world problems, such as providing forecasts, decision support, and
25 policy analyses for specific applications based on empirical data. However, estimation of parameters remains a main obstacle for most applications. For example, in the research of
Gnann et al.(2015) a very large number of input parameters were needed from different data sources such as future price estimates of batteries, gasoline, diesel and electricity. Further, parameters regarding user driving profiles were estimated from two different data sets (one
GPS tracked and one from panel surveys) raising questions of consistency.
We conclude that aggregate econometric models can reflect diffusion but not explain it.
In contrast, in ABM one can specify complex utility functions to explain behaviour including influence of others, or market penetration of a product, but fitting such parameters is difficult and reliability of forecasts might be limited. To explain and calibrate the adoption process, specific diffusion models that have been used extensively in marketing literature may therefore be seen as a bridge between these two.
3.3.2. Mathematical modelling of innovation diffusion
Diffusion of innovation theory emerged in the 1960s has attracted strong academic interest in different disciplines. In particular, the model developed by Bass (1969), which characterizes the diffusion of an innovation as a contagious process initiated by mass communication and propelled by word-of-mouth, is widely cited and applied in researches.
Different to ABMs, mathematical modelling of innovation diffusion aims to describe the adoption process through mathematical function rather than simulation. Aggregate diffusion models are approaches based on formulations of differential equations to specify the flows between mutually exclusive and collectively exhaustive subgroups, e.g. adopters and non-adopters (Chatterjee and Eliashberg, 1990).
The basic diffusion theory is simple and intuitive. Diffusion is defined as the process by which an innovation is communicated through certain channels over time among members of a social system. Innovations diffuse into society following a logistic growth curve. Early
26 demand for an innovation motivates additional future demand (Mansfield, 1961). Rogers
(1962) defines the following five classes of adopters that influence the uptake of a certain technology across various disciplines: innovators, early adopters, early majority, late majority and laggards. Following Rogers’ theory, Bass (1969) divided adopters into two distinct groups: innovators and imitators with the latter comprising the remaining four classes of adopters listed above. The technology diffusion literature stresses the importance of the role of those two different types of adopters in shaping the market penetration rate of a new product or service. Innovators are individuals who “decide to adopt an innovation independently of the decisions of other individuals in a social system” while imitators are adopters that “are influenced in the timing of adoption by the pressures of the social system”
(Higgins, 2012). Bass formulates the probability that consumers will make an initial purchase at a given time t as 푃(푡) in below equation as a linear function of the number of previous buyers:
푓(푡) = 푃(푡) = 푝 + 푞 ∙ 퐹(푡) (3-1) 1−퐹(푡)
with p as the coef ficient of innovation; q as the coef ficient of imitation; 푓(푡) the likelihood of purchase at t and 퐹(푡) as the cumulative proportion of adopters by time t. p reflects the percentage of adopters that are innovators while q reflects the effect on imitators with an increase in the number of previous adopters. We note that earlier Mansfield (1961) formulated the cumulative sales of a good/service by using a logistic model which can be seen as a special case of the Bass model (p = 0).
Enhancements to aggregate diffusion models have been proposed by Robinson and
Lakhani (1975), Thompson and Teng (1984) and Kamakura and Balasubramanian (1988).
Specifically noteworthy is the Generalised Bass Model (GBM) by Bass, Krishnan and Jain
27 (1994) who incorporated the effects of price, advertising and other marketing variables into the model parametrization. The formulation of the GBM is shown in the following:
푓(푡) = (푝 + 푞 ∙ 퐹(푡)) ∙ 푥(푡) (3-2) 1−퐹(푡)
∂P(푡) 휕퐴(푡) 푥(푡) = 1 + β + β max(0, ) (3-3) 1 ∂t 2 휕푡
where 푥(푡) is current marketing effort factor,퐴(푡) is advertising expenditure at time t,푃(푡) is a price index at time t, and훽1 and 훽2 are interpreted as measuring the effect of price and advertising.
Due to the rapid development of technologies, successive generations of a technology compete with earlier ones, and that behaviour is the subject of models of technological substitution. Building upon the Bass diffusion model, Norton and Bass (1987) extended the model by including both diffusion and substitution and provide therefore a basis for assessing and forecasting the influence of recent technologies on earlier ones.
3.3.3. Individual heterogeneity
Different from aggregate diffusion models, disaggregate models of adoption consider the individual heterogeneity and formulate the probability that an individual adopts an innovation as a function of the characteristics of the decision-maker, attributes of the alternative, communication channels in the temporal dimension of the diffusion process.
To explain the observed S-shape curve in adoption, Rogers (1962) and Russel (1980) developed different models around the hypothesis of population heterogeneity. Rogers (1962) thought that individuals have different thresholds for adoption and the thresholds are normally distributed. Individuals for which the value of the innovation is larger than their threshold will choose to adopt it. Therefore, “innovators” are those with low thresholds and will be the first adopting. As innovation becomes widely adopted, social pressure raises the utility of the new product and more and more people will choose to adopt. On the other hand, Russell (1980)
28 proposed that income heterogeneity and product price explains to a large degree different adoption thresholds. When the price of the innovation falls to below thresholds, adoption will be triggered. Later, advanced threshold models were incorporated with dynamic optimization, such that a decision-maker is making a trade-off between the expected decrease in price in the future and the current benefits from adoption (McWilliams and Zilberman, 1996).
One of the first micro models of innovation diffusion was introduced by Chatterjee and
Eliashberg (1990), who proposed an analytic method to aggregate individual-level behaviour based on specific heterogeneity assumptions. A closed formulation of an interface between individual and aggregate level behaviour to link the decision making and aggregate dynamics was proposed.
Above contributions focused on using revealed preference (RP) data to estimate parameters that describe adoption and using these to forecast future adoption. The models have obviously limited power to forecasting the demand for new products or transportation innovations that do not yet exist. One way to overcome this problem is by designing SP experiments to measure consumers’ preferences over hypothetical alternatives including new products/service. Some studies assessed the sensitivities to attributes of the new technology
(Hidrue et al., 2011; Ito et al.,2013) while others focused on estimation and forecasting the market share under certain scenarios (Mabit and Fosgerau, 2011; Glerum et al., 2013).
Problems of SP approaches on the other hand are that consumers may react differently to hypothetical experiments than they would if facing the same alternatives in a real market.
Furthermore adoption and diffusion of a new technology is a temporal and social process which is difficult to capture with SP surveys. Considering these points integrated approaches are a more promising approach. Brownstone et al. (2000) showed that RP data appear to be critical for obtaining realistic choice and scaling information, and SP data are important for obtaining information about attributes not available in the marketplace by using joint RP/SP
29 models. Jensen (2016) established a model that combines advanced choice models with a diffusion model to take social influence into account in forecasting the potential market for electric vehicles.
3.3.4. Space heterogeneity
Most research focuses on the heterogeneity of individuals while the geographical location of potential adopters, heterogeneity of space, has received comparatively less attention. In a theoretical analysis, Goldenberg (2000) examines innovation diffusion by
“percolation theory”, which describes the heterogeneity of the population in a spatial context, and precisely defines the micro-structure of the population. In an empirical study, Baptista
(2000) found that there were significant regional effects on the rate of diffusion by examining the diffusion of numerically controlled machines and microprocessors in the regions of the
UK.
We propose that especially to model usage adoption for transportation systems, differences in service levels across space can not be ignored. El Zarwi (2017) tried to take this into consideration by quantifying the spatial impact of the new transport service in discrete mixture models. This approach therefore combines an explanation of individual and spatial heterogeneity. It might have some disadvantages though if aiming to explain the effect of facility extensions. Further, we will not follow this approach in this thesis due to a lack of user attributes for all three datasets that will be used. Instead we will follow a more aggregate approach.
3.3.5. Time Granularity
We finally note the importance of how large time intervals are used in adoption models.
Annual data was used in the majority of empirical, aggregate studies. However, in many practical situations, annual data are not sufficient and system operators want to have
30 predictions for shorter time intervals. Not surprisingly, diffusion models with shorter than annual data intervals generally outperform those with only longer data intervals (Putsis, 1996).
Short term prediction, in particular in collaboration with modelling spatial heterogeneity, raises though also new challenges.
Using quarterly or monthly data creates the issue of dealing with seasonal effects that are important for many transport systems. Putsis (1996) estimates the adoption of five consumer products by using annual, quarterly, and monthly data. Since the inherent seasonal nature of quarterly and monthly data, in his work such data series was seasonally adjusted using the moving average method before estimation. However, he concluded that monthly models have no advantage over diffusion models on quarterly level for his example.
One possible explanation is the time lag between the consumers being exposed to information and their response to this, which is not explicitly considered in diffusion models.
In the Bass model, for example, adoption at time t is a time-independent function of current cumulative adopters. For annual, and possibly seasonal data, the time lag between information spread and decision making might be insignificant compare to time granularity of data, but possibly not shorter time intervals.
3.3.6. Comparison and Summary
We summarized the discussed of innovation diffusion methodologies with its advantages and drawbacks in Table 3.1, as we will later continue this discussion of methods in Chapter 4 and to propose, what we believe, a new approach for diffusion model with short time- intervals.
31 Table 3.1 Innovation Diffusion Models/Methods
Disaggregate Diffusion Method Aggregate Diffusion Model Econometric Time series model Simulation Model Model
Repeated changes in Temporal Attributes of the system Socio-economic Effect Dimension psychological factors Factors Socio-economic Factors effect of social Socio-economic factors Spatial or network Effect interactions and media
Level System Level System Level Individual Level Individual Level
revealed preference (RP) time series data revealed preference Data revealed preference time revealed preference time series detailed individual (RP) time series data required series data data information individual information SP surveys
Easy to understand and repeated changes in Temporal better behavior Advantage account for more factors calculate Dimension interpretation
Disadvanta Poor interpretability and Huge and Detailed account for less variables Difficult in Calibration ge forecasting Individual Information
3.4. Data Analysis Methods on User behavior change
Several discrete-time panel analysis methods, such as Markovian models, the logistic model, structural equations models have been applied in dynamic travel behavior analysis of panel data (Kitamura, 1990). Logistic models and structural equations models are both powerful tools in dealing with the panel data. These methods can be used to explain how behavior is affected by different variables.
3.4.1. Stochastic Process Modelling
Markov chain models, instead are concerned with describing the stochastic evolution of the process. In a Markovian process, the behaviour at any given time point can be expressed by a set of discrete states and the behavioural process evolves as transitions are made from one state to another state over time.
32 Markov-Chain Model
A significant body of literature related to transportation demand forecasting has addressed different applications of Markov models and general stochastic process modelling, particularly focusing on day-to-day dynamics (Cantarella and Cascetta, 1995; Watling, 1996).
Most of this literature addresses under what circumstances (multiple) equilibria occur, as well as the supply and demand interaction dynamics. In contrast in the work presented here we focus on estimation of the transition matrix parameters of such a stochastic process.
More generally, Markov models have found wide application in the social sciences, especially in the study of data that record life history events for individuals. Methods for the analysis of panel data under a Markov model have been discussed by Bartholomew (1982) and Singer (1981). In those studies, methods are developed to infer the parameters of a
Markov process based on a matrix of transition probabilities between states, estimated on data from discrete time points.
Markov models have though also some important limitations as discussed in Kalbfleisch and Lawless (1985). They are unable to handle unequally spread observation times, do not produce standard errors tests and cannot handle covariance analysis. Kalbfleisch and
Lawless’s (1985) main contribution are the introduction of algorithms for maximum likelihood estimation for parameters of the models that will be also applied in this research.
Partially following these issues and applied to panel data analysis this means that a) Markov models only offer the transition results, but do not give detailed explanations for these transitions, b) the time-homogeneity assumptions in Markov models can lead to substantial errors as this is rarely the case in reality and c) the assumption of a constant population is often not realistic.
33 Hidden Markov Models
Markov chain is useful when we need to compute a probability for sequences of events that we can observe. However, in many cases the events we are interested in may not be directly observable. Hidden Markov Model (HMM) allows us to talk about both observed events and hidden events that we think of as causal factors in our probabilistic model. In simpler Markov models (like a Markov chain), the state is directly visible to the observer, and therefore the state transition probabilities are the only parameters, while in the hidden Markov model, the state is not directly visible, but the output (in the form of data or "token" in the following), dependent on the state, is visible.
Since that Hidden Markov Model is becoming one of the most important machine learning models It has been widely used in the pattern recognition and image processing area, such as image segmentation, handwritten word recognition, or even gesture recognition. It also used for a range of applications in the transport literature. It have been used to describe and evaluate traffic flows in the network (Zhu et al, 2016), to characterize activity sequences and impute trip purposes (Liu et al, 2015; Han and Sohn, 2016), to detect driving fatigue
(Rashwan, 2013) as well as to model driving behaviour (Zou et al, 2006; Tang et al, 2015).
3.4.2. Marketing concepts adapted in this research
Lifecycle Concepts
Dealing with the second and third issues is topic of this paper. We aim to consider that for transport applications there are “new users” entering into the system and “old users” dropping out. In order to do so we draw from concepts in the marketing literature where ideas such as “customer life cycle” and “ability and willingness to purchase” are well established
(George, 1968; Jap and Ganesan, 2000).
Life-cycle is a very broad concept, used in fields such as politics, economy, environment, technology and society. Its basic meaning can be popularly understood as "from
34 cradle to grave" of the entire process. The customer lifecycle describes key milestones that every customer goes through over the course of the relationship with a brand. Customers sign up, they make their first purchase and some turn into repeated buyers; eventually some customers stop purchasing the product. Usually, five stages can be distinguished according to
Jap and Ganesan (2000) which we suggest can apply similarly to understanding the behavior of a population exploring new transport options:
1. Exploration stage: A person has become aware of the new product/ transport system and does the first purchase/ gives the new transport system a try.
2. Build-up stage: The customer/ traveler is increasingly familiar with the product/transport system and would like to enhance purchase/travel frequency.
3. Maturity stage: The purchase/ travel frequency remains fairly constant.
4. Decline stage: Purchase/travel frequency reduces over time as another product/transport service starts to become a better option.
5. Deterioration stage: The customer/ traveler stops using the product/service and is unlikely to return.
Ability and Willingness Concepts
Another general (marketing) concept that we suggest is worth adapting to our analysis is a consumer’s/ traveler’s ability and willingness to purchase a product/use a transport service.
Product purchase likelihood is a function of both (financial) ability to buy and willingness to buy (George, 1968). Ability to buy is represented primarily by the income but also for example access to a store and prerequisites. In the transport case we slightly modify this concept by considering the general potential demand as “ability”. That is, only persons with some base demand that might be satisfiable with the new transport scheme of interest have an ability to use it. We therefore refer to potential demand of a user to describe the total
(maximum) demand that could be satisfied by the new transport system. In our case study it
35 denotes for example the maximum number of trips that a user might make during a specific time period. This maximum or potential demand will be influenced by a range of external factors such as e.g. in the case of students using an on-campus shared bicycle scheme, whether it is term time or not.
In contrast willingness to buy depends primarily on attitudes and expectations of an individual. That is, a person might have the financial resources and access to purchase and use a product but is not willing to buy it unless the price has dropped or is not willing to use it more than a certain level. Applied to transport, we define accordingly willingness to use to describe the eagerness of a person to actually use the new transport mode given a potential demand. More specifically in our case study it means that a person might have to make several trips on campus (potential demand) but is only interested or “willing” to use the new mode for a certain fraction of these trips. Over time, once getting to know the new scheme, the willingness to use might increase and a larger proportion of the trips will be made by the new transport scheme.
3.5. Summary
In this chapter, we first have an overview of demand analysis for shared mobility service.
It is interesting that most works which mainly on factors of demand, use linear regression model, while researches on demand estimation propose combined models, such as Agent-
Based Model with Decision Choice Model, Probit Model with Utility Model and
Microsimulation with Activity-Based approach. Besides, papers focused on predicting future demand almost always rely on non-parametric statistical methods, like Neural Networks,
Gradient Boosted Machines, Decision forest, etc. However, development of system, which is the key points for new transport system, is seldom considered in previous researches.
36 Then, we review adoption models in macro and micro level, such as Econometric time series model, agent-based model, aggregated and disaggregated innovation diffusion, and make a comparison. The adoption in short intervals and space heterogeneity are main problems we have to solve later. Moreover, we focus on the other part of our research, Data
Analysis Methods on User behaviour change. An introduce of Markov model, Hidden
Markov Model, Lifecycle Model, and concepts “potential demand and willingness” related to our proposed model is made. Detailed explanations for transitions, time heterogeneity transition and dynamic population of system are the key points in later works. In the next few chapters, we would like to propose our new models to solve the problems.
37
38 CHAPTER 4. ADOPTION AND DIFFUSION OF NEW
SERVICE
4.1. Introduction
As mention in Chapter 1, we divide our research into two parts: adoption and diffusion of new service; and behaviour dynamics. In this chapter, our objective is to develop a methodological framework to model the adoption and diffusion process by considering facility extensions (eg. new station establishment) in the development of new transportation system. Further, we aim to distinguish different adoption rates in different parts of a city. We suggest that spatially diverse adaptation rates are an important feature of many emerging transportation systems.
The core idea of our methodology is the decomposition of the total market into several smaller markets for station-based transport system/service based on their location. In Sections
4.2 to 4.5, based on the diffusion model of innovation introduced in 3.3 we offer a description of our methodological framework and details of the adoption models, including the adoption process, information diffusion model, a model aiming to identify “main stations”. After describing the base model a simplified model is described. Then in Section 4.6, a comparison between the Bass model and our adoption model shows the difference and improvement. In
Section 4.7 we utilise the least square estimation and gradient descent optimization algorithms to estimate the parameters. In Section 4.8, as an example for adaptation to a car share system, data from Toyota city are used to illustrate how well new adopters can be estimated and forecasted over time. Finally, in Section 4.9 some initial conclusions and possible future research is discussed.
4.2. Individual Adoption Process
39 Roughly in line with the aforementioned work of Rogers (1962) adoption can be considered a four stage process. (Rogers distinguishes further trial and adoption in the diffusion process, which is not of interest to our work where we focus on initial usage).
Firstly, in the knowledge stage, individuals receive some information to learn about the existence of the transportation service at time t. i.e. the information that a new station s was opened was received by person j at time t. Diffusion of information is affected by formal sources of information such as advertisement and mass media, and informal sources of information, such as word of mouth from other adopters. After receiving the information, person j will evaluate the service to decide the willingness to use it at some later time t according to the attributes such as fare, accessibility, quality of equipment, ease of use as well as his/her demand. In the following decision stage, person j will decide whether to adopt to the service or not at time t+1 according to the evaluation made during the persuasion stage. Social effects, individual preference and the evaluation will both influence their decisions. Finally, at time t+1, person j will registers to the new system/service. If one has decided against the system during the decision process one might be convinced though at a later stage and repeat the decision making process until eventual adoption.
Figure 4.1 The adoption process
40 We aim to model this adoption process, but from usage records we can not distinguish decision and implementation stage nor the knowledge and persuasion stage. We model the probability of individuals learning about the existence of new services and making evaluations at time t, in order to implement their decision at time t+1 or later. The proportion of the market that decided not to adopt can reassess their evaluation each time interval. In other words, the time lag between knowledge plus evaluation and implementation is set to one time period.
4.3. Individual adoption Classification
As mentioned before, Bass divided the market into innovators and imitators, also referred to as “followers” who are influenced in their decision-making by the proportion of those having adopted. This distinction is not fully accurate in our case due to information only dispersing gradually through the system and the system also only gradually expanding. For example, a person might adopt late, but still be called “innovative” if s/he is adopting the service as one of the first persons in his/her neighbourhood. We therefore classify the population into following three groups: Fast-adopters, Hesitant-adopters, and Non-adopters with following definitions:
Fast-Adopters quickly adapt to the new service after receiving information and/or the system becoming attractive to them. These are also often adopters who have an urgent, or currently unsatisfied travel demand that can be covered by the new service/system and are therefore glad to adopt quickly after obtaining the necessary information.
Hesitant-adopters progressively adopt to the new service. This might be because they are hesitant or because they do not immediately see the usefulness of the system or want to wait until the system has expanded to such a degree that its usefulness is higher than a certain utility threshold as introduced by Rogers (1962). We emphasize an important difference to the
41 imitators in the Bass model is that Hesitant-adopters are not necessarily influenced by others.
We assume that the average accept probability can be modelled by a constant as well as factor reflecting how many people have already updated (follower effect). The “hesitant effect” is used to model that persons might need more than one time interval to be persuaded to adopt the system. Only if this effect is ignored, the two groups can be considered the same.
Finally, in any population there will be Non-adopters, who will never adopt to the new service. This might be again for various reasons including not having any demand or interest in the new service.
4.4. Methodology
4.4.1. Information Diffusion Model
There are two main ways of information spread that might need to be distinguished in an adoption model from a modelling perspective. Firstly, spread through advertisement or mass media, and secondly “word-of-mouth” communication. The main difference is that the effect of the latter will depend on how many users have already been addressed and therefore can further spread the information. Besides, both types of information distribution can be spatially diverse. Therefore, information spread should be a time and space depending function.
To simplify the model, we assume that the probability for individuals to obtain the information in one area in one time period is a constant. We do consider though that information spread might start well before the start of the service so that a proportion of users will be informed at “time zero” when the system starts its operation. With this the information diffusion model can be formulated as follows:
푔푠(푡) = 푎푠 ∙ (1 − 퐺푠(푡 − 1)) (4-2)
퐺푠(푡) = 퐺푠(푡 − 1) + 푔푠(푡) (4-3)
표 퐺푠(푡푠 − 1) = 퐼푠 (4-4)
42 where
퐺푠(푡), 푔푠(푡): (Cumulative) percentage of market size that receive information regarding station s by/at time t
푎푠: Probability to obtain the information of station s (information diffusion speed)
퐼푠: Proportion of individuals receiving the information of station s when the station is opened.
표 푡푠 : Opening time period of station s
4.4.2. Adoption Model
With this we can establish our adoption model. Firstly, utilising the user classification introduced in Section 4.3 we obtain:
푓 ℎ 푓푠(푡) = 푓푠 (푡) + 푓푠 (푡) (4-5)
푓푠(푡): Ratio of new adopters to the total market for station s at time t.
푓 푓푠 (푡): Ratio of new fast-adopters to the total market for station s at time t.
ℎ 푓푠 (푡): Ratio of new hesitant-adopters to the total market for station s at time t.
푓 푓푠 (푡) depends on 푝푠 which denotes the ratio of leading-adopters in the population and the information spread. Besides, as explained in Section 2.1, with less than annual data we suggest that seasonal effects can not be ignored. Therefore, we introduce 훿(t) as a seasonal coefficient in our model.
푓 푓푠 (푡) = 푝푠 ∙ 푔푠(푡) ∙ 훿(t) (4-6)
For the gradual, hesitant adopters the afore discussed follower effect and continuous information spread is leading to (4-7).
표 ℎ (푞 ∙ 퐹푠(푡 − 1) + 푐) ∙ (퐺푠(푡 − 2) − 퐹푠(푡 − 1)) ∙ 훿(t) 푡 ≥ 푡푠 + 1 푓푠 = { 표 (4-7) 0 푡 ≤ 푡푠 with
43 푐: Constant “hesitation” effect, to denote the re-accept rate for hesitant-adopters
푞: Follower effect, to denote the importance of influence of others
퐹푠(푡): Cumulative proportion of adopters at time t around station s
Since we assume that it takes (at least) one time period to make a decision after obtaining information, the new hesitant-adopters in time t already obtained the information in 푡 − 2 and failed to adopt in time t-1.Therefore, we use 퐺푠(푡 − 2) and퐹푠(푡 − 1) rather than 퐹푠(푡) in the Bass model without explicit information spread.
Now we can update the cumulative proportion of those having adopted with
푝 (8) and obtain the attracted, primary users by station s, denotes by 푁푠 (푡), with
(9) where 푀푠 denotes market size or total number of potential users for station s.
퐹푠(푡) = 퐹푠(푡 − 1) + 푓푠(푡) (4-8)
푝 푁푠 (푡) = 푀푠 ∙ 푓푠(푡) (4-9)
4.4.3. Station Demand Attraction Model
Since the system attractiveness is determined by the synergy of the stations
푝 providing together a good service, we suggest that taking 푁푠 (푡) directly as a measure of how many users are attracted due to the existence of station s is not a good estimate and a redistribution or balancing model is needed.
Our reasoning is that, unless the user makes only roundtrips, he will use the new transport system in several areas of the city. This leads us to distinguish the
“primary” and “secondary” usage areas. With the former, we mean the area that mainly attracted the user to join the service, for example, observing the existence
44 of the service around his home. With the latter, we mean destinations one might visit with the new transport scheme regularly or occasionally after having joined.
In databases of user records, the two might be difficult to distinguish though, if a number of destinations are visited regularly. Furthermore, it might not necessarily be the actual frequency of trips but the improved accessibility to some destinations that convinced a user to join.
Figure 4.2 Illustration of the station attraction model
푝 We refer to the new primary users as 푁푠 (푡) and the secondary (or related)
푟 new users as 푁푠 (푡). Suppose that each new user is observed on average at a total of A stations in the initial time period when he joins the system, that is one primary, base station and A-1 secondary stations. Given this assumption, we
표 obtain following relationships where 푁푠 (푡) is the estimated total number of new users attracted, at least partially, by the existence of station s.
표 푝 푟 푁푠 (푡) = 푁푠 (푡) + 푁푠 (푡) (4-10)
45 푟 푝 ∑푠 푁푠 (푡) = (퐴 − 1) ∑푠 푁푠 (푡) (4-11)
푝 Figure 4.2 illustrates the main idea with A=3 for all users and with 푁푠 (푡)
표 equal to one for each station. The (true) number 푁푠 (푡) of persons being (partially) attracted to the system due to existence of stations S1 to S4 is 1,3,4,4. However,
푝 from the adoption model we observe only 푁푠 (푡) equal to one for each station so
푟 that we need to obtain the “correction factor” 푁푠 (푡).
For this we make following assumption. For individuals, the probability to be attracted due to a station existence has a positive correlation with the current potential market (퐺푠(푡) ∙ 푀푠 ). The rationale is that the potential market also reflects the general station attractiveness and that in general demand distributions are not random but are focused on some key points in the network.
We multiply by 퐺푠(푡) to reflect that information provision is a prerequisite for being attracted by a station.
Now the model can be formulated with (12) to (14). We assume that 퐴 is constant and obtained from a prior data analysis on the average number of stations visited by new users during their initial usage period. With this we can obtain 푁푖,푗(푡) by considering the attractiveness of station j compared to the
푝 overall attractiveness of all stations, multiplied by (퐴 − 1) ∙ 푁푖 (푡).
퐺푗(푡)∙푀푗 푝 푁푖,푗(푡) = 푆 ∙ (퐴 − 1) ∙ 푁푖 (푡) (4-12) ∑푗=1 퐺푗(푡)∙푀푗
푟 푆 퐺푗(푡)∙푀푗 푆 푝 푁푗 (푡) = ∑푖=1 푁푖,푗(푡) = (퐴 − 1) ∙ 푆 ∙ ∑푖=1 푁푖 (푡) (4-13) ∑푗=1 퐺푗(푡)∙푀푗
푝 푆 표 푁푗 (푡) 퐴−1 퐺푗(푡)∙푀푗 ∑푖=1 푁푗 (푡) 훼푗(푡) = 표 = 1 − ∙ 푆 ∙ 표 (4-14) 푁푗 (푡) 퐴 ∑푗=1 퐺푗(푡)∙푀푗 푁푗 (푡)
46 푝 With 푁푖 (푡) as before and
푁푖,푗(푡) : Number of new adopters primarily attracted by station i and secondarily by station j at time t
푟 푁푗 (푡): Number of new adopters also attracted by station j as “secondary” station at time t
훼푗(푡): Ratio of “primary” new adopters to observed new adopters at station j at time t
Figure 4.3 Relationship of attracted and observed new users in one station
Figure 4.3 illustrates the relationship between the primary and secondary attracted users in connection with the information diffusion model. In the initial time periods, 퐺푗(푡) is likely to be small, so that 훼푗(푡) will be close to 1, meaning that the red and green curves overlap.
The larger 푀푗 is larger, the smaller 훼푗(푡) in later periods when 퐺푗(푡) is close to 1. If all stations have similar potential markets훼푗(푡)will converge over time to 1/퐴.
47 4.4.4. Reduced Model
This grouping leads to a significant reduction in parameters. Furthermore, through estimation of the full model we find that within the groups some of the parameters are significantly correlated: M and a, M and p, as well as a and I have a relatively strong linear relationship (|S|>0.6, see Appendix). Without grouping none of these correlations are significant.
Therefore, to reduce the parameters further, and considering that a, p and I should be in the range of 0 to 1, we utilize a logistic function to present these relationships.
1 푎푘(푠) = 1 2 (4-14) 1+푒−훼푘(푀푠−훼푘)
1 푝푘(푠) = 3 4 (4-15) 1+푒−훼푘(푀푠−훼푘)
1 I푘(푠) = 5 6 (4-16) 1+푒−훼푘(푎푠,푘−훼푘)
1 6 Where 푘(푠) indicates the group of station s and 훼푘 to 훼푘 are the six group specific coefficients.
With these simplifications, the parameter set 휽 can be presented and divided as following:
푔 Two global parameters (system level) 휽 = [푞, 푐]; twelve time related parameters 휽풕 =
[훿1, ⋯ , 훿12] where 훿1can be fixed as reference variable; six station group parameters 휽풌 =
[훼푘1, ⋯ , 훼푘6] and n local parameters (station level) 휃푙 = [M푠] where n indicates the station numbers. The total parameter set 휽 = [휽품, 휽풕, 휽풌, 휽풍] hence consists of 37+n parameters to be estimated for the reduced model compared to 13+4n variables in the full model.
4.5. Illustration and Comparison
48 In Figure 4.4 and Figure 4.5, a comparison between ten different adoption curves created with the Bass model and our model is shown. In Table 4.1, we give the parameters of these curves.
Table 4.1 Parameters of models
Curve Model Parameters Shape index
1 푞푏=0 푞푏/푝푏=0
2 Bass Model 푞푏=0.08 푝푏=0.02 푞푏/푝푏=4
3 푞푏=0.16 푞푏/푝푏=8 4 q=0 q/c=0 5 Our Model q=0.08 c=0.02 a=0 p=0.02 I=1 δ=1 q/c=4 6 q=0.16 q/c=8
7 a=0.3 p=0.2 I=0.2 8 a=0.1 p=0.2 I=0.2 Our Model q=0.08 c=0.02 δ=1 q/c=4 9 a=0.3 p=0.1 I=0.2
10 a=0.3 p=0.2 I=0.1
Since the Bass model does not include an explicit information diffusion model nor seasonal effects, we expect that for I=1, a=0, and 훿 = 1 we can observe similar curves. We observe that this is indeed the case for 푝 = 푝푏,푞 = 푞푏,푐 = 푝푏.
The follower effects, the S-shape curve due to market saturation are further observed in both models. As shown in the figure, q/c in our model, and 푞푏/푝푏 in the Bass model will decide the shape of the adaption curve in long-term. When q/c or 푞푏/푝푏 is smaller one, there exists no peak, the new users will continue to decline (curve 1 and 4). In contrast, if the value is larger one, the curve will raise to a peak and subsequently drop (curve 2,3,5,6). The larger, the earlier and steeper the peak.
Figure 4.4 illustrates that we can obtain curves similar to the Bass curve in some condition, however, a small time lag exists between the Bass model and our model, since
“carryover effect” is considered in our model. In we furthermore illustrate the effect of gradual information diffusion in conjunction with fast adopters.
49 When 퐼 < 1, 푎 > 0, 푝 > 0, different from the Bass model, the curves can initially slowly, continuously increase (curve 9), or initially go down (curve 7), or even have a peak (curve 10) or low point (curve 8) in the initial time period. Generally, when 퐼 < 푎, an initial peak can be observed. On the contrary, when 퐼 > 푎, instead an early drop in adopters can observed (curve
8). This is reasonable since more people obtained the information before opening leads to more adopters at beginning.
0.06 Bass Model,curve 1 Bass model,curve 2 0.05 Bass Model, curve 3 Our Model,curve 4 0.04 Our model,curve 5 Our model,curve 6 0.03
0.02 Proportion of new adopters new of Proportion 0.01
0 0 5 10 15 20 25 30 35 Time period since operation
Figure 4.4 Comparison of models with focus on long-term trends
Besides, p being large means fast-adopters will take up most potential market, therefore, the curve will decline quickly at beginning. Following this, therefore a low value of p means that there are few quick adopters in the market and the number of adopters will increase progressively until it eventually declines due to market satisfaction.
Therefore, our model allows for two peaks, which we observe also in our subsequent case study and which could not be explained with the Bass model. The initial peak of subscribers might come through advertisement and currently latent demand. The second peak might occur during later time periods when the market enters saturation. Finally, we remind
50 that this section illustrates the curves on system level though we establish our model for different regions (car sharing stations in the case study) and consider the interaction of these as described in previous section.
0.045 Bass model, Curve 2 Our model, Curve 7 0.04 Our Model,Curve 8 Our model, Curve 9 Our Model, Curve 10 0.035
0.03
0.025
0.02 Proportion of adopters new
0.015
0.01 0 2 4 6 8 10 12 14 16 18 20 Time periods since operation
Figure 4.5 Comparison of models with focus on initial time periods
4.6. Parameters Estimation
We obtain the best fit model parameters by least square estimation. The formulation is shown as follows:
푆 푇 표 2 argmin J(휽) = argmin ∑푠=1 ∑푡=1(푦푠,푡 − 푁푠 (푡))) (4-15) 휃
With 푦푠,푡 as the observed new users at time t in station s and 휽 as the parameters set we want to estimate.To do so we make use of the well-known gradient descent method, which is a first-order iterative optimization algorithm. To find a local minimum of the function using gradient descent, one iteratively takes steps proportional to the negative of the gradient (or of the approximate gradient) of the function at the current point. The process is repeated until a sufficiently accurate value is reached. For more details we refer the reader to e.g. Snyman
(2005).
51 4.7. Case Study
4.7.1. Ha:mo RIDE car sharing system
Ha:mo RIDE is a one-way car sharing system operating with small electric vehicles.
Once the user has registered, s/he s can reserve vehicles by smartphone from any station and return the vehicle at whichever station is convenient. This system was introduced in Sept
2013 in Toyota City, Japan, as well as later in Tokyo, Grenoble and Okinawa. In the beginning, Ha:mo RIDE in Toyota City had only a few stations. By the end of 2016, after several extensions, there were 59 stations (see Figure 4.6). In this case study, we analyse monthly adoption using the first 40 months of individual rental records until Dec 2016.
Figure 4.6 Location of Ha:mo stations
52 4.7.2. Full and Reduced Model Specification
Above introduced model could be estimated by fitting a set of four parameters
{풂, 푰, 풑, 푴} for each station leading to a large number of parameters. We refer to this as the
“Full model”. To avoid possible overfitting stations are divided into four groups with group instead of station specific parameters. We define following groups:
Residential: Predominantly land-use around the station is residential. Most of the users live around the station.
Business: Station is located near factories or in the CBD area. Most of the users are employees of factories or companies; the main travel purpose is commuting.
Public Service: Station is located near buildings such as government, hospital, museums or shopping malls. Most of the users visit these places with high frequency.
Transit Hub: Station is located near public transport facilities, such as railway stations or major bus stops and users come from all areas.
53 4.7.3. Estimation and Forecasting of New Adopters
300 Observed new adopters
250 M1:Bass Model (system),R2=0.162,adj.R2=0.074 M2:Bass Model (station),R2=0.083,adj.R2=-0.076 200 M3:Full Model without time coef.(system),R2=0.778,adj.R2=0.722 150
100
50 Relative Relative Number New of adopters
0 0 5 10 15 20 25 30 Time periods since operation
Figure 4.7 Estimated New adopters of system
The data of the first 32 months of operation are used to calibrate the models which leads to the estimated results shown in Figure 4.7. For confidentiality reasons, we conceal the real value but report all values as relative to a baseline, which we set as 100 in month 22. We report in the figure six estimated models and the observed new users. Two of these are based on Bass’ model. The first one “Bass model (station level)” (M1) is the model as introduced in
Equation 1. The second one, “Bass model (station level)” (M2), is the same one but estimated separately for each station and then aggregated to a system. Then three models based on the full model are reported. In M3 we only estimate on system level so that the model contains 6 parameters, whereas in M4 we estimate at station level but omit the 11 temporal parameters.
In M5 we keep all parameters. Finally the reduced model (M6) introduced in previous section is shown.
We report both R2 and adjusted R2 to illustrate that the differences in goodness of fit cannot be explained well only due to the additional parameters. We further note that for the models on station level the R2 and adjusted R2 are not fully comparable, since we fit the
54 parameters to not only match the system level estimate but also the station level estimates.
For comparability, all R2 values refer though only to the fit on system level.
We observe that the Bass model at system level has poor ability to describe the actual curve and, interestingly, the Bass Model estimated at station level performs even worse (in fact the adjusted R2 is negative, indicating that a constant would be a better estimate). The
Bass model misses in particular the early peak. This illustrates that a different approach is required for estimation on spatial level where the stations cannot be considered separately.
In contrast, our model with explicit consideration of information diffusion captures the early peak and consequently performs much better. The models further show that considering the spatial differences is important as it raises the R2 to over 0.9 and the adjusted R2 to 0.881.
Omitting the time coefficients reduces the model fit to 0.82. Detailed analysis shows that the time coefficients are important to capture the drop in new users during the winter season.
Finally, the Reduced Model performs very similar to the Full Model, so that we suggest that the Reduced Model (M6) might be preferable due to easier interpretation of the significantly less parameters.
Comparison of Estimation and Forecasting
Having obtained the parameter estimates with data from the first 32 months, we use data from months 33 to 40 without considering new stations opened during this period for forecasting. We then use these forecasts plus the actual data from the new stations to obtain our estimated total new users for this time period and compare to the observed data. The results are shown in Figure 5. We use the same models M3 to M6 as in Figure 6, but revised by this adjustment for new stations and name them as RM4 to RM6. For comparison, we further add the original M6 i.e. without correction for new stations.
Figure 4.8 shows the goodness of fit. We observe that for prediction the reduced model
(RM6) outperforms the full model (RM5). This can be explained by the fact that less model
55 parameters reduce the risk of overfitting the training data and increase the forecasting power.
In addition, the decline of MAPE (Mean Absolute Percentage Error) and RMSE (Root Mean
Square Error) from RM3 to RM5 gives further evidence that space heterogeneity and seasonal effects are important to consider for forecasting. Finally, the comparison between M6 and
RM6, shows that the effect of facility extensions has been very important even for short-term demand prediction.
120
110
100
90 adopters 80 Observation RM3,RMSE=11.237,MAPE=0.097 Relative Relative Numberofnew 70 RM4,RMSE=9.448,MAPE=0.086 60 RM5,RMSE=6.711,MAPE=0.055 33 34 35 36 37 38 39 40 Time periods since operation
Figure 4.8 Prediction of new adopters
4.7.4. Parameter analysis
Having shown the overall model fit, we now discuss the interpretability of the parameters. We take the values estimated with the Reduced Model for this. First the global parameters are discussed in subsections 4.4.1 and 4.4.2 before the station group specific parameters are discussed in 4.4.3.
Social influence and “hesitation”
The social influence or follower effect is described with q. The value is estimated as
0.048, which means that 100 system users attract nearly 5 more users. The value is similar with the estimated value of 푞푏 in case studies with Bass model and monthly data, which ranges from 0.02 to 0.06 (Putsis,1996).
56 In contrast, c describes the “hesitation factor”. The estimate of c is nearly 0.001 suggesting that 0.1% of the hesitant-adopters within the market size who refuse to adopt at first will adopt to the system independently the following month. This appears to be low but needs to be considered with relation to the market size estimation. For example, in month 32, we estimated a total of 108 new adopters, among these 60 are fast adapters. From the remaining 48 users, 42 are due to the “follower effect” and 6 are due to independent reconsideration according to our model.
Seasonal effects
1.20 1.15
1.10 (Sep = = 1) (Sep
훿 1.05 1.00 0.95 0.90
0.85 Time coefficient coefficient Time 0.80 Dec Jan Feb Mar Apr May Jun Jul Aug Sep Oct Nov Months in one year
Figure 4.9 Estimated time coefficient
As shown in Figure 4.9, the monthly coefficients 훿 can be roughly divided into three groups. From Dec to Mar, 훿 is lower than 0.95, from April to July, 훿 is in the range of 1.05 to
1.15, and from August to November 훿 is in the range of 0.95 to 1.05. Since the Ha:mo vehicles have only a simple foldable roof and are not equipped with a heating system and given fairly cold winters in Japan this trend is understandable. Further we note that the system is not operating during the New Year holidays, which likely contributes further to the lower 훿 in January.
57 Station group specific parameters in reduced models
Figure 4.10 Boxplot of parameters a, p, I, M
In the full model, we have four station specific parameters {풂, 푰, 풑, 푴} . Figure 4.10 shows the mean and distribution of the four parameters among the stations. We observe that there are large differences in the mean values and range of parameters for different areas. For example, Transit Hub stations have a large potential market (M) and information diffusion speed (a), but low fast-adopter ratios (p). This appears reasonable as transit hubs are, by definition, busy places. Our results suggest that in these places over time users have learned to combine transit with one-car sharing. In contrast, residential stations have a low potential
58 market (M) but consistently high values of fast-adopters ratio (p). This suggests that in residential areas some (low level of) latent demand existed that started using the service once it opened. However, there are few users continuing to adapt to the system over time.
We note that car ownership in Toyota city is high, possibly explaining this. Stations in business areas and in public service areas have the lowest mean values of initial information
(I) and information diffusion speed (a) respectively. As Toyota city (unlike most other
Japanese cities) does not face severe traffic congestion and parking place shortage most trips in the city centre are made by private car, possibly explaining these results. To understand and explain the station specific parameters as well as their relationships in more detail we require an explicit discussion of our case study city and its demand patterns which is beyond the scope of this paper.
4.8. Summary
In this Chapter, we propose a novel methodological framework to predict the number of users registering for a new transportation system due to the existence of specific stations. Our approach is based on classic product diffusion models but we discuss the adjustments that need to be made for modelling the specifics of transport “products”. In particular we discuss the need to model the spatial heterogeneity of transport systems. Whereas the quality of products for which Bass and others developed their models will not vary depending on the location of the user, access time, distance to destinations and availability of the service will influence the attractiveness of transportation services. Furthermore, in contrast to other production adaption literature we aim to model fairly short time horizons, in our case months instead of years. This requires us to model the information diffusion process explicitly. These considerations led to a model with six main parameters: initial information spread, speed of information distribution, market size, innovation rate, hesitation effect and follower effect. To
59 acknowledge that users are not attracted to the system due to existence of a single station but that they are attracted by the combination of stations we further introduced a submodel that acknowledges the synergy effect of the stations so as to not overestimate the attractiveness of a single station.
Our models are applied to data from the first 40 months of operation of the Ha:mo RIDE car sharing system in Toyota. We could observe initial sudden changes and then relatively stable patterns of new users. With the information diffusion process, our model can explain the observed curve well. We found in our case study that fast-adopter are the majority of the new adopters. Further hesitation effects are significant but also at a low level. These are in parts bad news for the system as it suggests that not much demand growth can be expected over time and dropout users might not be sufficiently replaced. Though we leave a detailed discussion with inclusion of socio-demographics and city characteristics for further work, we show that our estimated parameters can be interpreted and appear meaningful to better understand the demand developments.
We found that our model performs well in estimation and forecasting demand. To avoid overfitting and acknowledge correlation between our six parameters we further demonstrate that simpler models can be build. In this paper, we discussed a rough classification of stations into four types and found that assuming constant parameters for each station type does not reduce the model fit significantly and in fact improves the forecasting power. Our focus has been on the description and demonstration of the methodological framework. In further work we will test different classifications, further explore the relationship between the parameters as well as their relationship to network specifics and geographic details. This as well as analysis of parameter stability depending on opening time of the station we suggest also as directions for further work
60 CHAPTER 5. BEHAVIOR DYNAMICS: LIFECYCLE
MODEL
5.1. Introduction
Understanding long-term demand dynamics remains an important challenge for transport.
In most cases, the future demand is uncertain, particular if there are changes in the supply system. Demand predictions for new transport systems are though often difficult and there exist urgent need to revisit demand modelling for both new and existing modes. How travellers adapt to the new available options, recover from interruption of usage, or even drop-out after initially trying the new services are our questions of concern.
Panel data is an effective way to observe these processes accurately (see Kitamura,
Yamamoto, and Fujii 2003). Given the advantages compared to time series and cross- sectional data, panel data have received increasing attention recently. Our analysis is centred on a Markov model approach that utilizes such tracking data. Markov models have been proven to be an important method for the analysis of such data, though there are a number of shortcomings.
The objective of this chapter is to formulate this approach so that it clearly describes and explains the different changes of behaviour over time by using panel data. The structure of
Chapter 5 is structured as follows. In section 5.2, we hence first the limitation to the Markov model in the application of new transport system and then proposed a new methodology combined lifecycle model with Markov model to solve the problems partly. Section 5.3, we discuss how this process might be calibrated by observations from a panel study using the maximum likelihood estimation together with Newton’s iteration method. In Section 5.4,
Panel data obtained from Kyoto University’s bicycle share system are used to illustrate the
61 approach. Finally, the chapter concludes by discussing findings from the proposed survey and will further discuss the limitation of this approach which leads to an extension in the next chapter.
5.2. Model Conceptualization
5.2.1. Notations
Following is a short summary of the main notation that will be used throughout this chapter and discussed in subsequent sections.
Table 5.1. Notations in Lifecycle Modeling
Type Variable Description
t Discrete time periods with t = 0, 1, 2,..
M Set of states users can be in. In our case study this is the usage frequency group.
m Number of states in set M Time Independent 흓 State transitions matrix for users in the system with element 푝 Variables 푘푖
흓푒 State transitions matrix for users entering the system with element 푝푘푖
흓표 State transitions matrix for users drop out with element 푝푘푖
푝푘푖 The probability to transfer from state k to state i
푿(푡) Observed system state at time t as aggregation of vector 푥푗(푡)
풙푗(푡) Observed state vector of person j at time t with binary elements 푥푖푗(푡)
푥푖푗(푡) Whether or not person j is in state i at time t (binary)
푸(푡) Estimated system state at time t as aggregation of 푞푗(푡)
풒푗(푡) Estimated state probability distribution of person j at time t with elements 푞푖푗(푡)
푞푖푗(푡) Probability of person i being in state j at time t Aggregate potential demand for all users in the system at time t as aggregation of Time Dependent 푫(푡) vector 푑푗(푡). Variables 풅푗(푡) Estimated state probability distribution of person j at time t with elements 푑푖푗(푡)
푑푖푗(푡) Whether or not the potential demand of person j is in state i at time t (binary)
푫풆(푡) Potential demand by users who have entered the system at time t
푫풐(푡) the potential demand for users leaving the system at time t Matrix denoting the change in potential demand from time t-1 to t caused by 횫(푡) exogenous factors
푾(푡) Probability matrix of willingness to use with elements 푤푖푘(t)
62 푤푖푘(t) Probability of actual demand in state k and the potential demand in state i
푛(푡) Number of users in the system at time t
푛푒(푡) Number of new users at time t
푛표(푡) Number of drop-out users at time t
5.2.2. Life-Cycle Model
Suppose the process to be measured with panel data can be represented by a set of discrete states. These discrete states can represent categories, frequency counts or measurements. Regardless of what the states represent, it is assumed that for every person a transition from one state to another can take place between adjacent time periods and the process is in exactly one state between two successive transitions. It is also assumed that these transitions are probabilistic, and the transition function does not change over time (time- homogeneity).
Denote the discrete time periods by the letter t (with t = 0, 1, 2,.). Let M present the set of all possible states and m the number of states according to usage frequency (frequency increase from state 1 to state m).
We now utilize the concept of user life cycle, where ‘birth’ means a person uses this system for the first time. We denote this as State 0, and state ‘death’ means that s/he will drop out and not return again, we denote this as State m+1. Therefore, there are m+2 states in set M.
When a person enters into the system from State 0, he can transfer between states 1 to m according to his/her usage frequency at the discrete time periods. State m+1 is an absorbing state that once entered the user can not leave again. This lifecycle process is shown in below figure. We note therefore that in comparison to above quoted literature, the “system member” state includes build-up, maturity as well as decline and that a user can move forth and back between these states.
63
Figure 5.1 User life cycle
Let 푿(푡) be the observed system state and풙푗(푡) be the person or person group j specific vector state at time t with elements 푥푖푗(푡) ⊆ (0,1) denoting whether a person j is in state i or not. 푿(푡) can be presented by aggregation of 풙푗(푡). Each person must be in exactly one state at each time t so that 푥푖푗(푡) takes binary values with constraint ∑푖=1…푚 푥푖푗(푡) = 1.
We are interested in estimating the transition probabilities between subsequent time epochs. For this we define 푸(푡) as estimated states of the system with vector 풒푗(푡) as the estimated probability mass function for person j which we refer to as the “state probability distribution”. We further define 푞푖푗(푡)as the probability of person j being in state i at time t.
Due to potential sampling limitations, including potential errors and discretization of the states, we presume that 푞푖푗(푡) should be between 0 and 1 but not include the boundaries. As we will discuss this assumption will be useful for our parameter estimation. Further, clearly each person in the system must be in one of the m states at any time t, so for any j
∑푖=1…푚 푞푖푗(푡) = 1 must hold.
Following our previous discussion we further define potential demand as the possible maximum usage in the system. The willingness to satisfy the potential demand by using our transport system of interest will then determine the actual use frequency based on the potential demand. In line with this, we define 퐷(푡) as the potential demand for the system with vector 풅푗(푡) as the potential demand for person j at time period t. We define this as the highest state among the m usage states that can be possibly achieved by the user. The
64 elements 푑푖푗(푡) ⊆ (0,1) then denote whether the potential demand for a person j is in state i or not.
Each person must have exactly one potential demand state (the highest achievable state) at each time t so that 푑푖푗(푡) takes binary values with constraint ∑푖=1…푚 푑푖푗(푡) = 1. The number of persons in each potential demand state, 푫(푡), can then be presented by aggregation of 푑푖푗(푡).
1 ifpotentialdemandofperson푗isstate푖 푑 (푡) = { (5-1) 푖푗 0 otherwise
We further definethe probability that the potential demand states transfers into a specific actual usage state with the 푚 × 푚 “willingness to use” probability matrix 풘(푡) with elements
푤푖푘 denoting the probability of being in actual demand state k given that the potential demand is i. Considering that actual demand is depending on potential demand and that actual demand can not exceed potential demand the matrix must fulfill constraints (5-2) and (5-3); that is, all matrix entries above the main diagonal should be zero and each row should sum up to 1.
∑푖=1…푘 푤푖푘(푡) = 1(푘 ≤ 푖) (5-2)
푤푖푘(푡) = 0(푘 > 푖) (5-3)
Our afore defined person-specific state probability distribution 풒푗(푡) can now be obtained by multiplication of vector 풅푗(푡) and matrix 풘(푡). We note that with this, we obtain also 푞푖푗(푡) → 0 for all states i > k where k denotes the potential demand of person j.
풒푗(푡) = 풅푗(푡) ∙ 풘(푡) (5-4)
We further define the three Markovian transition functions 흓푒, 흓 and 흓표 , which represent the transition probabilities of the processes to update the estimated state probabilities. 흓푒 is a 1 × 푚 vector with its denoting the probability of state transitions from state 0 to i for new “entering” users. 흓 is a 푚 × 푚matrix denoting the probability of state transitions between states 1 to m for continuous system members and 흓표 is a 푚 × 1 vector
65 denoting the probability of state transitions from state k to state m+1 for users dropping out of the system. We denote all elements of the three transition matrices with 푝푖푗 where i and j range from state 0 to State m+1 as shown with (5-5), (5-6) and (5-7).
흓푒 = [푝01 ⋯ 푝0푚] (5-5)
푝11 ⋯ 푝1푚 흓 = [ ⋮ ⋱ ⋮ ] (5-6) 푝푚1 ⋯ 푝푚푚
푝1(푚+1) 흓표 = [ ⋮ ] (5-7) 푝푚(푚+1)
For users in the system we can update their actual demand as in (5-8).
풘(푡) = 풘(푡 − 1) ∙ 흓 (5-8)
Different assumptions for the potential demand 풅푗(푡) for person j are feasible. A constant 풅푗(푡) would indicate that the potential demand is time independent. Note that under this assumption we can also obtain following relationship for user j who remains in the system:
풒푗(푡) = 풒푗(푡 − 1) ∙ 흓 ∀푡 (5-9)
If an adaptation effect is considered in that users require time to adjust their behavior and/or the (new) transport scheme induces additional demand of the travelers in the system then a continuous growth over time should be assumed. Alternatively, the potential demand can be used to indicate seasonal effects. For example, in the case study described later we presume that the demand of a person is constant during term time but drops during periods without lectures. To account for such potential demand dynamics we introduce a Matrix 횫(푡) denoting the change in potential demand from time t-1 to t caused by exogenous factors. With this we obtain (5-10) and combining (5-4), (5-8) our state probability density function obtains its final form (5-11).
66 풅푗(푡) = 풅푗(푡 − 1) ∙ 횫(푡) (5-10)
풒푗(푡) = 풅푗(푡 − 1) ∙ 횫(푡) ∙ 풘(푡 − 1) ∙ 흓 (5-11)
Let further 푛(푡), 푛푒(푡)and 푛표(푡) present the total number of (continuous) users, new users and dropping out users at time t respectively. Similarly to 푫(푡), we also define 푫푒(푡) and 푫표(푡) in order to distinguish the initial demand when users enter the system and the final demand before users drop out. With this the estimated system state 푸(푡) can be calculated as in (5-12).
푸(푡) = (푫(푡 − 1) + 푫푒(푡 − 1) − 푫표(푡 − 1)) ∙ 횫(푡) ∙ 풘푗(푡 − 1) ∙ 흓 + 푛푒(푡) ∙ 흓푒 (5-12)
5.3. Estimation of parameters
5.3.1. Overview
To obtain the parameters for the approach described in previous section, three steps can be distinguished that are outlined in the following: State Identification, Transition Function
Estimation and Potential Demand Estimation. First we identify the observed usage frequency states for users at different time periods from the panel data. The key task of this part is to distinguish the drop out state (State m+1) and the inactive state (State 1). Stages 2 and 3 are then identification of the previously introduced transition matrices and potential demand as will be described in the following.
5.3.2. Identifying States
Both States 1 and m+1 denote inactive users. The difference is that users in State 1 are only temporary inactive whereas users in State m+1 have dropped out. The difficulty is hence to distinguish in which of the two states the users are, as these can often not be distinguished directly from the observed data unless users clearly “sign-out”. For demand forecasting distinguishing these states is important though in order not to overestimate the likelihood of users returning.
67 One might estimate the drop-out rate by analysing whether there are any usage records in later time period for a user once he has become inactive in one time period. A naïve analysis would lead though to overestimation of users in State m+1 for a time limited panel data set.
Let the final time period in the data base be 푡푛. The more time periods before and including
푡푛 there are without user records the more likely a person is in State m+1. In other words, the later a user becomes inactive, the less one can be confident that s/he has dropped out and is not just temporarily inactive.
Figure 5.2 Distinguishing temporarily inactive and drop-out users
We therefore propose an approach to revise the number of users in the two states. As shown in Figure 2, it can be assumed that the ratio of users who “made their last ride” and transfer into the absorbing State m+1 among active users is a constant 휋표. Further, among
“living”, eventually returning users the probability for a user to remain in State 1 is 푝11. For an inactive person at time t, the probability to remain continuously in State 1 from time t to time t+n can therefore be calculated as:
푛 휋(푛) = (1 − 휋표) ∙ 푝11 (5-13)
68 Therefore, a continuous no usage record from time t to time t+n, means that with a probability of 푟(푛) such a user should be classified as an inactive user:
휋(푛) 푟(푛) = (5-14) (휋(푛)+휋0)
′ With this 푛표(푡), the revised number of users dropping out at time periods t, can be represented as in (5-15) where 푡푛 presents the final time period.
푛 (푡)(1−휋 )∙푝 (푡푛−푡) 푛′ (푡) = 0 0 11 (5-15) 표 (푡 −푡) 휋0∙((1−휋0)∙푝11 푛 +휋0)
Our parameter of interest, 휋표, can then be estimated as in (16) where the denominator are the total inactive users at time t.
′ ∑푡 푛표(푡) 휋표 = (5-16) ∑푡(푛표(푡)+푛1(푡))
Since 푛표(푡) and 푛1(푡) are observed and 푝11 is estimated as part of the transition matrix
흓 as described in the following section, this becomes an equation with unknown 휋표 (on both left and right hand side of the equation). By inserting (5-15) into (5-16) and solving the equation for 휋표, its value can be obtained.
5.3.3. Estimation for transition function
Following our model set up, in this section we estimate the parameters of the Markovian transition functions 휙푒, 휙 and 휙표. The objective is to maximize the likelihood of correctly predicting the state of each person in time period 푡 + 1 based on state of the person at the time period t by using one step transition probabilities. We formulate this as follows:
푥 (푡) ∗ 푖푗 퐿 (풒|풙, 휙) = ∏푡 ∏푗(푡) ∏푖 (푞푖푗(푡)) (5-17)
69 j depends on time t, since here j only presents the users in the system, not including the persons that have not yet entered or have already dropped out. As we want to maximize likelihood we can consider the log likelihood function L:
max 퐿(풒|풙, 휙) == ∑푡 ∑푗 ∑푖 푥푖푗(푡) ln 푞푖푗(푡) (5-18)
푙 Since the parameters we want to estimate are the 푝푘푖 of the transition function 휙푙 for
푙 stage l , an expression of the log likelihood function L as functionality of 푝푘푖 must be obtained. We remind that following (5-8) we obtain 푞푖푗(푡) = ∑푘 푞푘푗(푡 − 1)푝푘푖. First, let us
푙푠 define 푛푖푘(푡) as the number of people who are at time 푡 − 1 in state k stage l and in the target time 푡 in stage s state i
푙푠 푛푖푘(푡) = ∑푙 ∑푠 푛푖푘(푡) = ∑푗 ∑푙 ∑푠 풆푖푗(푡 − 1) ∙ 풒푙푗(푡 − 1) ∙ 풆푘푗(푡) ∙ 풒푠푗(푡) (5-19)
We now expand the log likelihood function into
퐿(풒|풙, 흓) = ∑푡 ∑푗 ∑푖 ∑푘 푥푘푗(푡 − 1) 푥푖푗(푡) ln 푞푖푗(푡) (5-20)
By adjusting the order of summation and utilizing 푛푘푖(푡) the resulting function is shown in (5-21) with constraints (5-22) and (5-23).
푙 퐿(풒|풐, (흓|흅퐿)) = ∑ ∑ ∑ ∑ ∑ 푛푖푘(푡) ∙ δ푖푘(푙, 푠, 푡) ∙ ln(푝푖푘 ∙ 휋푙푠) 푡 푖 푘 푙 푠
퐿(흓) = ∑푡 ∑푖 ∑푘 푛푘푖 (푡) ln(푝푘푖) (5-21)
∑푖=1…푚 푝푘푖 = 1 ∀푘 (5-22)
0 < 푝푘푖 < 1 (5-23)
There appear to be m2 parameters in 퐿(흓), however, due to constraints (31) there are only m (m-1) free variables 푝푘푖 to be estimated. To maximise 퐿(흓), we aim to obtain the necessary optimality conditions for the partial derivatives:
70 휕퐿(흓) = 0∀푘, 푖 (5-24) 휕푝푘푖
Since we can not solve these equations directly, we make use of Newton‘s iterative
휇 (푛) method for finding the roots of a differentiable function f. Let 풁 [푝푖푗 ] presents the estimated values after the 휇th iteration.
(휇) 푝11 풁휇 = ( ⋮ ) (5-25) (휇) 푝푚(푚−1)
We start the process with some arbitrary initial value 풁0.Then we find the “better guess”
풁1.The process is repeated until a sufficiently accurate value is reached.
푓(풁휇) 풁휇+1 = 풁휇 − ′ (5-26) 푓 (풁휇)
5.3.4. Revision of Willingness Matrix
Following our discussion in Section 3we presume that the actual demand (willingness to use) can not exceed the potential demand. With the estimation of 흓 and as in previous section and transforming this into actual estimated demand 풘(푡) which is though not necessarily observed. To ensure constraints (5-11) and (5-12) are observed we require a modification process. For this we modify the estimated matrix 풘(푡) with (5-27) and (5-28). In words, the actual demand is corrected downward to the (maximum) potential demand.
푤푖푘(푡) ⟵ ∑푖=푘…푚 푤푘푖(푡) (5-27)
푤푖푘(푡) ⟵ 0(푘 > 푖) (5-28)
5.3.5. Estimation of potential demand
The potential demand cannot be identified directly with the approach introduced so far. Different assumptions might be possible as discussed in the introduction. A simple, conservative approach is to assume the potential demand at all time periods is the highest demand observed by the user during any time period. Especially for users entering the system early this appears to be a reasonable assumption. For users entering late, one might have the “reversed bias” as for the drop-out users though in that the potential demand has not been
71 reached due to the too short observation period. For the case study described in the following we ignore this problem, as only very few users enter the system during the latter months of our panel data observation period.
We do consider though the reduced potential demand during some periods. In the case study it is the decrease in demand during the off-term period. We consider that the potential demand decrease in the summer period is proportional to the usage during term time multiplied by the proportion of school holidays during the month. With this we obtain our demand transition matrix 흓푑(푡).
5.4. Case study
5.4.1. The COGOO System
Figure 5.3 Location of stations in COGOO of Kyoto University
Bicycle sharing, a sustainable form of transportation, is relatively new, highly visible additions to urban transportation system, which provide opportunities to cycle or combine cycling with other modes of transportation. In recent years, more and more bikeshare systems were set up over the world, so we are very interested in the user adaptation and behaviour changes in these new systems (Schoner et al, 2016).
Since the popularity of bicycles, managing parked bicycles and specifically abandoned bicycles are a major challenge for universities. As part of efforts to encourage bicycle usage
72 but at the same time reduce the number of abandoned bicycles, a bicycle sharing service called "COGOO" has been introduced to the University Campus.
The COGOO service provides free bicycle rentals to Kyoto University students, faculty and staff. Users can register via mobile phone and pick up or drop off a bicycle from any of 10 COGOO parking lots (see Figure 5.3). Since this system was introduced in March 2014, it has 1,600 registered members who used it for more than 14,000 times accumulatively. We could obtain individual rental records for 13 months until April 2015. (Unfortunately since then the service has been suspended due to usage rules not being kept by students. Bicycles were not returned properly to parking lots and usage time limitations were not kept. This is further discussed in Nishigaki et al (in press).) We distinguish five different states for each person that are {inactive, few, sometimes, often, always} according to the use frequency (see Table 5.2). The time intervals between subsequent time points are set to one month.
Table 5.2 State divisions
No States Frequency
1 inactive 0
2 few 1-3 3 sometimes 4-10 4 often 11-20 5 always >20
5.4.2. Aggregate Data Analysis
The number of users in States 1 to 5 in different months are shown in Figure 3. On an aggregate level one might distinguish following time periods:
The first five months might be classified as “start-up period”. As might be expected, the number of active users is continuously growing during this initial time period. Noteworthy is that though that at the same time, after the initial two months, also the number of inactive users steadily increases. This might indicate users who only once tried the new system but then do not use it continuously.
In months six and seven which are August and September 2014 we can observe a “Reduced demand period”. This time period is the summer break in the University. Obviously, the number of active users are negatively affected by this as students will come less to campus. Therefore, the number of inactive users reaches its peak.
73 We can then observe then a recovery from summer break. Generally the number of active users keeps quite stable during the remaining observed months, though among the inactive users a growth trend is maintained. Compared with the data from before summer break, a reduction of medium and high frequency users (States 3-5) is observed. The distribution of different states also remains fairly stable during these months.
400 State 1 State 2 State 3 State 4 State 5 350 300 250 200 150
100 Numberusers of 50 0 0 1 2 3 4 5 6 7 8 9 10 11 12 13 Months since start of operation (time periods)
Figure 5.4 Number of users for different states
5.4.3. Estimated Parameters
Table 3. Estimated Monthly Transition Matrix
State 1 2 3 4 5 Exiting Entering -- 0.91 0.082 0.008 0 -- 1 0.615 0.367 0.021 0.000 0.000 -- 2 0.365 0.427 0.091 0.006 0.000 0.110 3 0.101 0.482 0.370 0.046 0.003 0.006 4 0.000 0.055 0.527 0.341 0.077 0.000 5 0.000 0.000 0.000 0.318 0.682 0.000 Exiting ------1.000
Through the method we introduced before the estimated transition matrix shown in
Table 3 has been obtained. The grey shaded values denote the transition matrix 흓, the top row the matrix 흓푒 and the right column the matrix 흓표.
Considering 흓, we observe that most of the users in all the states maintain in the state which they were in the last period. Besides, we find that the probability of jumps between more than one status level (e.g. state 1 to 3 or state 4 to 2) is very low. This suggests that
COGGO users tend to change their habit gradually.
74 Looking at 흓푒, compared with the transition matrix for users staying in the system, we observe that the behaviour of new users is different compared to inactive users (state 1), though both did not use the system before. This difference appears to justify our approach in distinguishing 흓푒 and 흓. Considering 흓표, we estimated the probabilities of transition from
States 4 or 5 to dropping out was zero and observed that almost all dropping out users came from state 2, and. This means that for COGGO “sudden exits” are very rare and rather giving up this transport mode is a gradual process.
5.4.4. Results based on Transition probabilities
The users entering and dropping out of the system reflect the attractiveness of the scheme to travelers. As shown in Figure 5.5, the number of new users increases at the beginning but then continuously decreases. The number of estimated users dropping out increases during months 4 and 5 and then remains stable. We also observe that our estimate for dropping-out users appears to be not significantly influenced by the summer break which appears reasonable.
250 800 700 200 600 150 500 In(observed) 400 Out(estimated) 100 300
200 the system 50
100 Numer of in and out users and ofusers out Numer in 0 0 1 2 3 4 5 6 7 8 9 10 11 12 13 remaining in users Number of Months since start of operation (time periods)
Figure 5.5 Users entering and exiting COGOO
75 600 500 400 300 200
Numer of users 100 0 1 2 3 4 5 6 7 8 9 10 11 12 13 Months since operation state 2 state 3 state 4 state 5
Figure 5.6 Estimated potential demand for users in the system
As noted we consider the potential demand for a user to be constant except for the summer months. However, since there are users entering into and dropping out of the system in every time period, the total potential demand for the system is changing over time as illustrated in Figure 5.6. Especially, in the summer break the number of potential high frequency users drops, and there are more users who make use of COGGO only a few times.
5.4.5. Estimation results of different models
To evaluate the model goodness of fit let 퐸푗(푡)and 퐴푗(푡) represent the estimated and actual number of users at time t respectively. Δ푖(푡) is the difference between the two for state i at time t. The MAE (Mean Absolute Error) and MAPE (Mean Absolute Percent Error) can then be calculated by the following equations:
Δ푖(푡) = 퐸푖(푡) − 퐴푖(푡) (5-29)
푚 MAE = ∑푖=1 |Δ푖(푡)| (5-30)
푚 ∑푖=1|Δ푖(푡)| MAPE = ( ⁄ 푚 ) × 100% (5-31) ∑푖=1 퐴푖(푡)
76 40%
35%
30% M1 M2 25%
20% MAPE 15%
10%
5%
0% 2 3 4 5 6 7 8 9 10 11 12 13 Months since start of operation
Figure 5.7 MAPE errors of the two models
To show the effectiveness of our model, the prediction errors of two models, the model proposed in this paper (M1), and a simpler Markov model (M2) without the states “birth” and
“death” are compared.
Since the states of the two models in this case are different (M1 with 7 states, and M2 with only 5 states), we compare the estimated results of the active states (states 2 to 5) only.
The MAPE of these models are shown in Figure 5.7. It is clear that M1 has a higher accuracy than M2 in most time periods. Besides, we also notice that at the adaptation stage, the error of
M2 decreases with time, but the error of M1 remains fairly stable.
This can be explained by considering that Model 1 considers more user states, in particular the afore mentioned difference in behaviour of users entering the system newly.
Misjudgement of these users’ behaviour during their early months of COGGO membership affects the result of estimation seriously. However, this effect reduces with time passing.
Furthermore, M1 considers the decreased demand during the summer months, which clearly improves the model fit.
5.5. Summary
77 The paper proposes a novel approach to describe the gradual change of behavior over time. We envisage this approach to be particularly useful for describing adaptation to new transport solutions and significant infrastructure investments where users over time learn to appreciate the new or improved system and start using it more. The solution approach is based on Markovian updating. We firstly discuss common issues of Markovian approaches used such as the assumption of time-homogeneity and a constant population. Time- homogeneity assumptions are not always suitable since additional/reduced demand at specific time periods are a common feature. We therefore distinguish actual demand (willingness-to- use) and potential maximum demand. The latter can change over time to allow controlling for specific high or low demand periods within the Markovian model. We secondly draw on the idea of “lifecycle stages” to reflect the dynamically changing total number of potential users and in particular to distinguish inactive users from those that have dropped out. We present an estimation method to obtain the drop-out rate. The transition rates are estimated so as to maximize the likelihood of fitting our observations. For this we utilize a variant of the
Newton method where the transition rates are firstly transformed into unconstrained parameters.
The model is applied to panel data from Kyoto University’s bicycle share system. Over the first 13 months of operation we could observe how usage first increased and then decreased. We forecast the usage with a simple Markov model and our advanced model and find with our method an improved model fit in predicting usage due to above introduced ideas.
Our results illustrate that new users behave generally different to other users suggesting the importance to distinguish adaptation for new and established users. We obtain a MAPE <10% for our preferred model which generally indicates a good model fit. This encourages us to further investigate the use of our models to estimate the behavior changes also for other applications.
78 There are still a number of issues that need to be addressed in further work. Firstly, the sample size and duration of time period of our case study are not fully sufficient for capturing the characteristic of high-frequency users and long-term behavior analysis. Large data sets and more case studies are essential to improve the model. If such data would be available one might also consider distinguishing transition matrices for the “build-up”,
“maturity” and “decline” stages, together with an estimation when a transport system moves into these stages. Our current work further considers replacing user states based on frequency only with states based on “multi-dimensional factors” including, besides frequency, spatial spread in usage and spread by time-of-day.
Finally, beyond estimation, there are still some key issues that need to be discussed such as “critical points” in the transition matrices that distinguish whether a system with a certain pool of incoming users would mean the system continuously grows. Related to this are issues of stability analysis and (long-term) equilibria, if there are any. In particular of interest will be how resilient systems might be against demand-shocks that we can create in our approach through the potential demand vector.
79
80 CHAPTER 6. EXTENSION OF LIFECYCLE MODEL
6.1. Introduction
Based on the work in Chapter 5, we extend our lifecycle model from basic 3 stages into 5 stages to deal with the problem that observed huge difference of behaviour changes in the early and later time periods of individual lifecycle.
The objective of this Chapter is to extend the previous lifecycle model so that it clearly describes and explains the different behaviour changes over time. The remaining of Chapter 6 is structured as follows: In Section 6.2 we then offer a description of the stochastic process of discrete behaviour observed at discrete time periods. In section 6.3, we discuss how this process might be calibrated by observations from a panel study using the maximum likelihood estimation together with EM algorithm. In section 6.4, data obtained from Free Floating Car share service in Montreal is used to illustrate the approach and analysis the impact of SBcs experience and facility extension on user behaviors in FFcs. In section 6.5,We then conclude and discuss possible future research.
6.2. Extension of Life-cycle Models
6.2.1. Notations
Denote the discrete time periods by the letter t (with t = 0, 1,⋯). Let L present the set of all possible stages and l present the number of stages according to our life-cycle model. As mentioned, five stages exist in lifecycle, noted as (푩, 푮, 푴, 푹, 푫)ϵ퐋. Similar with stages, let
M present the set of all possible states and m present the number of states according to usage frequency (frequency increase from state 1 to state m), noted as (1, ⋯ , 푚)ϵ퐌.
Let 푿(푡) be the observed system state and풙푗(푡) be the person or person group j specific
푖 vector state at time t with elements 푥푗 (푡) ⊆ (0,1) denoting whether a person j is in state i or
81 not. 푿(푡) can be presented by aggregation of 풙푗(푡) . It can be expressed as
1 푚 풙풋(푡)=(푥푗 (푡), ⋯ , 푥푗 (푡)) and 푿(푡) = ∑푗 풙풋(푡). Each person must be in exactly one state at
푖 푖 each time t so that 푥푗 (푡) takes binary values with constraint ∑푖=1…푚 푥푗 (푡) = 1.
Different from states which can be observed, stages are latent variables. Let 푸(푡) be
푙 stages of the system and 풒푗(푡) with vector 푞푗(푡) as the estimated probability mass function
푙 for person j which we refer to as the “stage probability distribution”. 푞푗(푡)is the probability
퐵 퐺 푀 푅 퐷 of person j being in stage l at time t and 풒풋(푡)=(푞푗 (푡), 푞푗 (푡), 푞푗 (푡), 푞푗 (푡), 푞푗 (푡)) and
푸(푡) = ∑푗 풒풋(푡).
We are interested in estimating the transition probabilities between subsequent time
̃ 푖 epochs. For this, we define 푿(푡) 풙̃푗(푡) and 푥̃푗 (푡) as estimated states variables for 푿(푡) 풙푗(푡)
푖 and 푥푗 (푡). Due to potential sampling limitations, including potential errors and discretization
푖 푙 of the states, we presume that 푥̃푗 (푡) and 푞푗(푡) should be between 0 and 1 but not include the boundaries. Further, clearly each person in the system must be in one of the l stage and m
푖 푙 states at any time t, so for any j ∑푖=1…푚 푥̃푗 (푡) = 1,∑푙=B,G,M,R,D 푞푗(푡) = 1 must hold.
We further define the Markovian transition function 흅 in stages and 흓풍 in states for different stages l (l=B,G,M,R,D), which represent the transition probabilities of the processes to update the estimated stage and state probabilities. 흅 is 5 × 5 matrix denoting the probability of stage transitions between stage B to D. For different stages, the forms of matrices 흓풍 are different.흓푩 is a 1 × 푚 vector for new “entering” users since before initial usage, all people are in state 1 (no usage). 흓푮, 흓푴, 흓푹 are 푚 × 푚matrices denoting the probability of state transitions between states 1 to m. And 흓퐷 is a 푚 × 1 vector for “dropping out” users since if one transfer to stage D, s/he will keep in state 1 (no usage). We denote all
푙 elements of the transition matrices with 푝ik where i and k range from state 1 to State m. We
푇 note 훟= (흓푩, 흓푮, 흓푴, 흓푹, 흓푫) including all transition matrices in stages to present the state transition in lifetime.
82 휋BB ⋯ 휋BD 훑 = [ ⋮ ⋱ ⋮ ] (6-1) 휋DB ⋯ 휋퐷퐷
푙 푙 푝11 ⋯ 푝1m 흓풍 = [ ⋮ ⋱ ⋮ ] (l=B,G,M,R,D) (6-2) 푙 푙 푝m1 ⋯ 푝mm
6.2.2. Formulations of the Models
Figure 6.1 Life Cycle of Individuals
A diagram for lifecycle model is shown in the Figure 1, using a directed graph to picture the stage and state transitions. We set the rules that a user can move forward or stay in these stages but cannot move backward.
Further transitions 휋BB , 휋BM , 휋GD , 휋MD are forbidden in our model. The resulting transition matrix훑 is shown in Table 6.1. Our rationale for the additional restrictions are as follows: Stage B just presents the trials of the new service, users should not stay at this stage after entering so that we remove 휋BB. Besides, since B is the original stage and D is the absorbing stage, they can hold uniqueness. However, uniqueness of M,G,R cannot be guaranteed if we include all stage transitions (Upper triangular in Transition Matrix흅). For example, for stage G the forward stages are G,M,R,D and backward stages are B and G. We denote this as G:(B,G)-(G,M,R,D). Similarly, we can also denote M and R as M:(B,G,M)-
(M,R,D) and R: (B,G,M,R)-(R,D). Assuming that G,M,R are an identical stage O, the model can be simplified to G: (B,O) - (O,D) M: (B,O) - (O,D) R: (B,O) - (O,D), and we cannot reject the hypothesis these stages are the same.
83 We want G to reflect the adaptation process after entering in early lifetime and R to reflect the decline process before dropping out in late lifetime. Except short-time users, all users must go through G after B and R before D, therefore 흅푩푴,흅푮푫 and흅푴푫 are removed.
In this way, for users with a lifetime of one time period, one transition B to D occurs and for users with a lifetime of two time periods, the two transitions B to R and R to D must exist.
Longer-term users usually should go through all five stages.
Table 6.1 Transition Matrix π for Life Cycle
STAGE B G M R D
B - 휋퐵퐺 - 휋퐵푅 휋퐵퐷
G - 휋퐺퐺 휋퐺푀 휋퐺푅 -
M - - 휋푀푀 휋푀푅 -
R - - - 휋푅푅 휋푅퐷
D - - - - 휋퐷퐷
The stage level is assumed to be time-homogeneous and it is assumed that the Markov property holds, i.e. the probability of moving to the next stage depends only on the present stage. This is formulated with (6-3 and (6-4 :
Pr(푄(푡 + 1) = 푎|푄(푡) = 푏) = Pr(푄(푡) = 푎|푄(푡 − 1) = 푏) (6-3)
Pr(푄(푡 + 1) = 푎|푄(1) = 푎1, ⋯ ,푄(푡) = 푎푡) = Pr(푄(푡 + 1) = 푎|푄(푡) = 푎푡) (6-4)
At the state level, the probability of moving to the next state depends on the present state, and the stage. This can be expressed with (6-5) and (6-6).
Pr(푋(푡 + 1) = 푥|푋(푡) = 푦,푄(푡) = 푎) = Pr(푋(푡) = 푥|푋(푡 − 1) = 푦,푄(푡 − 1) = 푎) (6-5)
Pr(푄(푡 + 1) = 푎|푄(1) = 푎1, 푋(1) = 푥1, ⋯ ,푄(푡) = 푎푡, 푋(푡) = 푥푡)
= Pr(푄(푡 + 1) = 푎|푄(푡) = 푎푡, 푋(푡) = 푥푡) (6-6)
Note that under this assumption, for user j in stage l we can update their state as in
84 푞푗(푡) = 푞푗(푡 − 1) ∙ 훑 (6-7)
풙푗(푡) = 풙푗(푡 − 1) ∙ 풒푗(푡 − 1) ∙ 훟 (6-8)
Combining (6-7) and (6-8), our afore defined person-specific state probability distribution 풙̃푗(푡) can now be obtained by 풙풋(푡) and transition matrix 훑 and 훟:
풕−ퟏ 풙̃푗(푡) = 풙풋(푡 − 1) ∙ 풒풋(0) ∙ 훑 ∙ 훟 (6-9)
Following our previous discussion in states updating in individual level we further expand our works in system level in two parts: in real time period and in lifetime periods.
Firstly, we define 푡푟as the discrete real time periods (푡푟= 0, 1, 2, since the operation of the system) and 푡푐 as lifetime periods (푡푐 = 0, 1, 2, since the adoption of users).
In “life time” domain, all users start at the same time period in stage B (푡푐= 0) and population of the system is constant. For all users,풒풋(0) = (1,0,0,0,0) holds, and we can note it as 풒푩. Therefore, with (11), the state distribution of the system 푋̃(푡) can now be updated as:
푡푐−1 푋̃(푡푐) = ∑푗 풙̃푗(푡푐) = 푿(푡푐 − 1) ∙ 풒푩 ∙ 훑 ∙ 훟 (6-10)
In “real time” domain, since there are new adopters, the population is dynamic. To account for such population dynamics we introduce a vector 횫퐗(푡푟 − 1) denoting state aggregation of 풙풋(푡푟) for new adopters 푛퐵(푡푟) before adoption. With this the estimated system state 푋̃(푡) can be calculated as in (6-12).
횫퐗(푡푟 − 1) = (푛퐵(푡푟), 0, ⋯ ,0) (6-11)
̃( ) ∑ ( ) ( ) ( ) X tr = j(tr) 퐱̃j tr = (퐗 tr − 1 ∙ 퐐 tr − 1 ∙ 훑+횫퐗(tr − 1) ∙ 퐪퐁) ∙ 훟 (6-12)
6.3. Estimation of parameters
To obtain the parameters for the approach described in previous section, two steps can be distinguished that are outlined in the following: (1) State and first and last usage identification and (2) transition function estimation. First we identify the observed usage frequency states for users at different time periods from the panel data. From the first usage we can further
85 identify the birth stage, but identifying all other states including “death” is not as straight forward. Last usage does not necessarily mean “death” as the user might just be temporarily inactive and return to the scheme in a future time period after the end of our observation period. In (1) we hence propose a probabilistic correction method considering the amount of time from last usage until the end of our observation period. Details of this approach are shown in section 5.4.2. In summary, from the first step we can identify the observed states
풒푗(푡), the birth stage, but the other latent stage memberships 풒̃푗(푡) need to be estimated together with the transition probabilities.
Following our model set up, in this section we estimate the parameters set 휽 including the Markovian transition functions 훟 for states and 훑 for stages. The objective is to maximize the likelihood of correctly predicting the state of each person in time period 푡 + 1 based on state of the person at the time period t by using one step transition probabilities. We formulate this as follows:
i xj(tc) ∗( ) ∏ ∏ ∏ i( ) L 훉 = tc j(tc) i (x̃j tc ) (6-13)
j depends on time t, since here j only presents the users observed, not including the persons that have not recorded in database. As we want to maximize likelihood we can consider the log likelihood function L:
̂ 푖 푖 휽 = arg max 퐿(휽) = arg max ∑푡 ∑푗(푡 ) ∑푖 푥푗 (푡푐) ln 푥̃푗 (푡푐) (6-14) 휽 훟,흅 푐 푐
푙 Since the parameters we want to estimate are the 푝푘푖 of the transition function 흓풍 for
푙 stage l, an expression of the log likelihood function L as functionality of 푝푘푖 must be obtained.
Expanding (9) we can obtain
푖 푖 푙 푙 푥̃푗 (푡푐) = ∑푘 ∑푙 ∑푠 푥푗 (푡푐 − 1) ∙ (푞푗(푡푐 − 1) ∙ 휋푙푠) ∙ 푝푘푖 (6-15)
푖 푘 We remind that following (6-7) we obtain 푞푗(푡푙) = ∑푘 푞푗 (푡푙 − 1) ∙ 푝푘푖 . First, let us define 푛푖푘(푡 − 1, 푡) as the number of people who are at time 푡 − 1 in state i and in the target
86 푙푠 time 푡 in state k,푛̃푖푘(푡푐 − 1, 푡푐) as the estimated number of users transfer from stage l to s and state i to k.
푙푠 푛푖푘(푡푐 − 1, 푡푐) = ∑푙 ∑푠 푛̃푖푘(푡푐 − 1, 푡푐) (6-16)
푖 푙 푘 푠 = ∑푗 ∑푙 ∑푠 푥푗 (푡푐 − 1) ∙ 푞푗(푡푐 − 1) ∙ 푥푗 (푡푐) ∙ 푞푗 (푡푐) (6-17)
We now expand the log likelihood function into
( ) ∑ ∑ ∑ ∑ ∑ ∑ 푖,푙( ) 푘,푠( ) 푖( ) 퐿 휽 = 푡 푗(푡푐) 푖 푘 푙 푠 푥푗 푡푐 − 1 ∙ 푥푗 푡푐 ∙ ln 푥̃푗 푡푐 (6-18)
By adjusting the order of summation and utilizing 푛푖푘(푡 − 1, 푡) the resulting function is shown in (6-19) with constraints (6-20) and (6-21)
휽̂ = arg max 퐿(휽) 휽
∑ ∑ ∑ ∑ ∑ 푙( ) 푙 = arg max 푡푐 푖 푘 푙 푠 푛푖푘(푡푐 − 1, 푡푐) ∙ 푞푗 푡푐 − 1 ∙ 휋푙푠 ∙ ln(푝푖푘 ∙ 휋푙푠) (6-19) 흓푳,흅
푙 ∑푙=퐵,퐺,푅,푅,퐷 휋푙푠 = 1, ∑푖=1…푚 푝푖푘 = 1∀푘, 푠 (6-20)
푙 0 < 푝푖푘 < 1,0 < 휋푙푠 < 1 (6-21)
Our models involve latent variables in addition to unknown parameters, therefore the equations cannot be solved by known data observations directly. Here EM algorithm is used to estimate the parameters and latent variables in our models. The EM algorithm seeks to find the MLE of the marginal likelihood by iteratively applying these two steps (15):
a. Expectation step (E step): Calculate the expected value of the log likelihood function with respect to the conditional distribution of latent variables under the current estimate of the parameters
b. Maximization step (M step): Find the parameters that maximize this quantity.
This suggests an iterative algorithm, in the case where both 흅 and 흓푳 are unknown in our models:
87 1.First, initialize the parameters in 흅 to some random values.
2.Compute the probability of each possible value of in 흓푳 given 흅
3.Then, use the just-computed values in 흓푳 to compute a better estimate for the parameters in 흅
4.Iterate steps 2 and 3 until convergence.
6.4. Case study
6.4.1. The Communauto Car-sharing System
Car sharing, a sustainable form of transportation, is relatively new, highly visible additions to urban transportation system, which provides sharing access to transport service.
In recent years, more and more car-sharing systems were set up over the world, so we are very interested in the user adaptation and behaviour changes in these new systems.
Communauto, the oldest carsharing operator in North America (1994), offers a Station- based Car-sharing service (SBcs) in Montreal since 1995. Later in 2013, this company introduced a new Free Floating Car-sharing service (FFcs) called Auto-mobile. First, they started the FFcs service with 24 electric vehicles (EV) and a service area of 8.01 km2. As they expanded the service area (SA), they increased the car fleet with mostly hybrid cars (HV) and more electric vehicles. In total, they expanded the SA on five occasions between June 2013 and May 2017. As of May 2017, about 545 hybrids and 85 electric cars are part of the Auto- mobile fleet while the SBcs service comprises over 1030 vehicles amongst 413 stations. We have more than one million individual records of FFcs with over 15000 users in 48 months.
The information contains pick up time, location. Further, we also hold information about registration date for both FFcs and SBcs in Montreal are also used in this research. In this research only the information about the aggregate monthly usage frequency of users is used and the registration date.
88 Here we show the number of new users and total usage of system in Figure 6.2 overtime to have a preliminary understanding the development of FFcs service in Montreal. The system are still in the quick development, usage of system is under the continued growth. With established of new service, the number of new users has fluctuated greatly.
Figure 6.2 Introduce of FFcs service in Montreal
89 80000 800
70000 700 Total_Usage New Users 60000 600
50000 500
40000 400 Usage Usage 30000 300
20000 200 Number new of users 10000 100
0 0 0 5 10 15 20 25 30 35 40 45 Time periods since operation
Figure 6.3 New users and usage of system overtime
We distinguish six different states for each person according to the use frequency (see
Table 6.2). The time intervals between subsequent time points are set to one month.
Table 6.2 State Divisions
States Usage Frequency (times in one month)
1 0 2 1-2 3 3-6 4 7-15 5 16-30
6 >30
6.4.2. Estimation Results
In Chapter 5, lifecycle model with 3 stages, Birth, Maturity, and Death, was proposed to describe usage dynamics. While in chapter 6, extended lifecycle model with 5 stages was established to solve the problems in the previous model. In this section, we will make a comparison between these two models to verify the improvement of the extended model. Here we note the previous model as 3-stages, and new model as 5-satges.
90 Estimation in Lifetime
The estimated Stage Transition Matrix and State Transition Matrices are shown in Table
6.3 and It is obviously since adding two stage G and R, more parameters need to be estimated, in 5-stages model the number in stage level is 12 while in 3-staged model only 4 parameters.
Looking at the parameter in states transition, in 흓푩 the parameters are the same due to the same data set. Considering 흓푮 and 흓푹, the new added stages in the extended model, comparisons to 흓푴 are made. In Stage G, results that values near the diagonal of matrix are lower than the ones in stage M, means that people are more active in Stage G, no matter in increasing or decreasing the usage. In Stage G, the value in Lower triangle matrix, especially transition probability to state 1 (inactive), are higher than the ones in Stage M, which tell us the significant drop in usage in stage R.
Considering 흓푀, since in 3-stage model estimation, stage G,M,R in 5-stages model are all treated as stage M, transition probabilities to state 1, state 5, and state 6 are lower obviously. It suggests that in estimation result of 3-stages model more users will in state 2 to 4 and less inactive and high frequency users compared to 5-stages model.
Table 6.4. In Stage Growing and Recession, Green values mean that the parameters in 5- stages model are lower than the ones in Stage maturity while red ones indicate the opposite.
In Stage Maturity, Green values mean that the parameters in 3-stages model are lower than the ones in 3-stage model and red ones also indicate the opposite.
Table 6.3 Transition Matrix in stages for 5-stages and 3-stages model
B G M R D Stage 5-stages 3-stages 5-stages 3-stages 5-stages 3-stages 5-stages 3-stages 5-stages 3-stages
B - - 0.716 - - 0.847 0.158 - 0.126 0.153
G - - 0.707 - 0.279 - 0.014 - - -
M - - - - 0.981 0.962 0.019 - - 0.039
R ------0.772 - 0.228 -
D ------1.000 1.000
91 It is obviously since adding two stage G and R, more parameters need to be estimated, in
5-stages model the number in stage level is 12 while in 3-staged model only 4 parameters.
Looking at the parameter in states transition, in 흓푩 the parameters are the same due to the same data set. Considering 흓푮 and 흓푹, the new added stages in the extended model, comparisons to 흓푴 are made. In Stage G, results that values near the diagonal of matrix are lower than the ones in stage M, means that people are more active in Stage G, no matter in increasing or decreasing the usage. In Stage G, the value in Lower triangle matrix, especially transition probability to state 1 (inactive), are higher than the ones in Stage M, which tell us the significant drop in usage in stage R.
Considering 흓푀, since in 3-stage model estimation, stage G,M,R in 5-stages model are all treated as stage M, transition probabilities to state 1, state 5, and state 6 are lower obviously. It suggests that in estimation result of 3-stages model more users will in state 2 to 4 and less inactive and high frequency users compared to 5-stages model.
Table 6.4 Transition Matrix in states for 5-stages and 3-stages model
Stage Birth
State 1 2 3 4 5 6
5-stage 3-stage 5-stage 3-stage 5-stage 3-stage 5-stage 3-stage 5-stage 3-stage 5-stage 3-stage
1 - - 0.6259 0.6259 0.2313 0.2313 0.086 0.086 0.0363 0.0363 0.0205 0.0205
Stage Growing
State 1 2 3 4 5 6
5-stage 3-stage 5-stage 3-stage 5-stage 3-stage 5-stage 3-stage 5-stage 3-stage 5-stage 3-stage
1 0.6056 - 0.3194 - 0.0445 - 0.0180 - 0.0125 - 0.0010 -
2 0.5046 - 0.2768 - 0.1473 - 0.0496 - 0.0201 - 0.0018 -
3 0.2296 - 0.2743 - 0.2932 - 0.1508 - 0.0399 - 0.0122 -
4 0.1025 - 0.1236 - 0.2433 - 0.2989 - 0.1724 - 0.0594 -
5 0.0505 - 0.0625 - 0.1010 - 0.2139 - 0.3582 - 0.2139 -
6 0.0297 - 0.0169 - 0.0254 - 0.0508 - 0.2034 - 0.6737 -
Stage Maturity
1 2 3 4 5 6 State 5-stage 3-stage 5-stage 3-stage 5-stage 3-stage 5-stage 3-stage 5-stage 3-stage 5-stage 3-stage
1 0.7123 0.6710 0.202 0.2389 0.0689 0.0731 0.0128 0.0131 0.0031 0.0030 0.0009 0.0010
2 0.3696 0.3507 0.3534 0.3771 0.2156 0.2140 0.0526 0.0499 0.007 0.0067 0.0017 0.0015
92 3 0.1521 0.1472 0.2704 0.2926 0.3643 0.3590 0.1794 0.1693 0.0293 0.0278 0.0046 0.0042
4 0.0467 0.0473 0.101 0.1190 0.2779 0.2872 0.3926 0.3767 0.1605 0.1484 0.0213 0.0214
5 0.0208 0.0200 0.0229 0.0312 0.0705 0.0871 0.2503 0.2639 0.4565 0.4335 0.1791 0.1643
6 0.0072 0.0078 0.0078 0.0092 0.0122 0.0193 0.0313 0.0487 0.2193 0.2487 0.7222 0.6663 Stage Recession
1 2 3 4 5 6 State 5-stage 3-stage 5-stage 3-stage 5-stage 3-stage 5-stage 3-stage 5-stage 3-stage 5-stage 3-stage
1 0.9032 - 0.0914 - 0.0054 - 0.0000 - 0.0000 - 0.0000 - 2 0.7473 - 0.1970 - 0.0557 - 0.0000 - 0.0000 - 0.0000 - 3 0.5801 - 0.0634 - 0.3440 - 0.0125 - 0.0000 - 0.0000 - 4 0.3086 - 0.0508 - 0.2756 - 0.3651 - 0.0000 - 0.0000 - 5 0.1719 - 0.0595 - 0.2228 - 0.3937 - 0.1522 - 0.0000 - 6 0.2626 - 0.0300 - 0.1749 - 0.3470 - 0.1856 - 0.0000 -
Observed and Estimated States and stages
Figure 6.4 Estimation and observation of two models in lifetime
93 To evaluate the model goodness of fit let 퐸푗(푡)and 퐴푗(푡) represent the estimated and actual proportion of users at life time t respectively. RMSPE (Root Mean Square Percentage
Error) can then be calculated by the following equation:
푇 푚 2 sqrt(∑푡=1 ∑푖=1(퐸푖(푡)−퐴푖(푡)) ) RMSPE = 푇 푚 × 100% (6-22) ∑푡=1 ∑푖=1 퐴푖(푡)
As shown in Figure 6.4, it is obviously that in state1 to 4, 5-stage model in can fit observation curve much better than 3-stages model. The RMSPE of 3-stages model is 7.17% while the value of 5-stages model is 1.92%. However, in high frequency state 5 and state 6, due to the reduction in user number, more fluctuations are observed. Thus, the gaps between observation and estimation for both two models still exist.
Forecasting in Real time
Dropping Out Users 400 Observation (Revised) 350 Estimation (5-stages model) 300 Estimation (3-stages model) 250 200 150
Number of users of Number 100 50 0 0 5 10 15 20 25 30 35 40 45 Time Periods since operation
Figure 6.5 Dropping Out Users
94 Active Users 7000
6000 Estimation (3-stages model) Estimation (5-stages model) Observation 5000
4000
3000
NumberUsers of 2000
1000
0 0 5 10 15 20 25 30 35 40 45 Time periods since operation
Figure 6.6 Active Users in System
In Figure 6.5 and Figure 6.6, estimation of dropping out users and active users by two models and observation are shown. In drooping out users estimation, value of 3-stages model is higher than 5-stages ones in all time periods. And before time period 35 performance of 5- stage model is better while in later periods the estimation of 3-stages is more closer to observation. In active users estimation, there is no doubt that 5-stages model is better than 3- stage model.
Estimation in Real time 5S E 2 5S E 3 5S E 4 5S E 5 5S E 6 2500 3S E 2 3S E 3 3S E 4 3S E 5 3S E 6 O 2 O 3 O 4 O 5 O 6 2000
1500
1000 Number of Users 500
0 0 10 20 30 40 Time perrid since operation Figure 6.7 Estimation of active users states in real time
95 Finally, looking at estimation of the active users (without state 1) in states level (see
Figure 6.7).Here we use note 5-stages and 3-stages model as 5s and 3s, Estimation and observation as E and O, and state 2-6 as 2-6. For example, 3s E 5 means the estimated result of 3-stages model in state 5. The RMSPE also used to measure the performance of two models in real time. The values of 3-stage model and 5-stage are 16.07% and 13.93%, which are much higher than the values in the life time estimation 7.16% and 1.92%. Though the 5-stages model is much better than 3-stages model in both life time and real time, the errors of 5-stages model in real time, especially in high frequency state 5-6, are still larger than we expected.
From observation, we doubt that there may exist three main factors in this case study to impact the user behavior significantly. First one is seasonal effects, we observed annually fluctuation, especially in winter. Besides, we also doubt the experience of station-based service have large impact on users behavior in this case. Finally is facility extension which may impact not only the number of new users but also users behaviors in system. Since that we will make detailed analysis on impact of experience and facility extension in following sections.
6.4.3. Impact of Previous Experience
Estimation in Lifetime
As mentioned, Communauto, the car sharing service operator, first offers SBcs service and later FFcs service. Since that, some user of FFcs service have the experience of using
SBcs service. In this research, we want to make comparison of these two user groups to show the impact of previous experience on later behavior changes. Here we note users who have the experience as E, and users without experience as N.
Through the method we introduced before, the estimated Stage Transition Matrix and
State Transition Matrices are shown in Table 6.5and Table 6.6. Green values mean that the
96 parameters for non-experience users are lower than the ones for experienced users while red ones indicate the opposite.
Transition Matrix in stages
푛 푛 푒 푒 Stage B: It is obviously that π퐵푅 and π퐵퐷 have higher value than π퐵푅 and π퐵퐷 which means non-experience users more likely to drop out or decrease usage after initial month.
푛 푒 Stage G: Since π퐺퐺 is much lower than π퐺퐺, for non-experience users, they will have shorter time periods at stage G which indicates that the quicker adaptation.
Stage M: Experienced users will stay longer at stage M means there exists more long- term users.
푛 푒 Stage R: Since π푅푅 is higher than π푅푅, for non-experience users, they will have longer time periods at stage R.
Table 6.5 Estimated Parameters for Stage Transition
B G M R D Stage E N E N E N E N E N
B - - 0.9061 0.8962 - - 0.0460 0.0485 0.0479 0.0553 G - - 0.7961 0.3899 0.1765 0.5627 0.0274 0.0474 - - M - - - - 0.9825 0.9702 0.0175 0.0298 - -
R ------0.4590 0.6010 0.5410 0.3990 D ------1.0000 1.0000
Transition matrices in states for stages
퐵,푛 퐵,푛 퐵,푛 퐵,푛 Considering 흓푩 , the lower 푝12 and higher values of 푝13 푝14 푝15 , compared to experienced users, indicate that non-experienced users are more likely to have higher frequency in the initial time period.
Looking at 흓퐺 , since all the values of the upper triangle matrix are higher for non- experienced users, we can infer that quicker adaptation for non-experienced users in Stage G.
Then, for non-experienced at stage M, still most upper triangle values are a little bit higher but no obvious differences exist. Especially when we compare 흓퐺 and 흓푀 for state 1 to 3, it is a
97 bit counterintuitive in stage growth, lower probability for increasing but higher probability for reduction in usage. It suggests that often most users after an initial usage might not immediately increase usage but keeping low frequency until seriously using it (entering into state 3-6) after some time.
Table 6.6 Estimated Parameters for State Transition
Stage Birth (B)
State 1 2 3 4 5 6 E N E N E N E N E N E N
1 - - 0.6790 0.4268 0.2274 0.3001 0.0698 0.1430 0.0193 0.0770 0.0046 0.0531
Stage Growing (G)
State 1 2 3 4 5 6 E N E N E N E N E N E N 1 0.6961 0.6413 0.2294 0.2490 0.0645 0.0996 0.0100 0.0100 0.0000 0.0001 0.0000 0.0000
2 0.5435 0.4034 0.2681 0.3327 0.1331 0.1859 0.0435 0.0629 0.0091 0.0096 0.0027 0.0055
3 0.2599 0.1756 0.2842 0.2774 0.2684 0.3257 0.1401 0.1599 0.0362 0.0496 0.0112 0.0117
4 0.1346 0.0644 0.1389 0.1260 0.2479 0.2603 0.2735 0.3123 0.1560 0.1753 0.0491 0.0616
5 0.0846 0.0280 0.0769 0.0483 0.1231 0.1018 0.2615 0.2087 0.2692 0.3893 0.1846 0.2239
6 0.0588 0.0258 0.0294 0.0185 0.0294 0.0221 0.1971 0.0590 0.2271 0.2362 0.4582 0.6384
Stage Maturity (M)
1 2 3 4 5 6 State E N E N E N E N E N E N
1 0.7194 0.7057 0.1996 0.1985 0.0661 0.0751 0.0119 0.0151 0.0025 0.0048 0.0006 0.0009
2 0.3736 0.3570 0.3535 0.3573 0.2139 0.2192 0.0509 0.0550 0.0071 0.0085 0.0011 0.0030
3 0.1588 0.1499 0.2757 0.2645 0.3603 0.3601 0.1748 0.1837 0.0262 0.0353 0.0042 0.0066
4 0.0468 0.0533 0.1076 0.0997 0.2812 0.2817 0.3929 0.3780 0.1525 0.1645 0.0190 0.0227
5 0.0187 0.0237 0.0242 0.0292 0.0776 0.0706 0.2681 0.2366 0.4460 0.4518 0.1654 0.1882
6 0.0093 0.0090 0.0084 0.0072 0.0152 0.0135 0.0398 0.0257 0.2291 0.2133 0.6981 0.7313
Stage Recession (R) 1 2 3 4 5 6 State E N E N E N E N E N E N
1 0.9760 0.8484 0.0104 0.1324 0.0136 0.0192 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000
2 0.5229 0.9717 0.3542 0.0198 0.1229 0.0085 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000
3 0.3098 0.8484 0.0972 0.0296 0.5930 0.0950 0.0000 0.0270 0.0000 0.0000 0.0000 0.0000
4 0.0278 0.5693 0.0447 0.0569 0.3253 0.2258 0.6022 0.1480 0.0000 0.0000 0.0000 0.0000
5 0.0318 0.2120 0.0314 0.0876 0.1209 0.3246 0.5453 0.2620 0.2706 0.1138 0.0000 0.0000
6 0.0230 0.4042 0.0212 0.0367 0.1342 0.1756 0.4687 0.2453 0.3529 0.1382 0.0000 0.0000
98 Finally, in stage R, as expected, almost no one will transfer to higher frequency state for both the experienced users and no-experience users. However, most of the experienced users in all the states maintain in the last state or transfer to the state just one state lower than last state. We can further observe a quicker decline in usage for no-experience users. Since further,
푛 푒 as discussed before, π푅푅 > π푅푅 there tends to be a longer recession time for non-experience users. Taking these results together, we can infer that there is a higher proportion of inactive users (not dropping out yet but no usage currently) among the non-experience users.
Observed and Estimated States and Stages
Figure 6.8 Estimated and Observed State Distribution
99 We obtain RMSPE푒=1.28% and RMSPE푛=1.34% which show the effectiveness of our models. Estimated results and observed data for the two user groups and the difference of estimated results are shown in Figure 6.8. From the fitting curves and evaluation index, we can see that the model can reflect not only initial changes but also long-term trend perfectly.
Besides, the difference declines for state 1 and increase continually in state 3-6, which means a faster loss of high frequency users for non-experience users.
According to the estimated parameters, lifetime and distribution curve for stages are shown in Figure 6.9, lifetime distribution curves we find that there is a higher proportion of
(fairly) short-term users and less long-term users among non-experienced users. From the estimated results, we can obtain that the average lifetime for experienced users is 57.6 months but only 33.5 months for non-experience users. Looking at detailed data for stages: On average experienced users stay 1.6 months in stage G, compared to 4.9 months for non- experienced users; in stage M, the values are 57.1 and 33.5 months for experienced users and non-experience users respectively; and in stage R, the values are 1.8 and 2.5 months.
We suggest that at the beginning experienced adopters may use station-based and free- floating carsharing system at the same time, so that they will not be in a hurry to enhance the usage frequency in new service. On the other hand, non-experience adopter may be more eager to experience the FFcs. However, they also earlier drop out and instead experienced users show higher stability and loyalty.
100
Figure 6.9 Lifetime and Stage Distribution
6.4.4. Facility Extension
Table 6.7 Service Areas extension of FFcs in Montreal
Service Areas Opening time(since operation) Area（KM2） Active Vehicles
1-PLT Jun-13 (1) 8.0 24
2_RSMT Oct-13 (5) 18.1 24
3_CDN Nov-13 (6) 30.2 64
4_SO Jun-14 (13) 43.1 102-182
5_EST May-15 (24) 78.1 215-543
6_CIRQUE May-17 (48) 85.0 565
101 As mentioned in section 6.4.1, with the development of FFcs service, more and more service areas are becoming available to service users. As shown in Table 6.7, from Jun-13 to
May-17 (data records) there are 5 times extension in service area. Area 2-4 are opened in a short time successively, the impact of each area would be overlap and difficult to distinguish.
Besides, the facility extension in May 2015 makes the total service areas increased from
104km2 to 177.5 km2 (shown in Figure 6.10). Due to the location in urban area, the huge impact of area 5 to the system will be analysis and discussed in this section. Additionally, since area 6 only affect the last month in our data set, we will not consider it in this research.
Thus, we note time from Jun-13 to April 15 as T1, time periods after May 2015 as T2 and make a comparison between these two time periods in user behaviour by using 5-stages lifecycle model.
Figure 6.10 Map of Facility extension in May 2015
102 Estimated Parameters
Through the method we introduced before, the estimated Stage Transition Matrix and
State Transition Matrices for T1 and T2 are shown in Table 6.8 and Table 6.9. Green values mean that the parameters for users in T2 are lower than the ones in T1 while red ones indicate the opposite.
Transition of Stages
푇2 푇2 푇1 푇1 Stage B: It is obviously that π퐵푅 and π퐵퐷 have higher value than π퐵푅 and π퐵퐷 which means more users will drop out or decrease usage after initial month in T2. Besides, significant increment of new users after extension is observed in this case study. In other words, facility extension attract more users who just want to have a trial to new service
푇2 푇1 Stage G: Since π퐺퐺 is higher than π퐺퐺, after extension, new users will have longer time periods at stage G which indicates that the slower adaptation. Also, similar with Stage B, more users will transfer to recession stage in T2.
Stage M: Users in T2 will stay a little bit shorter at stage M means there exists less long- term users than T1.
푇1 푇2 Stage R: Since π푅푅 is higher than π푅푅 , for users in T2, they will have longer time periods at stage R.
In sum, after service area extension, more new user are attracted, however, among them short-time users take up higher proportion.
Table 6.8 Transition Matrix in stage for time before and after facility extension
B G M R D Stage T1 T2 T1 T2 T1 T2 T1 T2 T1 T2
B - - 0.808 0.731 - - 0.097 0.122 0.095 0.147 G - - 0.726 0.762 0.259 0.206 0.015 0.032 - - M - - - - 0.982 0.980 0.018 0.020 - -
R ------0.740 0.700 0.260 0.300
D ------1.000 1.000
103 Transition Matrices of states
Table 6.9 Transition Matrices of States for time before and after facility extension
Stage Birth (B)
State 1 2 3 4 5 6 T1 T2 T1 T2 T1 T2 T1 T2 T1 T2 T1 T2 0.6702 0.6045 0.2325 0.2307 0.0748 0.0915 0.0185 0.0449 0.0040 0.0285 1 - -
Stage Growing (G)
1 2 3 4 5 6 State T1 T2 T1 T2 T1 T2 T1 T2 T1 T2 T1 T2 1 0.6467 0.5905 0.2694 0.2794 0.0645 0.1065 0.0190 0.0230 0.0004 0.0005 0.0000 0.0001 2 0.5497 0.5077 0.2608 0.2509 0.1427 0.1584 0.0363 0.0589 0.0100 0.0189 0.0005 0.0051 3 0.2811 0.2175 0.3079 0.2618 0.2463 0.3048 0.1253 0.1594 0.0340 0.0453 0.0055 0.0122 4 0.1463 0.0951 0.1125 0.1239 0.2563 0.2404 0.3313 0.2938 0.1188 0.1838 0.0350 0.0630 5 0.1789 0.0369 0.0638 0.0567 0.1277 0.0936 0.1702 0.2266 0.3404 0.3596 0.1189 0.2266
6 0.1111 0.0324 0.0149 0.0202 0.0224 0.0283 0.0408 0.0445 0.1134 0.2286 0.6973 0.6459
Stage Maturity (M)
1 2 3 4 5 6 States T1 T2 T1 T2 T1 T2 T1 T2 T1 T2 T1 T2
1 0.7604 0.6947 0.1706 0.2135 0.0573 0.0731 0.0106 0.0136 0.0010 0.0039 0.0001 0.0011
2 0.4071 0.3600 0.3374 0.3576 0.2004 0.2196 0.0505 0.0531 0.0043 0.0077 0.0003 0.0021
3 0.1960 0.1427 0.2826 0.2678 0.3345 0.3706 0.1629 0.1829 0.0228 0.0307 0.0012 0.0053
4 0.0660 0.0434 0.1270 0.0966 0.3072 0.2730 0.3678 0.3968 0.1241 0.1667 0.0079 0.0235
5 0.0282 0.0202 0.0465 0.0210 0.1395 0.0648 0.3605 0.2413 0.3654 0.4639 0.0598 0.1889
6 0.0070 0.0073 0.0225 0.0065 0.0674 0.0113 0.1461 0.0295 0.4145 0.2164 0.3426 0.7290
Stage Recession (R)
1 2 3 4 5 6 State T1 T2 T1 T2 T1 T2 T1 T2 T1 T2 T1 T2
1 0.8332 0.8965 0.1514 0.0914 0.0154 0.0121 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000
2 0.7473 0.7768 0.1970 0.1830 0.0557 0.0402 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000
3 0.5801 0.6231 0.0634 0.0634 0.3440 0.3040 0.0125 0.0095 0.0000 0.0000 0.0000 0.0000
4 0.3086 0.3086 0.0508 0.0508 0.2756 0.2756 0.3651 0.3651 0.0000 0.0000 0.0000 0.0000
5 0.2819 0.3324 0.0595 0.0795 0.2228 0.2028 0.3937 0.3437 0.0422 0.0417 0.0000 0.0000
6 0.3526 0.5668 0.0300 0.0330 0.1749 0.1449 0.3370 0.2470 0.1056 0.0083 0.0000 0.0000
104 퐵,푇2 퐵,푇2 퐵,푛 퐵,푛 Considering 흓푩, the lower 푝12 푝13 and higher values of 푝14 푝15 , compared to user in T1, indicate that users in T2 are more likely to have higher frequency in the initial time period.
Looking at 흓퐺, since almost all the values of the upper triangle matrix are higher for users in T2, which means quicker adaptation. Since T2 users stay longer in stage growth with quicker in usage, it make users enter into maturity stage with higher frequency preference. For
T2 users in stage M, also most upper triangle values of 흓푀 are higher, which suggests that after facility extension stable/long-term users increase the usage frequency overall.
Finally, in stage R, as expected, almost no one will transfer to higher frequency state for both time periods. Moreover, the only higher values in transitions to state 1 and lower in all other values in T2 indicated that users are more likely to be inactive and quicker decline in usage after facility extension.
Estimation in Lifetime
Estimated results and observed data for the two user groups and the difference of estimated results are shown in Figure 6.8. From the fitting curves and evaluation index, we obtain RMSPE푇1=1.53% and RMSPE푇2=1.74% which show that the performances in two periods are both better than using all data as a whole (1.92%). Besides, the difference in user distribution between two time periods keep stable overtime in all states. It suggest that the difference in T1 and T2 have no relationship with time and mainly caused by the new service area.
105
Figure 6.11 Estimation of states in lifetime
Estimated lifetime and distribution curve for stages in T1 and T2 are shown in Figure
6.12. From the lifetime distribution curves we find that there is a higher proportion of (fairly) short-term users (less than 6 months) but similar long-term users (longer than 12 month) among users in T2. From the estimated results, we can obtain that the average lifetime for T1 users is 50.9 months but only 42.3 months for T2 users. Looking at detailed data for stages:
On average users in T1 stay 3.65 months in stage G, compared to 4.20 months for users in T2; in stage M, the values are nearly 54 and 50 months for experienced users and non-experience users respectively; and in stage R, the values are 3.8 and 3.3 months. The main difference in stage level would be more short-term users in T2 while in states level there are more high frequency users (state 5-6) in T2 than ones in T1.
106
Figure 6.12 Estimated lifetime and stages distribution
6.4.5. Model Comparison
ESTIMATION OF STATES
2500 5S E 2 5S E 3 5S E 4 5S E 5 5S E 6 3S E 2 3S E 3 3S E 4 3S E 5 3S E 6 EN E 2 EN E 3 EN E 4 EN E 5 EN E 6 2000 O 2 O 3 O 4 O 5 O 6 2T E 2 2T E 3 2T E 4 2T E 5 2T E 6
1500
1000 Number of user of Number
500
0 0 5 10 15 20 25 30 35 40 45 Time periods since operation
Figure 6.13 Estimation of states in real time for models
107 Table 6.10 Performance of models in life time and real time
Errors in Errors in Models Real Time Life Time 3 stages Lifecycle Model 16.07% 7.17% 5 stages Lifecycle Model 13.93% 1.92% E 1.28% 5 stages Lifecycle Model (considering previous experience) 11.27% N 1.34% T1 1.53% 5 stages Lifecycle Model (considering facility extension) 9.77% T2 1.74%
In previous section 6.4.3-6.4.4, we estimate the parameters for 3-stages model,5-stages model, 5-stages model considering the previous experience and 5-stages model considering facility extension in both life time and real time. Here a comparison of these models on performance are made (see Figure 6.13 and Table 6.10 ). From 3-stages model to 5-stages model, errors decline from 7.17% to 1.92% in life time and 16.07% to 13.93% in real time.
With considering previous experience, we can reduce errors from 1.92% to 1.28% for experienced users and 1.34% for no experienced user in life time and 13.93% to 11.27% in real time. If we take the facility extension into consideration, lifecycle model can reduce the errors from to 1.92% to 1.53% for users in T1 and 1.74% for T2 users in lifetime, and also errors in real time from 13.93% to 9.77%. We can conclude that more stages in model and considering previous experience of users can large improvement in performance in life time while considering impacts of facility extension can reduce the estimation errors in real time significantly.
6.5. Summary
In chapter 6, we propose an improved approach to describe the gradual change of behaviour over time based on research in Chapter 5. We envisage this approach to be particularly useful for describing adaptation to new transport solutions and significant infrastructure investments where users over time learn to appreciate the new or improved system and start using it more. The solution approach is based on Markovian updating.
108 Usually, in Markovian approaches, the assumption of time-homogeneity and a constant population are essential. However, time-homogeneity assumptions are not always suitable in reality and population of system is dynamic due to the new adopters. We therefore draw on the idea of “lifecycle stages” to reflect the dynamically changing total number of potential users and assume that time-homogeneity and Markov property only hold in certain stages. For estimating parameters, we utilize EM algorithm to solve the function which maximizes the likelihood of fitting our observations with latent stages in user lifetime.
The model is applied to panel data from free floating car sharing system in Montreal. At first, we make a comparison of 3-stages model (proposed in Chapter 5) and 5-stages model
(extended model in Chapter 6). The results shows that 5-stages model have better performance in both life-time and real-time estimation. However, in real time estimation result have not our expectation, we doubt that other issues, such as pervious experience of
SBcs service and facility extension may also affect the demand dynamics in this case study.
According to estimation of our models ,the huge differences of behaviours exist in the process of initial trials, adaptation, maintaining, recession and dropping out. Besides, our estimation results illustrate that new users behave generally different to other users suggesting the importance to distinguish adaptation for new and established users. We obtain that for both non-experience and experienced user RMSPE in life time and real time decline which indicates improvement in model fitting. Later, in facility extension, we also compared the estimation parameters before and after new service areas adding to system. The results suggest that high-frequency long-term users and low-frequency short-term users both largely increased, which indicates users in system go into two extremes. Finally, we compared all mentioned models in this chapter. Performance goes better if more issues are considered in estimation. It encourages us to further investigate the use of our models to estimate the behaviour changes also for other applications.
109 There are still a number of issues that need to be addressed in further work. Firstly, in this research, we just estimate the parameters for two groups users in lifetime, however, when it comes forecasting in real time, more issues such as seasonal effects and number of new adopters should be considered.
Beyond estimation, there are still some key issues that need to be discussed. Our current work further considers replacing user states based on frequency only with states based on
“multi-dimensional factors” including, besides frequency, spatial spread in usage and spread by time-of-day.
110 CHAPTER 7. FRAMEWORK OF DEMAND
EVOLUTION
7.1. Introduction
In Chapter 4, we offer a description of details of our adoption models considering spatial heterogeneity and short intervals. In Chapters 5 and 6, we continue by first proposing the stochastic process based 3-stage lifecycle model to describe the dynamics of individual usages and system demand. Then according to observed problems in the case study, we extend our lifecycle model into 5 stages, considering factors, such as facility extension and previous experience. The models for adoption and behaviour dynamics were established separately in
Chapters 4-6, in this chapter we put all these model into a joined framework to describe and forecast evolution of demand the in system level.
This Chapter is organised as following: In Section 7.2, we propose our framework including main factors and methodology according to previous chapters. In Section 7.3, as an example for demand evolution of the car share system Ha:mo, data in Toyota city are used to illustrate how our framework can be used to estimate and forecast system demand over time.
Finally, in Section 7.4 some initial conclusions and possible future research is discussed.
7.2. Framework of demand dynamics modelling
According to the research in Chapters 4 to 6, our Framework can be constructed in three layers (Individual level, Spatial level and System level) and two sections (adoption and demand dynamics) (see Figure 7.1).
The core idea is that at first we establish a model at the perspective of individuals, as mentioned in Chapter 4.2, we conclude the 4-stage adoption process from previous research: knowledge, evaluation, decision and adoption. Also in Chapter 6, we extend behaviour
111 changes for adopters into 5 stages: birth, growing, maturity, recession and death. Combined with two parts, we establish the whole lifecycle model for individuals. Due to the overlap of stage Birth and adoption (both present the starting of new service), there are in total 8 stages.
In the spatial level, we aggregate the individuals with station/area of service by our models. In adoption aspect, we first propose the information spread model to estimate the information with knowledge of stations over time. Then we combine the two stages:
Evaluation and Decision, the diffusion model was established for station with considering the time lag between knowledge and adoption of individuals.
On system level, the demand attraction considers the synergy of stations to estimate the total potential demand and new adopters of system over time. The new adopters of system is also the input of demand dynamics. With new adopters and individual lifecycle model
(Hierarch Hidden Markov Model), individual state of usage over time can be estimated/ forecasted and then aggregated into demand dynamics of system(changes in the number of users in all states).
112
Figure 7.1 Structure of Framework in Demand Evolution
113 7.3. Case study
7.3.1. Ha:mo RIDE car sharing system
As mentioned in Chapter 4, Ha:mo RIDE is a one-way car sharing system operating with small electric vehicles. Once the user has registered, s/he s can reserve vehicles by smartphone from any station and return the vehicle at whichever station is convenient. This system was introduced in Sept 2013 in Toyota City, Japan, as well as later in Tokyo, Grenoble and Okinawa. In the beginning, Ha:mo RIDE in Toyota City had only a few stations. By the end of 2016, after several extensions, there were 59 stations (see ). In this case study, we analyse monthly adoption using the first 40 months of individual rental records until Dec 2016.
Figure 7.2 Ha:mo Stations in Toyota City
114 7.3.2. Estimated parameters
We take the values estimated with adoption model (the Reduced Model in Chapter 4) for this. The full set of estimated parameters and their standard errors are shown in Table 7.1. In general we observe that seasonal effects are highly significant as well as the follower effect and the station’s potential market.
Table 7.1 Parameter estimates and standard errors for the Reduced Model. Significant parameters at
the 95% level in bold
Standard Standard Level Parameter Values Level Parameters Values Error Error 훿9 1 - M9 175.84 12.26 훿1 0.816 0.037 M10 187.28 12.59 훿2 0.944 0.039 M11 169.99 13.09 훿3 0.913 0.040 M12 348.13 20.16 훿4 1.123 0.048 M13 15.54 9.84 훿5 1.054 0.044 M14 26.69 10.07 Time 훿6 1.140 0.044 M15 40.64 10.43 훿7 1.088 0.049 M16 50.16 10.65 훿8 0.969 0.048 M17 139.89 11.75 훿10 0.878 0.056 M18 62.92 11.16 훿11 1.030 0.047 M19 88.04 11.24 훿12 0.927 0.045 M20 399.63 21.83 c 0.001 0.003 M21 230.83 15.28 System q 0.053 0.003 M22 116.19 12.49 a11 0.005 0.005 M23 98.86 12.28 a12 0.304 1.130 M24 112.43 13.31 a13 0.012 0.012 M25 38.22 12.12 a14 -0.179 1.096 M26 76.19 12.68 a15 0.000 0.008 M27 243.15 24.04 Stations a16 0.749 0.825 M28 60.13 12.04 a21 -0.004 0.009 M29 35.92 11.78 a22 0.116 1.807 M30 1.24 11.80 a23 0.008 0.005 M31 2.72 9.55 a24 1.092 1.042 M32 57.34 13.25 a25 -0.005 0.004 M33 156.66 17.96 a26 0.750 1.254 M34 22.48 13.04 Station Groups a31 -0.031 0.084 M35 369.81 21.91 a32 0.876 5.447 M36 46.18 14.97 a33 0.025 0.013 M37 21.22 13.00 a34 0.446 1.495 M38 24.92 13.32 a35 -0.014 0.021 M39 36.45 14.27 a36 0.736 2.159 M40 37.38 14.34 a41 -0.006 0.006 M41 38.23 15.72 a42 -0.183 1.365 M42 36.13 13.80 a43 0.004 0.001 M43 75.71 16.69 a44 0.826 0.459 M44 7.23 11.10 a45 0.004 0.002 M45 29.34 14.07 a46 0.252 0.548 M46 32.76 14.53
115 M1 265.3 15.29 M47 7.94 11.19 M2 35.6 7.94 M48 65.52 18.48 M3 253.4 16.48 M49 68.88 19.94 M4 481.3 24.13 M50 15.49 13.96 Stations M5 131.4 11.15 M51 222.67 20.40 M6 66.6 10.06 M52 30.15 19.36 M7 67.9 10.08 M53 33.97 19.45 M8 313.4 17.18 M54 43.05 19.62
The estimated Stage Transition Matrix and State Transition Matrices are shown in Table
7.2 and Table 7.3.
Table 7.2 Stage Transition Matrix
Stage B G M R D B - 0.5721 - 0.106 0.3219 G - 0.618 0.278 0.104 - M - - 0.971 0.029 - R - - - 0.653 0.347 D - - - - 1
Table 7.3 State Transition Matrices
Birth 1 2 3 4 5 1 0 0.8563342 0.119137 0.019407008 0.005121 Growing 1 2 3 4 5 1 0.667 0.2794 0.0445 0.009 0.0001 2 0.509925 0.3659148 0.10589 0.016917293 0.001353 3 0.230284 0.3533123 0.290221 0.100946372 0.025237 4 0.09434 0.2075472 0.245283 0.320754717 0.132075 5 0.0625 0.0625 0.125 0.125 0.625 Maturity 1 2 3 4 5 1 0.757513 0.2144111 0.025444 0.001754771 0.000877 2 0.413248 0.4548729 0.125475 0.005203122 0.001201 3 0.11867 0.3411765 0.434783 0.094629156 0.010742 4 0.015267 0.0801527 0.341603 0.438931298 0.124046 5 0.030769 0.0153846 0.080769 0.261538462 0.610538 Recession 1 2 3 4 5 1 0.89521 0.09139 0.0134 0 0 2 0.7473 0.197 0.0557 0 0 3 0.5801 0.0634 0.344 0.0125 0 4 0.30855 0.0508 0.27555 0.3651 0 5 0.2619 0.0595 0.22275 0.36365 0.0922
116 7.3.3. Data Analysis
New adopter over time in spatial level and system level
The data of the first 32 months of operation are used to calibrate the models which leads to the estimated results shown in Figure 7.3. For confidentiality reasons, we conceal the real value but report all values as relative to a baseline, which we set as 100 in month 22. We report in the figure estimated models (the reduced model in Chapter 4) and the observed new users. R2 and adjusted R2 of our model are 0.916 and 0.879 shows our model can fit the observation well.
300
Observed new adopters Estimation 250
200
150
100 Number New of adopters
50
0 0 5 10 15 20 25 30
Time periods since operation
Figure 7.3 Observation and Estimation of new adopter
117
Lifetime and Life Stages of Users
1 State 1
0.8
0.6
0.4 Estimation Obsevation
0.2 Proportion of Users
0 0 2 4 6 8 10 12 14 16 18 20 1 State 2 0.8
0.6
0.4
Proportion of Users 0.2
0 0 2 4 6 8 10 12 14 16 18 20
0.12 State 3 0.1
0.08
0.06
ラベル 軸 0.04
0.02
0 0 2 4 6 8 10 12 14 16 18 20
118 0.025 State 4
0.02
0.015
0.01 Proportion of Users 0.005
0 0 2 4 6 8 10 12 14 16 18 20
0.01 State 5
0.008
0.006
0.004
Proportion of Users 0.002
0 0 2 4 6 8 10 12 14 16 18 20 Lifetime
Figure 7.4 Estimation of users states in lifetime
7.3.4. Forecasting
Long-term forecasting
In this case study, we forecast the demand evolution in 100 months to without facility extension and policy changes by our estimated model. The new adopter and dropping out users of system and users in the system are show in Figure 7.5 and Figure 7.6.
From the result, we can know that the new adopter will decline gradually without new stations, but it is obviously users in the system will continue grow for 12 months until month
40, then keep quite stable for 20 month until 60, later keep falling. Since that according to
119 increased number of system users, system can be divided in 3 stages: Growing, Stability, and
Decline.
Forecasting of In and Out of system 300 8,000
In Out 7,000 250 Accumulative Out Accumulative In 6,000 200
5,000 Inand Out
150 4,000 Users Users
3,000 100
2,000 Numbwe Numbwe of 50
1,000 Number of Accumulative Accumulative of Number Users InOut and
0 0 0 20 40 60 80 100 Time periods since operation
Figure 7.5 Prediction of In and Out of Ha:mo System without Facility Extension
1,600 350 User in the system
1,400 In - Out 300 Out) 1,200 250 -
1,000 200
800 150
600 100
400 50
200 0 Number of User NumberUser of inthe system
0 -50
0 20 40 60 80 100 Difference of Users thesystem in (In TIme periods since operation
Figure 7.6 Prediction of Users in the system
120 The observation of users states in first 32 month and estimation results in 100 months is shown in Figure 7.7,From the curve we found that the number of core users(high frequency users in state 4 and 5) will keep stable without facility extension. It will last more than 30 month until obvious decline. However, the low frequency users (state 2 and 3) have short growing and stable stages, less than 20 month the quick decline of number of users will emerge. It may explained by that high frequency users have strong willingness and long lifetime, and low frequency users may drop out quick. Since that, without new adopter attracted by new stations, the low frequency user may quick decline but core users will not lose.
7.4. Summary
In chapter 4, we predict the number of new users registering for a new transportation system due to the existence of specific stations. In Chapter 5 and 6, we describe the gradual change of behavior over time by using the approach based on Markovian updating. In this
Chapter, we combine our adoption model and life-cycle model from three levels (individual level, spatial level, system level) and two parts (adoption and behaviour changes) to forecast the demand evolution in both short-time and long-term.
Our models are applied to data from the first 32 months of operation of the Ha:mo RIDE car sharing system in Toyota. We found that our model performs well in estimation demand evolution over time. Besides, we also draw the conclusion that without facility extension the system users will continue to grow in the short time, then keep stable for quite long time and finally decline. Further, we estimate that the core users (high frequency user) will not be lost but keep using the system at a stable level.
121 600
E2 E3 E4 E5 O2 O3 O4 O5
500
400
300
200 Number of User NumberUser of indifferent states
100
0 0 10 20 30 40 50 60 70 80 90 100 TIme periods since operation
Figure 7.7 Prediction of Users in state
122 CHAPTER 8. CONCLUSIONS
8.1. Summary of Research
The overall objective of this thesis, i.e. explaining the demand evolution of new shared mobility system, have been broken down into two parts and seven tasks, which are: a) to understand the determining factors for aggregated observed adoption of shared mobility service; b) to develop new methodology to describe the adoption process at individual level, spatial level and system level. c) to consider the impacts of facility extension to forecast the new adopters for shared mobility system; d) to understand the determining factors and the impacts for user behaviour changes in shared mobility service; e) to develop new methodology to describe the demand dynamics/evolution at individual level and system level; f) to describe and forecast the demand evolution of new transport system with development. To accomplish the first objectives, Chapter 4 summarized the individual process, including knowledge stage, persuasion stage, decision stage and adoption, and analysis the factors which may affect the adoption for individuals in each stage. Advertisement and Word of month will affect information received in Knowledge stage, and Attributions of service, such as fare, travel time, will influences the service evaluation while accessibility of facility, like network of station, service areas, will decide the individual demand evaluation in Persuasion stage. In decision stage, individual preference and social influence from other users are main factors in the decision making. The second and third objectives are accomplished by propose new models to overcome the problems in previous methodologies. At first, we divide individuals into three groups according to response to new information: fast-adopters, hesitant-adopters and non-adopters, and stations/areas into four types based on land use: Residential Area, Business Area, Public Service Area, and Transit Hub. And then information diffusion model considering the impact of information spread in knowledge stage, adoption model with social influence in decision making, and Demand attraction model focusing on the synergy of the stations are established to describe the adoption process aggregated from individuals to space and from space to system. As an example for adaptation to Ha:mo, a car share system in Japan, data from Toyota city are used to illustrate how well new adopters can be estimated and forecasted over time. In Chapter 5 and 6, the fourth objective is accomplished by assessing the impact of factors in 2 case studies, COGOO,a campus bikesharing system in Kyoto Univeristy, Japan and AuM, free- floating carsharing service in Montral,Canada. In COGOO, we understand and explain sudden
123 reduce and recovery caused by the seasonal effects in summer break. In AuM, the impact of facility extension and pervious experience on users behaviour changes are discussed. Also in Chapter 5 and 6, we propose a novel approach to describe the gradual change of behaviour over time by using the approach based on Markovian updating. Usually, in Markovian approaches, the assumption of time-homogeneity and a constant population are essential. Actually, it does not hold. Drawing on the idea of “lifecycle stages”, “potential demand” and “willingness” from marketing, we assume that time-homogeneity and Markov property only hold in certain stages and seasonality will impact the potential demand. The final and ultimate objective is partly accomplished in the framework of methodology. We combine models from three levels (individual level, spatial level, system level) and two parts (adoption and behaviour changes) to forecast the demand evolution in both short-time and long- term.
8.2. Contributions to knowledge
This dissertation provides methodological, theoretical, and empirical contributions to the transportation field. In theoretical and methodological part, the first contribution is that considering information diffusion process in diffusion model, which can be used to explain the initial peak observed in data with short intervals. These contributions solve the problem that traditional diffusion model can only fit the annual data but lack of ability to explain data with short intervals, such as monthly data. Another contribution is the extension of aggregated diffusion model from system to spatial level. The core idea is that the decomposition of the total market into several smaller markets according to spatial characters and then with considering the synergy, these small ones aggregates into total market of system. Besides, in methodology part, using unbalance coefficient which calculated by in and out users in day time from trip data can easily classify stations/area and identify the type of land use rather manual investigation. Further, this dissertation contributes to methodology to describe individual behaviour dynamics, first, by introducing the concept “life-cycle” in marketing to present the process that from entering to leaving the system for individuals. Secondly, concepts that “potential demand” and “willingness” introduced from marketing can used to explain the observed phenomenon that sudden decline and recovery of observed usage due to seasonality. There two innovations help us to solve the two difficulties, dynamic population and time-heterogeneity in Transition, in applying Markov models in new transport service.
124 Moreover, the difficulty in distinguish in dropping out users exist since that they can not often be distinguished directly from the observed data unless users clearly “sign-out”. In order not to overestimate the likelihood of users returning, we propose a probability-based method considering time periods between observed last usage and final time period in database. It plays important role in state identification and parameters estimation in this research. Another important contrition in methodology is that the introduction of latent stages in life- cycle model, in this way we extend three stages into five ones, which can reduce the estimation errors and improve forecasting accuracy significantly Additionally, the empirical contribution is mainly on using three different case study from different shared mobility modes (Campus bikesharing, Station-based Carsharing, Free-floating Carsharing), cities (Kyoto, Toyota, Montreal), and market sizes (small, medium, large). The key findings are follows: 1.Two peaks in adoption and diffusion curve We observed two peaks in monthly data analysis in adoption, which is seldom mentioned in other related studies. The initial peak of subscribers might come through advertisement and currently latent demand. The second peak might occur during later time periods when the market enters saturation.
2. Diffusion patterns for stations In case study of Ha:mo, stations are divided into 4 groups according to land use: Residential area, Business area, Transition hub and Public service. We found that within the groups, some of the parameters are significantly correlated: M and a, M and p, as well as a and I have a relatively strong linear relationship, without grouping none of these correlations are significant. It shows that land use would be the key point affect the adoption pattern in spatial level.
3. Winter effects in adoption In case study of Ha:mo, we estimate the monthly coefficients 훿 ,which can be roughly divided into three groups. From Dec to Mar, 훿 is lower than 0.95, from April to July, 훿 is in the range of 1.05 to 1.15, and from August to November 훿 is in the range of 0.95 to 1.05. The observed winter effect can be explained by simple equipment of vehicle in heating and windproof and New Year holidays.
4. Characters in Transition Matrix We observe that most of the users in all the states maintain in the state which they were in the last period. Besides, the probability of jumps between more than one status level (e.g. state 1
125 to 3 or state 4 to 2) is very low. This suggests that users tend to change their habit gradually. Besides, probabilities of transition from high frequency state to dropping out was zero and almost all dropping out users came from low frequency users. This means that “sudden exits” are very rare and rather giving up this transport mode is a gradual process.
5. Sudden decline and Recovery in user behaviour changes In the case of COGOO, a campus bikesharing, we observed sudden demand decline in the summer break, the number of potential high frequency users drops, and there are more users who make use of only a few times, and after that the demand recovery immediately. To explain that we introduce the concepts, such as potential demand and willingness, to establish our new model.
6.Impacts of previous experience and facility extension on user behaviours In the case of AuM in Montral, we observed huge difference of user behaviour between users with experience of SBcs service and the ones without it, and also time periods before and after facility extension. In the previous experience of SBcs, non-experience adopter have quick adoption but lower life time and less high-frequency users. We suggest that at the beginning experienced adopters may use station-based and free-floating carsharing system at the same time so that they will not be in a hurry to enhance the usage frequency in new service but they have higher stability and loyalty. In the facility extension, the results suggest that high-frequency long-term users and low- frequency short-term users both largely increased, which indicates users in system go into two extremes.
8.3. Limitations of the study and opportunities for further works
Even though our framework of models performs well in estimation and forecasting adoption and demand dynamics for new transport system, there are still some limitations and a number of issues that need to be addressed in further work. In modelling part, to describe adoption process in spatial level and individual state transition, large number of parameters are need. For example, in adoption models the total number is n+37 (n is the number of stations in system), and in 5-stages life-cycle model, the number is 123 (stage transition 10 parameters, state transition 113 parameters). Since the numerous parameters, overfitting would be a risk in doubting the effective of our model. Actually, in this research, we discussed a classification of stations into four types and found that assuming constant parameters for each station type can reduce the parameter and also fit the model well, and in fact it improves
126 the forecasting power. In later works, with better understand of these parameters, it is feasible to reduce the number of parameters and improve forecasting ability at the same time. Besides, another limitation is the estimation for unknown new stations. Without observed data we can not forecast parameters and future demand for the new stations, since that the factors, decide six parameters of stations, are still not clear. Our focus has been on the description and demonstration of the methodological framework. In further work, we will test different classifications, further explore the relationship between the parameters as well as their relationship to network specifics, geographic details, and socio- demographic. This as well as analysis of parameter stability depending on opening time of the station we suggest also as directions for further work. As introduced in framework of methodology, it contains models in three levels (individual level, spatial level, system level) and two parts (adoption, behaviour dynamics). However, due to the complexity of users behaviour changes in space, we have not full understanding on these patterns in shared mobility service right now. User behaviour dynamics in spatial level is blank in our current research and will be important part in our future work. Moreover, in our current framework, the connection between adoption and behaviour dynamics is just in the system level, the adoption model forecast the number of new adopters in system for demand dynamics forecasting. In fact, in individual level and spatial level, adoption pattern of individuals and stations/areas would decide the demand evolution in the future to some extent. The relationship between adoption and later behaviour changes would be key work to have better understanding on demand evolution for shared mobility service. Beyond estimation and forecasting, there are still some key issues that need to be discussed such as “critical points” in the transition matrices that distinguish whether a system with a certain pool of incoming users would mean the system continuously grows. Related to this are issues of stability analysis and (long-term) equilibria, if there are any. In particular of interest will be how resilient systems might be against demand-shocks that we can create in our approach through the potential demand vector. Finally, though our methodology is of universal applicability and transplantability, it still needs real operation data for a period of time to calibrate the large number of parameters. It means that we can not forecast a new transport system in a new city before the establishment of the system. More data, such SP Survey before application of new system, may be needed to add to our work to understand how the willingness of potential users affect the parameters of system in demand evolution.
127 Reference
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