DEVELOPING A SYSTEM OF SYSTEMS FRAMEWORK FOR AN INTEGRATED TRANSPORTATION SYSTEM USING SYSTEM DYNAMICS

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DEVELOPING A SYSTEM OF SYSTEMS FRAMEWORK FOR AN INTEGRATED TRANSPORTATION SYSTEM USING SYSTEM DYNAMICS

Sayanti Mukhopadhyay1,2, Mohamed E. Hassan1 and Ali Shafaat1 1 Construction Engineering and Management, School of Civil Engineering, Purdue University , U.S.A 2 [email protected]

Abstract: Demand forecasting plays an integral role both in planning and managing urban transportation

infrastructure. Analyzing travel demand is an integral part of any transportation system. Different types of demand forecasting models are being used by transportation industries not only to plan for renovation and expansion but also to evaluate several policy scenarios associated with the particular infrastructure

system. The traditional demand forecasting models that exist mostly focus on individual transportation sectors such as air-transportation, highways, etc. and not much attention is given to consider the interdependencies and complexities among the various components and thus many-a-times ignore the

emergent behaviors. To overcome this deficiency, the research study applied a system-of-systems approach to forecast the overall public transport demand considering all the different sectors of the transportation network of an integrated public transport system. However, forecasting the public demand

for each transportation mode is a major challenge as it depends on several uncertain factors such as population growth, GDP growth of the country, traffic congestion on roads, average annual income of population, ticket prices, travel types and others. System dynamics modeling approach was adopted to

represent the information and physical flows among the different components / entities within a system at an aggregate level with high degree of accuracy. These types of models would help the decision makers in evaluating several policy scenarios by altering the model variables and developing investment

strategies for future transportation infrastructure planning. This research paper developed a conceptual framework to assess the public demand for individual transportation modes in an integrated transportation network using Abu Dhabi’s surface transport expansion and integration project as a case study .

1 INTRODUCTION

Abu Dhabi is undergoing a rapid and visionary transformation to get established as a world-leading city and the Abu Dhabi Surface Transport expansion and integration project is the core for such an

infrastructure expansion involving multimillion dollars of investments. The “Plan Abu Dhabi 2030” Urban Structure Framework Plan attempts to envisage the year 2030 and provide the basis for future growth accordingly. The Surface Transport Master Plan (STMP) commissioned in February 2008 developed the

conceptual transportation strategy into a detailed Master Plan and an implementation program based on the outline provided in Plan Abu Dhabi 2030. The plan addresses the regional transport needs of the Emirate as a whole, while focusing particularly on metropolitan Abu Dhabi. The challenges in this plan are

the current congestions, which are swiftly approaching to full capacity, as well as the drastic increase in demand owing to increasing population. The population increase is mostly due to an estimated 400% increase in gross area of the city, six million additional office space leading to huge economic growth, and

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a four-fold increase in the number of regional and international visitors (Abu Dhabi DoT 2009). Currently, private passenger car mode of transport is involved in around half of all daily person-trips while public bus

transportation is approximately one percent. Reliance on private cars and taxis is the main reason for congestion. As growth continues, a multi-faceted, multi-modal transport system will be vital to creating a vibrant, sustainable world-class city (Abu Dhabi DoT 2009). By 2030 the integrated public transport

network is expected to comprise of a high-speed rail service to Dubai; some 130 km of metro railway, regional rail connections; over 340km of tram lines served by bus feeder services and a passenger water transport network. The system will also include all of the supporting Intelligent Transport Systems (ITS)

and unified automatic fare collection systems (Abu Dhabi DoT 2009). Forecasting the demand on the overall network as well as its components is an essential task to facilitate proper design and management of the transportation system in order to meet its objectives.

The major objective of this paper is to develop a framework that would eventually foster the analysis of how the interdependencies between components of an integrated public transport can affect the overall demand based on the demand fluctuations of the individual modes of transport. The demand for

individual modes of transport is extremely uncertain as it depends on GDP, population, roads congestion, price, level of service of each mode, and congestion of each transportation mode all play an important role in determining the overall demand on the public transport network as well as the demand on the

individual modes. The System Dynamics model framework developed based on a SoS approach would allow to forecast the passenger demand for an integrated transport network based on the demand on individual modes once the real data is available. This would also provide a platform to the decision maker

to test a combination of policy scenarios designed to suffice the overall objectives of a Transport Integration Project. The following sections of the paper provide a description of the research objectives, a brief summary of the reviewed literature, model development methodology, model framework and finally a

discussion on the framework developed and conclusion.

2 BACKGROUND: SYSTEM OF SYSTEMS & SYSTEM DYNAMICS IN TRANSPORTATION DEMAND

A system-of-systems (SoS) is defined as a “set or arrangement of systems that results when independent and useful systems are integrated into a larger system that delivers unique capabilities” (Office of the Deputy Under Secretary of Defense for Acquisition and Technology 2008). A SoS can be differentiated

from a monolithic system based on several aspects such as autonomy, belongingness, connectivity, diversity, and emergence (Boardman and Sauser 2006; Liu 2011). Other advantages as offered by SOS approach include operational and managerial independence of the components, geographic distribution,

evolutionary behavior, emergent behavior and consideration of heterogeneity of the system components (Maier 1998; Delaurentis 2005). However, the two most important advantages as mentioned above are “operational independence” and “managerial independence” of the components. These aspects specify

that in a SoS the sub-systems are “useful in their own right and generally operate independent of other systems”.

System Dynamics (SD) modeling is one of the tools used for studying dynamic problems arising in

complex systems, such as social, managerial, economic, or ecological systems. As defined by Richardson (2011), SD is the use of informal maps and formal models with computer simulation to uncover and understand endogenous sources of system behavior”. Like some other modeling

approaches, most notably Agent-Based Modeling, SD is also a bottom up system modeling approach that aggregates representations of component processes and their relationships that helps to understand the underlying structure of the system (North and Macal 2007). SD can be further used to trace this behavior

over time at discrete points and to analyze how a change in a specific part of the system can affect that behavior (Martin & Forrester 2001). According to Richardson (2011), the SD approach involves defining problems dynamically, in terms of graphs over time; focusing inward on the characteristics of a sy stem;

considering dynamic behavior of a real system and formation of loops, feedbacks and circular causality; identifying independent stocks or accumulations (levels) in the system and their inflows and outflows (rates); formulating a behavioral model using a computer simulation model expressed in nonlinear

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equations; getting the outputs, deriving understandings and applicable policy insights from the resulting model; and finally implementing changes.

System Dynamics (SD) has been used repeatedly in modeling surface or air transportation networks for studying, inter alia, the effect of a set of identified factors on the demand on the said networks and others. Selected examples from the literature include the works of Wang, Lu, and Peng (2008), Haghani, Lee,

and Byun (2010), Suryani, Chou, and Chen (2010), Yevdokimov (2002), Wang et al., (2005), and Stave (2002). All the aforementioned research studies have treated the transportation network from a single mode perspective without recognizing that it is in fact composed of a group of interconnected systems.

This research builds on the aforementioned studies by viewing the surface transportation network from a system-of-systems approach through recognizing the managerial and operational interdependence of each transport mode whilst considering the interconnections and interdependencies between the SoS

components. It is worth mentioning that Agusdinata, Fry, and Delaurentis (2011) in their work followed a SoS approach to take into account the complexity of a multimodal transportation system in assessing the carbon emission impact of on-demand air service and automobiles.

3 MODEL FRAMEWORK DEVELOPMENT PHASES

The System Dynamics model framework based on System-of-Systems (SoS) approach was developed in two phases namely definition phase and abstraction phase. A description of each of these phases are

provided below:

3.1 Definition Phase

The definition phase encompasses identifying constituents of the SoS, mapping traits of the SoS and

categorize the network levels by utilizing the established SoS lexicon.

3.1.1 Constituents of the Systems of Systems

The integrated multimodal surface transport system of Abu Dhabi is solely targeted to provide an efficient and pleasant mode of transportation to the public that might include a number of modes of transport in a

single journey. The total demand on the integrated transportation system would be thus dependent entirely on the availability and convenience of the individual modes of transport. In order to suffice this motivation, the two major criteria that should be taken into account are a comprehensive planning from

macro level ensuring that all the individual modes of transport are effectively coordinated with each other and incorporation of Intelligent Transport Systems (ITS) such as automatic ticketing, travel planning, updates of departure and arrival times, etc. The individual modes of transport, referred here as

components of the transportation systems-of system (SOS) include roadways, high-speed regional train, metro network, tram network, bus service, ferry and water taxi service.

3.1.2 SOS Traits Mapping and Design Principles

The SOS traits and design principles needed to establish the Integrated Public Transportation System of

Abu-Dhabi as a system of systems comprising of different individual modes are identified in Table 1 (Maier 1999 and DeLaurentis 2005).

Table 1: SoS Traits Mapping and Design Principles

Trait/Design Principle Applicability

Managerial

Independence of the components

The component systems are acquired by separate program management offices

and run by separate operational units.

Operational

Independence of the

Operation would be mostly through the government action and would be run by

different public agencies at different levels independently, but with a common mission to provide optimized service to the public and also improving the

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Trait/Design Principle Applicability

components economic, environmental, social, and cultural scenarios for the Abu Dhabi city.

Geographically distributed

The individual system components are not collocated and are distributed according to their needs and accessibility.

Heterogeneity The constituent system components are significantly different from each other and they operate on different elementary dynamics

Stable Intermediate

Forms

A variety of stable intermediate forms, both in time and space, are evident in the

design of the component systems.

Policy Triage Individual system components are directed and controlled by the individual service providers maintaining a communication and a level of collaboration with

the other system components.

Leverage at the interfaces

Multiservice system of integrated public transport system concentrate on information transfer

Emergent behavior Demand forecast of the entire system is not evident from demand of the individual system components as they operate on different elementary dynamics

Networks Networks define the rules of connectivity between the different semiautonomous

system components

Ensuring Collaboration

All the systems should work collaboratively in order to provide both optimized service to the public and the expected profit to the government.

Directed SoS The integrated public transportation system will be developed and operated to fulfill a particular purpose of reducing congestion and provide best services to the public through formal organizations, policies, etc.

3.1.3 SOS Lexicon and ROPE Table

The following ROPE (Resource, Operations, Policy, and Economics) table (Table 2) shows the Abu Dhabi

Integrated Public Transport Network in SoS lexicon and taxonomy terms. This is considered to be an

important initial step in development of our model framework. Based on nature of the research problem described hereunder, the scope of the proposed model will tentatively be restricted to the Resources, Operations, and Policy elements of the β and the γ levels. As highlighted in the ROPE table, our focus is

mainly to study the interaction between the different modes of the transport system and how their interaction affect the overall transportation system of Abu Dhabi. Each mode is an independent system and thus their interaction is expected to reveal some of the interesting emergent behaviors for the overall

system, i.e. from a systems-of-systems perspective. This research covers both the vertical and horizontal interactions within the boundary specified in the above ROPE table.

Table 2: SoS Lexicon and ROPE Table

Level Resources Operations Policy Economics

α Vehicles and Infrastructure (buses,

ferries, metros, railways, trams, etc.)

Operating an individual resource (e.g. a bus, a

ferry, a metro)

Policies relating to single resource use

Economics of building/operating/

buying/selling/ leasing a single resource

β Set of resources performing a common

function (e.g. buses, ferries, metros)

Operating resource networks for common

function (e.g. Abu Dhabi bus network, ferries network, metro network)

Policies relating to multiple resource use

Economics of operating/buying/se

lling/leasing resource networks

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3.2 Abstraction Phase

Abstraction is the most important step in developing a framework for a model. Its main purpose is to identify the key entities of actors, effectors, disturbances, and interdependency networks. Lewe and DeLaurentis (2004) identified four categories of entities such as explicit, implicit, exogenous, and

endogenous. Entities are further classified as Endogenous-Explicit (Resource Network), Endogenous-Implicit (Stakeholder Network), Exogenous-Explicit (Disruptors), and Exogenous-Implicit (Drivers). Using the same approach, the following sections provide a description of the entities identified for our integrated

public transport network model.

3.2.1 Resource Network

At the beta (β) and the gamma (γ) levels of the transportation system, the resource network can be viewed as a set of interconnected entities, each represented by a transportation mode, all having the

common goal of reducing congestion and providing quality and convenient services to the public. The major modes considered in modeling Abu Dhabi’s surface transport network include highways , private transport (private vehicles

and taxis) and public transport (rail, metro, bus, tram, and water ferries)

systems. The attributes of these modes are assumed to be (1) average speed of

the mode; (2) accessibility and range; (3) operation cost; (4) fare; (5) capacity; (6) delay time; (7) intermodal

capability and (8) connection time. It is noteworthy that each transportation mode

has its own unique set of attributes that differentiates it from the other modes and

makes it a more favorable to a certain group of users (i.e. passengers). Figure 1 shows various transportation modes that are interconnected at the beta (β) level

forming the gamma (γ) level that comprises Abu Dhabi’s integrated public transport network. The transportation network of Abu Dhabi is further connected to that of other states within the United Arab Emirates forming the UAE’s national surface transportation system but it is not in the scope of this

research. Interactions and communications between the resource-network entities are expected to occur both horizontally (between the different modes as well as between the UAE states) and vertically (in a hierarchical sense) for management and coordination between the system components on technical,

γ Resources of multiple transport modes forming the Public

Transport Network

Operations of Abu Dhabi Public Transport Network

Policies relating to Abu Dhabi public transport network (e.g. unified

tickets for all systems)

Economics of Abu Dhabi public transport network

δ Resources of UAE surface transportation system

Operations of UAE surface transportation network

Policies related to surface transportation network all over UAE.

Economics of surface transportation

network in UAE.

ε Gulf Cooperation

Council (GCC) surface transportation network

Operations of GCC

surface transportation network

Policies relating to the

GCC surface transportation network

Economics of

surface transportation network of GCC.

Figure 1: Levels of the integrated transport network

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economic, policy, and administrative aspects. Such interactions and communications take place through the various federal and governmental bodies as described below in the “Stakeholders” section.

3.2.2 Stakeholders

Similar to any public transportation system, there is a wide range of stakeholders in Abu Dhabi integrated public transport network. As the project is in planning stage, several entities are being acknowledged as stakeholders of the transport network but not yet fully established. Users can be considered as primary

stakeholders in the transportation network. They are the ones who create the demand on the transport modes and their attributes would determine the most preferred mode of transportation on the beta (β) level. Each user has his/her special travel pattern, car availability, trip purposes, and personal

preferences; however, only the aggregation of these alpha (α) level attributes will show on our model as an aggregation. At the country level, federal institutions such as National Transport Authority (NTA) in United Arab Emirates are responsible for development and implementation of transport policy of the

entire country. At the state level, Department of Transport (DoT) is the main institution with responsibilities of developing general transport strategy, implementing the emirate’s air, land and sea transport policy, making recommendations to the government on setting up corporations in the related sectors, legislation,

privatisation and tariffs. Now, modeling the attributes and behaviors of such stakeholders through a System Dynamics approach can prove to be a challenging task due to the limitations of such modeling technique. However, the directed nature of this System-of-Systems, as mentioned above, and by

assuming that all stakeholders of relevance to our research problem, described herein, work together to achieve one single goal –rather than competing goals- made such modeling task feasible.

3.2.3 Drivers

Driver entities affect the behavior of the stakeholders and these can be categorized as economic,

societal, and psychological (Lewe, DeLaurentis, & Mavris 2004). These drivers play an instrumental role

in creating the demand on one or more of the transportation modes as well as in determining several transportation policies such as the tariff structure. Examples of drivers in our model include the following: (i) Population growth is deemed to be one of the core indicators of total demand on surface

transportation network; (ii) GDP growth is of pivotal importance because population and demographics are directly affected by a change of GDP in Abu Dhabi which subsequently impacts demand on the network and its components; (iii) Passengers’ behavior: Abu Dhabi government has declared its

ambitions of convincing residents to change their behavioral patterns and choose public transport for many of their daily trips in an attempt to reduce congestion and gas emissions from vehicles.

3.2.4 Disruptors

Disruptors are entities that are unfavorable and can affect the efficiency of the system. In the surface

transport network, disruptors can directly result in the decrease of demand on the entire network or on

one of the modes, each with a unique degree of effect. Examples of disruptors include (i) natural disruptors such as inclement weather. Abu Dhabi is known to have a hot arid climate throughout the summer and during the hot season the demand on transportation modes that may require short walks

between nodes (between metro stations) or waiting time in an open space (bus station) will decrease causing a mode shift by users and (ii) artificial disruptors such as financial crisis. A financial crisis will directly result in a decreased number of expatriate workers and tourists, which will eventually decrease

the total demand on the transportation network as the workers and tourists are believed to be the main potential users of the transportation network upon its completion.

4 MODEL FRAMEWORK

As highlighted earlier, total demand on the transportation network as well as individual demands on various transportation modes is believed to be influenced by several factors such as population, demographics and economy. To that end, the framework of our System Dynamics model is in form of a

causal loop diagram that is composed of multiple interconnected sub-models. The sub-models as shown in Figure 2 are: (1) population sub-model; (2) migration sub-model; (3) GDP sub-model; (4) car ownership

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sub-model; (5) demand and mode attractiveness sub-models. The sub-models are connected by means of feedback loops. Each feedback loop has either a reinforcing or a balancing effect. For example, a

population growth (out of the population sub-model) increases the congestion; on the other hand an increased fare for a transport mode will most likely result in decreasing the congestion in that mode. The relationships are based on information from existing literature, basic concepts and assumptions . The

different types of sub-models considered to be the building blocks for developing the framework of the requisite model are as follows:

Population Growth & Migration Sub-models

Typically, the population growth will directly lead to more travel demand. Demand on the individual modes will also change, thus affecting the total demand on the integrated transportation system. Total population on the other hand is affected by the birth and death rates.

GDP Sub-model As discussed before, increase in GDP of a country affects the travel demand by attracting more people to settle in that area. A decrease in GDP on the other hand might lead to emigration and thus decrease the overall travel demand and change demand on the individual travel modes.

Car Ownership Sub-model Car Ownership, also considered as a level variable, plays an integral role in determining the demand on the private transportation network. Higher number of car ownership might lead to higher road congestion

level and render the other modes of travel such as metro, rail and water ferry to be more convenient. However, the emergent behavior of the system cannot be predicted and it is unique for each individual scenarios.

Demand Sub-models The demand sub-models include multiple auxiliary variables such as private and public transport attractiveness, people availing private transport, bus demand, HSR demand, metro demand, tram

demand, and water ferry demand (shown in Figure 3). The attractiveness of each mode is assumed to be affected by road traffic congestion, fare, and level of service.

Figure 2: System Dynamics Paper Model – Part 1

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Bus Demand

Metro Demand

HSR Demand

Tram Demand

Water Ferry

Demand

Bus Fare

Bus Crowdness

Bus LOS

Bus Attractiveness

Metro Fare

Metro Crowdness

Metro LOS

Metro

Attractiveness

HSR Fare

HSR Crowdness

HSR LOS

HSR

Attractiveness

Total

Attractiveness

Tram Fare

Tram Crowdness

Tram LOS

Tram

Attractiveness

Water Ferry

Attractiveness WF Fare

WF Crowdness

WF LOS

<Metro

Attractiveness>

<HSR

Attractiveness>

<Tram

Attractiveness>

<Total Transport

Demand>

<Total Transport

Demand>

<Traffic

Congestion>

<Traffic

Congestion>

<Traffic

Congestion>

<Population

Growth Impact>

<Population

Growth Impact>

<Population

Growth Impact>

Figure 3: System Dynamics Paper Model – Part 2

5 RESULT DISCUSSION

The framework developed in this paper would provide an essential tool for analyzing how a demand change for a particular mode would affect the total demand on the integrated transportation system. This

would serve as an important decision making tool for the policy makers and investors to plan for the integrated transportation system. A major limitation of system dynamics model is that it requires mathematical relationships to run the simulation and study several scenarios and policies. Lack of data is

a major problem in developing such types of system of system models. However, as a proof of concept we developed a hypothetical situation and run the model with synthesized data. The outputs of the simulation with respect to different time periods is given in Table 3.

Table 3 - Base Model and Scenarios Parameters Values

Parameter Base Model (at t=360 months)

Scenario 1 Scenario 2

Population 6.5575 million capita 8.84527 million capita 3.93426 million capita

GDP $231,945 million/capita $398,875 million/capita $312,742 million/capita Migration 902,057 persons 2,191,580 persons 206,826 persons Private Transport Demand 256,733 (active) cars 367,571 (active) cars 214,193 (active) cars

Metro Demand 476,922 passengers 644,543 passengers 294,486 passengers Tram Demand 527,064 passengers 709,869 passengers 323,352 passengers Bus Demand 554,948 passengers 736,404 passengers 244,551 passengers

HSR Demand 373,289 passengers 502,995 passengers 229,214 passengers

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6 CONCLUSIONS AND LIMITATIONS

This paper presented a system dynamics model framework for an integrated public transport network based on a system-of-systems approach. The model can be used to forecast passengers demand on a public transport network as well as on individual modes such as bus, metro, tram, HSR, and water ferries.

The model can be further used to evaluate multiple scenarios by changing the values of variables and

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rates incorporated in the model to show how the demand will change if GDP, migration rate, fare, crowdness, and level of service are changed for example. Several constraints and assumptions were

made in developing and implementing the model. These include limiting the model to cover only passengers with no allowance for freight transportation, which resulted in omitting trucks and rail freight transport from the network. In addition, the model assumes that all stakeholders have the same objective

of providing quality transportation services to the residents of Abu Dhabi. Profit making by the operators of each transport mode is not recognized as an objective of the stakeholders. In other words, the different transportation modes do not compete with each other but rather collaborate. Since the actual project is

still in an early design phase, the capacity of each transportation mode as well as the fare are not yet determined.

References

Abu Dhabi Department of Transportation (DoT) (2009). Surface Transport Master Plan. Agusdinata, D. B., Fry, D. N., & Delaurentis, D. A. (2011). Policies to deal with multimodal transport

emissions: a system-of-systems approach. Transportation Planning and Technology, 34(2), 109-123.

Boardman, J., & Sauser, B. (2006, April). System of Systems-the meaning of. In System of Systems Engineering, 2006 IEEE/SMC International Conference on (pp. 6-pp). IEEE.

DeLaurentis, D. A. (2005). Understanding transportation as system-of-systems design problem. In 43 rd

AIAA Aerospace Sciences Meeting and Exhibit (p. 2005). DeLaurentis, D., & Callaway, R. K. (2004). A System‐of‐Systems Perspective for Public Policy Decisions.

Review of Policy Research, 21(6), 829-837. Haghani, A., Lee, S. Y., & Byun, J. H. (2010). A system dynamics approach to land use/transportation

system performance modeling part I: methodology. Journal of advanced transportation, 37(1), 1-41.

Lewe, J. H., & DeLaurentis, D. A. (2004). Entity-centric abstraction and modeling of future transportation architectures. In Proceedings of the 45th Transportation Research Forum, Evanston, IL, Paper 2C-4.

Lewe, J. H., DeLaurentis, D. A., & Mavris, D. N. (2004, August). Foundation for study of future

transportation systems through agent-based simulation. In 24th ICAS Congress. Liu, S. (2011). Employing system of systems engineering in China's emergency management. Syst ems

Journal, IEEE, 5(2), 298-308.

Maier, M. W. (1998). Architecting principles for systems-of-systems. Systems Engineering, 1(4), 267-284. Martin, L. A., & Forrester, J. W. (2001). The first step. MIT. North, M. J., & Macal, C. M. (2007). Managing business complexity: discovering strategic solutions with

agent-based modeling and simulation. Oxford university press, USA. Office of the Deputy Under Secretary of Defense for Acquisition and Technology, Systems and Software

Engineering (2008) Systems Engineering Guide for Systems of Systems, Version 1.0. Washington,

DC: ODUSD (A&T). Richardson, G. P. (2011). Reflections on the foundations of system dynamics. System Dynamics Review,

27(3), 219-243.

Sargent, R. G. (2001). Some approaches and paradigms for verifying and validating simulation models. In Simulation Conference, 2001. Proceedings of the Winter (Vol. 1, pp. 106-114). IEEE.

Sargent, R. G. (2010). Verification and validation of simulation models. Winter Simulation Conference

2011: 183-198. Stave, K. A. (2002). Using system dynamics to improve public participation in environmental decisions.

System Dynamics Review, 18(2), 139-167.

Suryani, E., Chou, S. Y., & Chen, C. H. (2010). Air passenger demand forecasting and passenger terminal capacity expansion: A system dynamics framework. Expert Systems with Applications, 37(3), 2324-2339.

Wang, J., Lu, H., & Peng, H. (2008). System dynamics model of urban transportation system and its application. Journal of Transportation Systems Engineering and Information Technology, 8(3), 83-89.

Wang, Y. P., Yang, Z. F., Li, S. W., Kui, H. L., & Wang, L. F. (2005). Prediction model of road

transportation volume based on system dynamics. Journal of Jilin University (Engineering and Technology Edition), 35(4), 426-430.

Yevdokimov, Y. (2002, July). Sustainable transportation system: a system dynamics approach. In

Proceedings of the 37th Annual Conference of Canadian Transportation Research Forum (pp. 12-15).