transportation part a

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A framework for evaluating the dynamic impacts of a congestion

pricing policy for a transportation socioeconomic system

Shiyong Liu a,1, Konstantinos P. Triantis b,*, Sudipta Sarangi c

a Research Institute of Economics and Management, Southwestern University of Finance and Economics, #55 Guanghua Village Avenue, Chengdu,

Sichuan 610074, Chinab Grado Department of Industrial and Systems Engineering, Virginia Polytechnic Institute and State University, System Performance Laboratory,

Falls Church, VA 22043, USAc Department of Economics, Louisiana State University, Baton Rouge, LA 70803, USA

a r t i c l e i n f o

Article history:

Received 10 August 2009

Received in revised form 23 March 2010

Accepted 24 April 2010

Keywords:

Congestion pricing

System dynamics

Social networking

Demand and supply dynamics

Linguistic variablesTraveler perceptions

a b s t r a c t

This paper provides a modeling framework based on the system dynamics approach by

which policy makers can understand the dynamic and complex nature of traffic congestion

within a transportation socioeconomic system representation of a metropolitan area. This

framework offers policy makers an assessment platform that focuses on the short- and

long-term system behaviors arising from an area-wide congestion pricing policy along

with other congestion mitigation policies. Since only a few cities in the world have imple-

mented congestion pricing and several are about to do so, a framework that helps policy

makers to understand the impacts of congestion pricing is currently quite relevant. Within

this framework, improved bus and metro capacities contribute to the supply dynamics

which in turn affect the travel demand of individuals and their choice of different transpor-

tation modes. Work travel and social networking activities are assumed to generate addi-tional travel demand dynamics that are affected by travelers perception of the level of

service of the different transportation modes, their perception of the congestion level,

and the associated traveling costs. It is assumed that the, population, tourism and employ-

ment growth are exogenous factors that affect demand. Furthermore, this paper builds on a

previously formulated approach where fuzzy logic concepts are used to represent linguistic

variables assumed to describe consumer perceptions about transportation conditions.

2010 Elsevier Ltd. All rights reserved.

1. Introduction and research context

Population growth and urbanization have increased traffic congestion in many parts of the world. An increasing numberof US highways and roads experience overwhelming traffic congestion problems, even though most Interstate physical and

safety conditions have been improved. According to a report by the Texas Transportation Institute (TTI), based on congestion

trends for 439 selected areas from 1982 to 2007, traffic congestion is costing Americans $87.2 billion (in constant 2007 dol-

lars) in wasted time and fuel annually (Schrank and Lomax, 2009). Many metropolitan areas in the world including but not

limited to London, Paris, Stockholm, Tokyo, and Beijing are experiencing serious traffic congestion that causes significant

economic losses. Nevertheless, interventions such as congestion pricing have been taken to counter congestion. One key

challenge is to evaluate the impacts of an intervention within a specific metropolitan area before and after it is implemented.

0965-8564/$ - see front matter 2010 Elsevier Ltd. All rights reserved.doi:10.1016/j.tra.2010.04.001

* Corresponding author. Tel.: +1 703 538 8431/8446; fax: +1 703 538 8450.

E-mail addresses: [email protected], [email protected] (S. Liu), [email protected] (K.P. Triantis), [email protected] (S. Sarangi).1 Tel.: +86 15008404175.

Transportation Research Part A 44 (2010) 596608

Contents lists available at ScienceDirect

Transportation Research Part A

j o u r n a l h o m e p a g e : w w w . e l s e v i e r . c o m / l o c a t e / t r a
http://dx.doi.org/10.1016/j.tra.2010.04.001mailto:[email protected]:[email protected]:[email protected]:[email protected]:[email protected]://www.sciencedirect.com/science/journal/09658564http://www.elsevier.com/locate/trahttp://www.elsevier.com/locate/trahttp://www.sciencedirect.com/science/journal/09658564mailto:[email protected]:[email protected]:[email protected]:[email protected]://dx.doi.org/10.1016/j.tra.2010.04.001


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The objective of this paper is to provide a modeling framework based on the system dynamics (SD) approach by which

policy makers can understand the dynamic and complex nature of traffic congestion within a transportation socioeconomic

system (TSES) representation of a metropolitan area. This framework offers policy makers an assessment platform that fo-

cuses on the short- and long-term system behaviors arising from an area-wide2 congestion pricing policy along with other

demandbased transportation policies. This can lead to the understanding of the dynamic long-term behavior of key variables

in the TSES with and without a congestion pricing policy being implemented. Since only a few cities in the world have imple-

mented congestion pricing and several are about to do so, a framework that helps policy makers to understand impacts of con-

gestion pricing is currently very relevant.

For illustration purposes, in this research framework, congestion pricing can be complemented with the funding of public

transportation (metro, bus, etc.) from the revenues that accrue from the implementation of congestion pricing implementa-

tion. The framework allows for the evaluation of this strategy whether the decision makers decide to do this or not. Funding

of public transportation modes can potentially changes users perceptions of the level of service associated with these modes

and their social networking activities3 that induce the mobility of people living around a metropolitan area. Additionally, in

this framework, we consider how users perceptions with respect to the congestion level, traveling cost, and level of service

of mass transit can affect the switching behavior of travelers among different transportation modes.

The structure of this framework is well grounded in the literature and practices of congestion pricing found in London

(Transport for London, 2008) and Stockholm (Special issue on Stockholm Congestion Charging Trial, Transportation Research

Part A, 2009). Consequently, this framework incorporates important subsystems and components for a system dynamics

model that can be simulated on a computer. With the availability of pertinent data, one can run simulation models once they

are formulated and analyze the impacts of a traffic congestion pricing policy in the TSES. Although we have incorporated

some specific features and evaluated one set of policies, our framework can be easily adapted to include other aspects

and evaluate alternative policies. Furthermore, the framework can be used to generate more than one simulation model. This

will be depend in part on the input afforded by the decision makers that potentially would use the model and the availability

of the existing data for existing congestion pricing schemes.

The primary motivation for using the SD approach is that we need to represent multiple and concurrent interactions

among variables that are incorporated in multiple feedback loops. This approach allows one to easily understand and inter-

pret these interactions. It should be noted that we are not suggesting that alternative modeling approaches could not be con-

sidered instead. However, we are using the SD approach to provide a framework that is reasonable for practitioners/decision

makers to use (Sterman, 2001).

Furthermore, one of the key strengths of the SD modeling paradigm is its ability to describe the dynamics of systems that

evolve continuously and with time lags or delays. This is important for our framework since we assume that we need to

study the impact of congestion pricing over many years and that key delays (e.g., delays associated with changing percep-

tions of consumers, with additions to existing infrastructure, etc.) manifest themselves over years. Finally, in the SD model-

ing paradigm we assume that some key relationships are non-linear (Sterman, 2001) (e.g., the relationship of the congestion

on roads and travel comfort of metro with the attractiveness of each mode respectively). This is important for our framework

since if we do not consider these non-linear relationships we are potentially ignoring the basic physics of systems and/or the

non-linear interaction of multiple factors that are part of decision making.

In the literature, one can identify many examples where the SD paradigm has been useful with respect to many applica-

tions starting with settling legal disputes (Cooper, 1980; Stephens et al., 2005), project management (Lyneis and Ford, 2007)

and public health (Sterman, 2006). While a number of researchers have used the SD approach to evaluate different transpor-

tation policies, there is very little research that evaluates the dynamics associated with the impacts of a congestion pricing

policy on the TSES within a pricing area.

From a methodological perspective, we are also suggesting that the linguistic or qualitative representation of perceptions

can be formulated with fuzzy logic and incorporated in the SD modeling paradigm. This idea builds on the work of Liu et al.

(forthcoming) and on the existing literature. For example, research on travel mode choice indicates that perceptions and

information about alternative modes of transportation are important issues to consider. Misperceptions act as a major bar-

rier for mode choice and information about cost, duration, comfort and convenience can lead to the consideration of alter-

natives (Kenyon and Lyons, 2003). Handy et al. (2005), report that car users in the US often lack information about other

modes of transportation. Rose and Ampt (2001) have a similar finding for Australia. Using data from Amsterdam, van Exel

and Rietveld (2010) report that distorted perceptions play a significant role in peoples decision to use cars. Kingham et al.

(2001) also find that concerns about travel time are a major obstacle in getting people to switch from cars to alternative

transportation modes. It has also been suggested that for perceptions about quality of service does affect the decision to

use mass transit (Tyrinopoulos and Antoniou, 2008; see also Friman and Fellesson, 2009). Note that in our framework per-

ceptions about both cars and mass transit are important.

Teodorovic (1999) provides numerous examples in transportation that constitute perceptions and where fuzzy logic can

be used to represent these perceptions. He states the human operators, dispatchers, drivers and passengers use perceptions

represented as linguistic information to make decisions, for example, choosing a route because there is considerable

2 Since the framework is grounded on the London congestion pricing scheme and this scheme is an area-based pricing policy, we use the term area-based

pricing policy throughout this paper.3 Social networking activities refer to any activities such as entertaining, meeting friends at outside establishments, etc. that typically generate mobility.

S. Liu et al. / Transportation Research Part A 44 (2010) 596608 597


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congestion on it. Furthermore, in transportation we make estimates (e.g., travel times) based on experience and intuition.

These estimates affect our perceptions, which change, as our information about these estimates are updated with a certain

time delay or lag. However, it should be noted within the SD modeling paradigm one typically uses lookup or table functions

to represent perceptions. The comparison between using table functions and fuzzy logic has been attempted initially by Liu

(2007) and is beyond the scope of this paper. However, our framework does not preclude the use of table functions to rep-

resent perceptions if one wishes to do so.

The typical starting point for investigating traffic congestion is by identifying the costs associated with it. First, there are

the time costs such as increased average travel time and unexpected delays. Second, one can identify physical costs such as,

extra fuel costs and faster depreciation of vehicles. Third, there are environmental costs associated with noise and air pol-

lution. Finally, one of the unintended consequences of traffic congestion is its detrimental impact on community life. Extra

travel time in daily commuting will cut short the involvement in community activity (Putnam, 2000).

Traditionally, predict and provide was the basic policy to manage transportation problems, though the theory of in-

duced travel demand contends that this policy will induce additional growth in traffic. Since traffic flows continue to outpace

the current resources available to improve the infrastructure and facilities, researchers and policy makers have begun to con-

sider strategies that focus on travel demand management (TDM) to encourage travelers to use the existing transportation

system in ways that are less likely to generate congestion. This has the advantage that it does not require costly new road

building. TDM strategies use a variety of mechanisms to change travel patterns, including facility design, improved transport

options, pricing, and land use changes. These affect travel behavior in many ways, including changes in trip scheduling,

route, mode, destination, and frequency choice and land use patterns.

TDM policies continue to dominate governmental agendas in many countries across the world (Santos, 2000). Various

TDM programs include, but are not limited to traffic congestion pricing, mass transit improvement, ridesharing promotion,

staggered working hours, pedestrian and bicycle facility improvement, telecommuting, and transportation-efficient land use

and so forth. Congestion pricing, long advocated by economists, uses market mechanisms to regulate more efficient use of

transportation resources. Efficient congestion pricing aims to charge users the value they place on using publicly provided

roads. However there is no single solution to controlling the growth in traffic congestion. Effective implementation of a con-

gestion pricing scheme potentially necessitates a more comprehensive policy requiring a combination of different TDM

schemes. Hence this research considers the combination of congestion pricing along with improvement in alternative trans-

portation modes while providing a subsidy for local residents and disabled populations as one such comprehensive policy.

The widely publicized implementation of a congestion pricing policy in London (Transport for London, 2008) and Stock-

holm (Stein, 2006) has been successful in mitigating traffic congestion to a certain extent. The adoption of a congestion

pricing scheme involves price setting, the redistribution of the revenues obtained from the scheme, and assessment of

the short- and long-term impacts on the economy and traffic congestion, etc. These different aspects have to be studied

exhaustively to prevent the problem of social exclusion that can cause public aversion to a congestion pricing strategy.

Giuliano (1992) introduced the political issues when evaluating a congestion pricing policy. May and Nash (1996) defined

a series of objectives for an urban transportation policy that simultaneously consider environmental, economic, social, and

transportation aspects. Therefore, policy-makers need to understand the impacts of the to-be-implemented policy for the

short and long term. It is also necessary to understand the multiple interactions of key concepts over time (dynamic com-

plexity) of the TSES.

The next section reviews the relevant literature on congestion pricing, social networking, dynamic modeling of transpor-

tation systems as well as the application of fuzzy logic in transportation system modeling. Section 3 of this paper provides an

overview of the designated system and subsystems. This section also describes the basic macro-level qualitative model. Sec-

tion 4 explains the supply and demand dynamics of the congestion pricing policy in the TSES. We also describe linguistic

representations of perceived traveler assessments that are used in the dynamic framework. Section 5 provides a concluding

discussion.

2. Literature review

Road user pricing as a means of mitigating congestion dates back to 1844 (Dupuit). Subsequently, economists Pigou (1920)

and Knight (1924) explored the theory of congestion pricing, though the issue had not yet become topical. In the 1960s, there

was a resurrection of research interest in congestion pricing due to the initiative ofVickrey (1969) as well as the publicationof

the Smeed Report (Ministry of Transport, 1964). During 1980s and 1990s, many congestion pricing schemes were attempted.

After deliberate planning, initiatives such as Electronic Road Pricing in Hong Kong, Rekening Rijden in the Netherlands, road

pricing in Sweden, and congestion metering in Cambridge, UK (Ison and Rye, 2005) were never successfully implemented. A

few schemes have been successfully implemented up until now, namely the Area Licensing Scheme in Singapore (Olszewski

and Xie, 2005), the toll rings in Norway, the London Congestion Pricing (Shaffer and Santos, 2003), and the Stockholm Road

Pricing (Stein, 2006). There are also several cases of congestion pricing in the US, i.e., the SR-91 (2002) Express Lane in Orange

County (FHWA, 2006); the I-15 demonstration project of congestion pricing in northern San Diego County ( Golob, 2001);

Bridge pricing in Lee County, Florida; and Oregon mileage-based pricing test (FHHA, 2006).

In order to examine how different groups of people are affected by a congestion pricing scheme, Levine and Garb (2002)

divided users into three groups: drivers who utilize the road before and after congestion pricing, drivers who get off the road

598 S. Liu et al. / Transportation Research Part A 44 (2010) 596608
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after the implementation of congestion pricing, and people who did not use the road before but start to drive with the im-

proved traffic situation. The conclusion of this research was that in the first two groups many ended up being worse off with

congestion pricing. However, congestion provides other benefits as well that can only be understood by examining the entire

TSES. For instance, Giuliano (1992) stated that road pricing is one of the few effective means to reduce the use of automo-

biles, and thus lower air pollution.

Congestion pricing and improvement of mass transit attempt to reduce the per capita surface occupancy, and hence

encourage efficient land use patterns. There are additional economic, social, and environmental impacts as well. Banister

(2002) argued that due to the implementation of congestion pricing land values and rental levels in the city center would

fall, causing the ever-increasing dispersal of activity from the city center. Giuliano (1992) indicated that the heavily popu-

lated downtown areas are competitively disadvantaged now because of congestion. For a more detailed understanding of the

economic impacts of congestion pricing, Whitehead (2002) presented two scenarios in which several major economic sectors

such as retail, tourism and residential development were evaluated. In the second scenario where congestion pricing reve-

nues would be invested in public transportation and the environment of the city center, retail activity in the city center could

increase with short-term fluctuations before full-fledged improvements are made. It was also claimed that in this scenario

with the prosperity of the local economy, the environmental quality and public transport would improve, and the tourism

industry could be boosted.

In terms of the use of the revenues obtained from congestion pricing schemes, policy makers could consider both eco-

nomic efficiency and equity (Litman, 2005). Goodwin (1990, 1995) recommended that the revenues should be invested in

three areas: road construction, tax relief, and public transit improvement. In our framework, the revenues can be distributed

to maintain the continuous implementation of traffic congestion scheme and to improve mass transit including bus and me-

tro capacity but do not have to be distributed if the decision makers decide not to do so. If sufficient improvements are made

because of the distributions, theoretically it is possible for the mass transit system to attract more travelers from the pool of

previous drivers who choose not to drive (Gonzales, 2005). As empirical evidence indicates, the London Congestion Pricing

scheme thus far has been quite successful in changing driving behaviors. In the first annual report for monitoring the impacts

in London, it was reported that one third fewer cars are entering the city center and 16% more buses are on the streets com-

pared to the period before the pricing scheme was instituted ( Shaffer and Santos, 2003). The sixth annual report (Transport

for London, 2008) shows that compared with 2002, cars and minicabs entering into central London pricing zone during

charging hours were reduced by 36%.

Furthermore, the social networking activities of people rely on different transportation modes especially, for a metropol-

itan area. Face-to-face communications and physical co-presence are very important to sustain normal social life and keep

solid social ties with business partners, family members and friends (Urry, 2003). However, co-presence cannot happen

without getting together. Consequently, all kinds of travel modes and forms are critical for establishing and maintaining dif-

ferent social networks. Since World War II, the average distance between where people live within social networks has in-

creased exponentially in the US, which has resulted from motorization, urban sprawl, airline deregulation, spread of the

internet, and frequent use of mobile equipment. Social networks are not as tight as before. People are widely distributed

in residential areas. Therefore, people have to travel long distances in order to have face-to-face meetings ( Axhausen, 2002).

Although mobility provided by the transportation system satisfies all kinds of social needs and improves quality of life, it

generates undesirable externalities i.e., pollution to the environment, accidents, and longer time in the automobile etc. that

reduce social welfare. In order to maintain the sustainable development of social and of transportation networks, policy

makers are making substantial efforts to reduce the adverse impact of transportation. What they are attempting to facilitate

is the maximization of social welfare by providing more affordable and feasible transportation services. Of course, the imple-

mentation of different policies can generate new short- and long-term adverse impacts. For example, without good planning

and understanding of the congestion pricing strategy, it could cause severe social exclusion problems. Therefore, it is neces-

sary to evaluate the transportation policies within the context of a TSES with an explicit social networking structure being

represented.

In order to obtain an understanding of different transportation policies, a number of researchers have used the system

dynamics (SD) approach to do transportation modeling. However, as mentioned earlier, there is very limited research that

evaluates the dynamic consequences of congestion pricing policies on a pricing area. The 1970s saw the dissemination of SD

in transportation modeling (Parthasarathi, 1974; Chen, 1975). Some researchers focused on regional infrastructure planning

(Drew, 1975, 1978; Wadhwa, 1975). Others applied SD modeling to economic and transport planning (Wadhwa and Dem-

oulin, 1978; Tanaboriboon, 1979). The modeling in 1980s focused on evaluating operational and transportation policies in

public transit (Stephanedes, 1981; Adler et al., 1980; Drew, 1989), on traffic flow, network geometry, and drivers behaviors

for urban road traffic systems (Charlesworth, 1985, 1987; Charlesworth and Gunawan, 1987). Haghani et al. (2002a,b) pre-

sented a model using SD to study the interactions between transportation and land use. Qian et al. (2006) used the SD ap-

proach to investigate traffic congestion problems in Shanghai.

Since transportation systems are subsystems of more complex TSESs, they usually include variables that describe individ-

uals perceptions when modeling travelers behaviors. These variables are typically hard to quantify. Moreover, it is impos-

sible to capture the characteristics of an individuals perceptions by using variables with crisp values. In transportation

studies, Teodorovic and Kikuchi (1990) used a fuzzy inference technique to characterize the drivers perception with respect

to travel time. Deb (1993) studied a mass transit mode choice problem in which human perception and belief with respect to

different transit modes were represented by a fuzzy set theory approach. Lanser and Hoogendoorn (2000) employed a



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quantification scheme in fuzzy set theory to model the travel choice behavior in public transport networks. Tuzkaya and

Onut (2008) applied fuzzy analytic network to transportation mode selection.

3. System/subsystem definitions within the traffic congestion pricing area

In order to evaluate the impacts of a traffic congestion pricing policy one needs to define the system and subsystem

boundaries that include all pertinent factors such as travel behavior, mode selection, social activities, etc. The TSES represen-

tation provided in this section includes transportation, social, political, and economic subsystems along with their interac-

tions and feedback mechanisms that occur between them. The domain of the political subsystem includes the transportation

related policies, such as, the traffic congestion pricing policy, the revenue distribution mechanism obtained from the conges-

tion pricing scheme and the interventions (such as subsidies) that counter social exclusion arising from the implementation

of the transportation policies. The transportation subsystem includes a definition of a congestion pricing area, the determi-nation of mass transit supply and demand, the measurement of congestion, the determination of peoples travel behaviors

and of their average travel expenses. The social subsystem provides a representation of the social networking structure, of

decision rules that address social equity, and the determination of peoples perceptions with respect to traffic congestion and

the level of service that is determined by the level of supply and demand, convenience, comfort, availability, and affordability

of mass transit. Within this subsystem the impact of social networking activities, and peoples perceptions on the dynamic

demand of mass transit modes and on travel behaviors are captured. Population growth is assumed to be exogenously deter-

mined and it affects the potential travelers around the designated pricing area. The economic system considers the invest-

ment in mass transit that includes the improvement of metro and bus within the congestion pricing area. It is assumed that

the growth of tourist base and employment base exogenously affect the congestion level of the designated area.

Fig. 1 shows a macro-level system/subsystem representation that illustrates the interactions of the systems and includes

the main components of a traffic congestion pricing policy.4 Lets consider a metropolitan area with considerable traffic con-

gestion. Assume now that a traffic congestion pricing policy is introduced to address this problem. The level of congestion in this

research is defined as the average density of the passenger car units over total lane miles, and the total charging hours per daywithin the congestion pricing area.5 With the implementation of this policy, some travelers who drive their own cars will switch

to mass transit due to the increased traveling cost. It is assumed that vehicles other than cars e.g., vans, trucks, etc., can be ex-

pressed in equivalent passenger car units (PCUs). The intent of the congestion pricing policy is to reduce the total passenger car

units (PCUs) running within the designated area. Over time of course the mitigated level of congestion encourages more switch-

ing from mass transit back to private cars and affecting social networking activities that ultimately change the demand dynam-

ics again.

With the pricing scheme, revenues accumulate over time and can be used to improve mass transit capacity and subsidize

some user groups. The improved mass transit capacity and travel affordability can boost the satisfaction of different traveler

groups. The satisfied user groups would generate more social networking activities that stimulate more demand for different

transportation modes. As a result, this reduces the ratio of supply to demand of mass transit. This in turn lowers user

Fig. 1. Representation of traffic congestion pricing policy in a transportation socioeconomic system.

4 For readers familiar with the SD approach, this is not a causal loop diagram since we do not assign link polarities.5

Note that this representation can be simplified if we do not consider the hours during which the congestion price applies and assume that the frameworkapplies only during the congestion pricing period.



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satisfaction. At the same time, travelers perceptions with respect to the level of service of mass transit and the cost over the

value of travel using private car affects the switching behavior between driving private cars and taking mass transit. Given

that many aspects of mass transit like ridership, frequency and availability, cannot always be accurately measured we rep-

resent the value of mass transit with perceptions (Arslan and Khisty, 2005). Moreover, the increased mass transit reduces the

space occupancy per traveler when compared with driving private cars. However, increased bus capacity also to a certain

extent increases the level of congestion since a generic bus occupies more PCUs than a car. Thus these four different percep-

tions variables affect the demand for different transportation modes.

With the switching among different transportation modes and the influx of new demand from increased social network-

ing activities, the level of congestion in the designated area is affected, along with the travelers perception about the level of

congestion. This in turn affects the switching and generation of new social networking activities. However, due to the exis-

tence of delays (or system inertia) namely information delays (e.g. the delay associated in the change of travelers percep-

tions with the changed level of mass transit service) and material delays (e.g., the delays associated with expanding mass

transit vehicle fleet by ordering and receiving metro cars and buses), the policy change will affect the system with a lag. This

contributes to the dynamics of the system. In this system, transportation policy makers are responsible for integrating

appropriate interventions in order to maintain the continuous implementation of the traffic congestion pricing scheme.

For example, they may adjust the fraction of the investment distributed to a specific transportation mode such as bus capac-

ity. Moreover, they might introduce other scenarios to mitigate traffic congestion based on the level of congestion and rev-

enue accumulation from the congestion pricing scheme.

4. Structures determining the demand and supply dynamics6

The overall conceptual framework was divided into segments so that key elements of the framework are highlighted. This

was done intentionally since it facilitates conveying the most important information for each segment of the model. We have

also made sure that the link polarities have been designated in the figures of this section. Furthermore, key feedback loops

that are emphasized in the main text of the paper are also highlighted in the figures. Note that links that are associated with

each of the stock variables are designated as rectangles in the figures. A positive link is exists between an inflow rate and the

accumulation or stock whereas a negative link exists between an accumulation/stock and the outflow rate.

Therefore, this section presents four stock and flow representations to illustrate how a TSES in conjunction with a traffic

congestion pricing policy is manifested in a system dynamics modeling context In order to understand what actually affects

the congestion level, travel demand and supply dynamics are addressed accordingly. Social network activities generate de-

mand for different transportation modes namely, car, bus, and metro. Demand for different transportation modes is also par-

tially determined by switching amongst these modes. It is obvious that riding both bus and metro can reduce the number of

PCUs per traveler within the congestion pricing area. However, choosing bus instead of metro in this framework leads to

increased bus usage that also increases the total PCUs running within the pricing area because one bus equals multiple PCUs.

4.1. Travel demand dynamics

To incorporate social phenomena in our framework, one of the major components of travel demand stems from social

networking activities that induce people to move within and around the designated congestion pricing area. To understand

the demand side dynamics in our formulation, please refer to Fig. 2.

Our social networking concept considers the needs for different transportation modes arising from the contact of non-

travelers with travelers and interactions among travelers themselves. In Fig. 2, one can see that the conversion rate from

potential travelers to travelers is determined by the contact of non-travelers with travelers, the defuzzified effect of peoples

perceptions on the probability of requiring mobility and a probability parameter for requiring mobility. The probability of

requiring mobility captures the idea that not every contact between individuals (social networking) can induce mobility

and is represented as the probability that a contact of non-traveler and traveler can induce mobility. The effect of peoplesperceptions on the probability of requiring mobility captures the extent to which an individuals perception affects an indi-

viduals travel choice and behavior. One could conduct a consumer survey to determine the usefulness of the different trans-

portation modes. This would provide information as to the relative desirability of each transportation mode.

These perceptions reflect ideas that are hard to quantify and are best modeled using linguistic variables and fuzzy set the-

ory. For instance, consider four linguistic variables, i.e. perceptions of individuals with respect to level of service of bus (asso-

ciated with bus supply and demand), perceptions of individuals with respect to level of service of metro (associated with

metro supply and demand), perceptions of individuals with respect to level of congestion, and the perceptions of individuals

with respect to cost and value of driving private car. The combined impact of these four linguistic variables on the generation

of new mobility can be quantified using fuzzy set theory. Hence the variable shown in the Fig. 2 is called the defuzzified

effect of perceptions.7 The number of contacts of non-travelers with travelers is calculated as the product of contacts with

6 For the detailed representation of the formulations used in the simulation model with and without traffic congestion policy please refer to Liu (2007).7

Note that based on the researcher or policy makers requirements these can also be modeled using standard non-fuzzy set theory techniques for example,one could use lookup or table functions.



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travelers and the potential traveler concentration. Potential traveler concentration is obtained by determining the fraction of

potential travelers in the total population around the designated pricing area. Contact with travelers describes the contacts that

occur among the existing travelers and is determined by a sociability parameter and the total travelers for the different trans-

portation modes. In the case of this variable, one could look at social interaction indices that exist from the sociology literature

or the small world literature to get some measure of sociability.

In this research, the supply and demand dynamics of the system are in part determined from the transportation infra-

structure as well as the implementation of a traffic congestion pricing policy for a pricing area. Note that the proposed con-

gestion pricing policy can be combined with other interventions namely the improvement of mass transit, the subsidizationof local residents, and disabled drivers. This means that the revenue accumulated from the traffic congestion pricing policy

can be distributed to finance the pricing scheme itself and improve mass transit capacity, namely, that of bus and metro.

Because of the improved mass transit capacity and related services, individuals tend to switch from solo driving to mass

transit. As a result of the switching from solo car driving to riding mass transit, the average traffic congestion level is

Fig. 2. Mobility induced by social networking activities.

Fig. 3. The effects of bus capacity change on congestion pricing.



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mitigated over the long run. Furthermore, people that live and work around the designated traffic congestion pricing area

tend to have more social networking activities (co-presence, which is realized by using different transportation modes) that

determine individuals mobility needs. As a result, this increases the demand for mass transit. After a lag, individual percep-

tions change with the declining ratio of mass transit supply to demand. Because of mobility needs, individuals could switch

back to solo driving. This increases the amount of revenue obtained through the traffic congestion pricing policy and thereby

the revenue available for the supply of mass transit capacity.

4.2. Supply dynamics of mass transit

In this section several critical loops are chosen to illustrate the supply dynamics of mass transit. Since the improve-

ment loops for bus and metro do not differ very much, in Fig. 3 we choose the mode of the bus transit to discuss relevant

Fig. 4. The effects of perceptions with respect to bus level of service on bus capacity.



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issues.8 In this paper, we consider bus transit and the switching behavior between car and bus since bus travel has two different

effects on the system. On the one hand, it can reduce the total PCUs by servicing more travelers than solo car driving. On the other

hand, it canincreasethe number of PCUs because each busis equivalent to several PCUs. Fig. 3 displays the loops that help explain

how the increase of bus capacity (the number of buses) can actually worsen the congestion situation. It also shows the carrying

capacity loop (which is a balancing or a negative feedback loop) constricting the capacity increase within the pricing area.

In loop R1 (reinforcing or positive feedback loop), increasing the number of total PCUs within the congestion pricing area

leads to a higher level of congestion within the pricing area during the pricing period. This leads to an increase in the external

cost per mile and a subsequent increase of the congestion price. With an increased congestion price, more revenues can be

generated. Notice that the pricing scheme in this research can take into account discounting and the exemption for local res-

idents, disabled people and public vehicles. With revenue being distributed to purchasing more buses, the total bus capacity

running within the pricing area increases even though bus aging reduces the capacity somewhat. Our framework allows for

material delays during the process of improving bus capacity due to delays in appropriating bus funding. This reflects various

types of government administrative delays for improving bus capacity and bus buildup delays. The increased number of

buses running within the pricing area undoubtedly boosts the total PCUs. Compared with the increased capacity of other

transit options such as metro, the increase in bus capacity has an effect of deteriorating traffic congestion. The (balancing

or negative feedback) loop B1 constricts the increase of buses due to the existence of an allowable bus carrying capacity

within the designated traffic congestion pricing area.

Fig. 4 shows that the number of travelers within the congestion pricing area increases due to improvements in bus capac-

ity (reinforcing or positive feedback loop R2). The higher the ratio of bus supply to demand (in terms of travelers), the higher

the perceived satisfaction with respect to the level of service. This increases the conversion rate from potential travelers to

travelers due to the social networking activities (refer to Fig. 2). The new converted traveler could take any transportation

mode. The new demand for travel also increases the demand for cars and consequently the total PCUs. This gives rise to in-

creased revenues from congestion pricing and increased bus capacity that amplifies the ratio of bus supply to demand.

In the balancing or negative feedback loop B2, new demand for bus decreases the ratio of bus supply to demand, and con-

sequently lowers peoples perceptions with respect to the level of bus services and this in turn decreases the conversion rate

from potential to actual travelers. The framework also allows for inertia, e.g., peoples perceptions gradually adjust to the

level of bus service thus affecting the bus supply and demand.

In Fig. 5, we examine the impact of individuals perceptions with respect to the bus level of service (associated with the

bus supply and demand), the level of congestion, and the driving cost of private car on the switching behavior from car to bus

(balancing or negative feedback loop B3). With increased bus capacity, travelers tend to have an improved perception with

respect to the level of bus service. This encourages the switching behavior from driving a private car to taking a bus, which

reduces the demand for cars and decreases the total PCUs running within the designated pricing area. The decrease in con-

gestion level leads to a reduction in the revenues generated from the congestion pricing scheme lowering the funds available

for bus capacity improvement. In the balancing (negative feedback) loop B4, one can see that with a higher demand for cars,

congestion worsens. The deteriorating traffic situation leads travelers to have a worsening perception concerning the level of

congestion. This promotes the switching behavior from car driving to bus riding and as a consequence reduces the demand

for car driving. In the balancing loop (B5), the unrestrained switching from other transportation modes to the bus is limited.

Due to the switching behavior from car to bus, the demand for bus service increases. This diminishes the ratio of bus supply

to demand and leaves a worse-than-before perception with respect to the bus level of service. Consequently, individuals ex-

hibit less switching behavior than before.

In the balancing loop B6, with the implementation of the traffic congestion pricing scheme, private car drivers face higher

costs than before. The perception of drivers with respect to driving cost enhances the switching behavior from car driving to

bus riding. The reduced car demand drives down the level of congestion and consequently the congestion pricing price. In

this figure, there are two sources of delays, which are the time for peoples perceptions to gradually adjust to the actual value

of the level of congestion and the cost of driving.

4.3. Representation and impact of linguistic variables

Individual perceptions can be represented by linguistic variables that are defined over multiple characteristics (each lin-

guistic variable is assumed to have three characteristics in this research, i.e., low, medium, and high corresponding to a three

point rating scale survey). The number of characteristics is decided by the survey format that one might use in eliciting data

and can vary based on the studys requirements. However, this increases the number of rules needed to be evaluated in the

model. This paper adopts the techniques introduced by Liu et al. (forthcoming) where fuzzy variables are used to represent

linguistic variables and relevant fuzzy rules are defined to compute the combined effect of multiple linguistic variables.

Linguistic or soft variables in social systems are conventionally represented by table or lookup functions in system

dynamics modeling (Sterman, 2000). These table functions are simple and easy to use but are unable to capture various char-

acteristics associated with each linguistic variable as well as their combinations.9 For example, travelers might consider the

8 This helps with the ease of exposition while also making the framework structure less complicated.9

Liu (2007) provided a preliminary comparison of the table function approach versus the use of fuzzy logic to represent linguistic variables. One could useeither approach within this framework.



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cost of driving cars, the convenience of taking the metro, and the level of traffic congestion related to both modes when choos-

ing either driving a car or riding the metro. For the aforementioned three factors, it is clear that different possibilities can arise.

One of these situations may be the high cost of driving private car, mild level of convenience of riding the metro, and very bad

level of congestion, which could lead a traveler to ride the metro. Another case may be the high cost of driving, very low level of

convenience of riding metro and mild level of traffic congestion, which might render the traveler to change from metro to driv-

ing a private car. The dynamic characteristics of the TSES can place travelers into any circumstance in which different combi-

nations of above three factors might appear. The fuzzy modeling of soft variables is a handy approach for dealing with such

situations.In our framework model, there are four linguistic variables describing travelers perceptions with respect to level of ser-

vice of mass transit (associated with ratio of supply to demand of bus and metro), level of congestion, and the cost of driving

cost a car. All four linguistic variables have a combined effect on the conversion rate of potential to actual travelers and on

the switching behavior among the different transportation modes. Due to the different combinations of the four linguistic

variables, it is necessary to define individual fuzzy rules for different switching scenarios following the technique detailed

by Liu et al. (forthcoming).

5. Discussion

There are two major contributions of this paper. First, this research provides a conceptual framework that describes traffic

congestion behavior of a transportation socioeconomic system (TSES) for an urban area over time. This allows for an initial

qualitative evaluation of a congestion pricing policy that considers both the short-term and long-term effects. A macro view

of the model structure was provided in Fig. 1 with subsequent Figs. 25 explaining the different subsystems involved and

their impacts on the TSES. Compared to alternative transportation planning and evaluating methodologies, the application

of system dynamics to assess transportation policies allows for the consideration of multiple and concurrent interactions

among variables that are incorporated in multiple feedback loops. This approach can complement other methods, such as

a static consideration of the congestion problem from a traditional OD (OriginDestination) perspective.

Second is the consideration of uncertainty associated with the representation of peoples perceptions in terms of the im-

pact of congestion. As stated earlier, previous research on travel mode choice indicates that perceptions and information

about alternative modes of transportation are important issues to consider and that misperceptions act as a major barrier

for mode choice. In this research, we suggest the use of fuzzy logic as a mechanism to capture these perceptions ( Liu

et al., forthcoming) without precluding the use of alternative methods such as table functions or other analytical approaches.

Although many modeling challenges exist, using a fuzzy logic to quantify perceptions as linguistic variables can capture the

rich meaning of such variables without filtering out useful details for decision making.

As part of this framework, policy makers and practitioners can identify loops that are responsible for travel demand and

mass transit supply dynamics. By observing the interactions of multiple feedback loops in this framework, they can appre-

Fig. 5. Effects of peoples perceptions on the switching behavior between bus and car.



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ciate the fundamental interactions that exist in a complex socioeconomic system. Within the framework, policy makers can

also see that the consequences of their policies and decisions are separated from them in time and space due to the presence

of material and information delays and how these delays affect outcomes in a TSES. A proper understanding of the systems

and subsystems of a TSES can help policy makers distinguish which endogenous and exogenous factors affect the system

behavior in critical ways. They can assist in identifying key performance metrics of the designed system accordingly and for-

mulate appropriate responses. Moreover, they will not be confounded by certain counter-intuitive or policy-resistant system

behaviors while implementing policies as they have already identified system structures that determine emerging behaviors.

Since only a few cities in the world have implemented congestion pricing and several are about to do so, a framework that

helps policy makers to understand impacts of congestion pricing is currently very relevant.

By using this framework, researchers and practitioners can make modifications on the system structure to evaluate the

impacts of supplementary strategies such as: new road construction, staggered work shifts, ride sharing, and telecommuting

considered individually or in any combination besides evaluating the impacts of the traffic congestion pricing policy. Sup-

pose the policy makers want to use a telecommuting policy to mitigate the worsening traffic congestion and evaluate the

impacts of implementing this policy. In the proposed framework this can be easily integrated with minor changes in existing

structure.

First, an additional stock needs to be added to represent the demand for telecommuting which in this case will be the

number of telecommuters. Similar to the demand for car, bus and metro, the demand for telecommuting comes from the

newly generated mobility due to the social networking activities, switching from car, bus and metro to telecommuting. Sec-

ond, another linguistic variable should be introduced to represent peoples perceptions with respect to the benefits of tele-

commuting. Given that people need incentives to change their current traveling behavior, investment should be allocated to

improve the infrastructure used by telecommuters such as FIOS (fiber-optic services). Additionally, normal travelers can also

get some allowance for adopting telecommuting instead of driving car or riding mass transit. Information and materials de-

lays show up in this changed structure in a similar fashion. The information delay will be the time for peoples perceptions to

gradually adjust to the improved telecommuting structure. Material delays involved include appropriation delays for fund-

ing the telecommuting infrastructure, and the building delay associated with these facilities. Consequently, the policy mak-

ers can evaluate the impacts of implementing telecommuting on the level of traffic congestion, social networking, and

switching behaviors between different transportation modes. Therefore, this framework can adapt to various policy require-

ments of policy makers in transportation.

On the other hand, without using this framework, one cannot simultaneously obtain the behaviors of multiple metrics

over time by endogenously considering all pertinent variables (could be hundreds of variables) in a complex TSES as a tele-

commuting policy is being implemented. Using alternative modeling paradigms, one might be able to get a relationship be-

tween two variables if both variables (e.g. level of congestion and switching behavior among different transportation modes)

are known to have certain relationship over time. However, in systems engineering, the premise is that system behaviors are

determined by a system structure. In a two-variable relationship modeling paradigm, the effect of one variables action on

another only represents a partial effect of that variable in a complex system, in which multiple variables actually exert effects

on this variable. Therefore, it is hard to evaluate the concurrent dynamic impacts of implementing a telecommuting policy

on multiple variables over time in this complicated system. The use of this framework can overcome this issue.

It is possible to expand the scale of this model to evaluate congestion pricings impact on environment, land use and

development, the local economy, population dynamics, and the concepts of sustainability and network resilience of a metro-

politan area to extreme events. Furthermore, in order to increase the usefulness of this approach, management flight sim-

ulator can be developed to let policy makers test different assumptions such as changing the building delay time for bus

and metro, increasing the congestion price, and increasing investment fraction coming from revenue obtained from conges-

tion pricing for the metro, etc.

A final word of caution: for such a complex framework, researchers may encounter a variety of challenges that include but

are not limited to data collection, group modeling, finding the equilibrium of the simulation model, loop knockout, calibra-

tion, policy optimization, validation, and verification issues once the simulation model is defined. In the context of this

framework, an initial data collection effort is based on the traffic congestion pricing policy implemented in year 2003 within

the London metropolitan area which is freely available at the Transport for London website. 10 Group modeling also called

group model building is where model building and refinement is conducted with direct involvement of client groups. For this

framework, this would require the participation of local transportation authorities to ensure at very minimum face validity.

Once a simulation model is developed, loop knockout analysis provides modelers/decision makers with an approach that deter-

mines whether links/relationships are critical by observing behavior anomalies generated when deleting these relationships.

Whereas, calibration is used as a way to find parameters for which one does not have data for (e.g., time with car before switch-

ing, time with metro before switching cannot be found from the London data that have been gathered). Policy optimization de-

notes the process of finding the maximum or minimum value of an objective function through manipulating a set of parameters

chosen by modeler. These parameters are typically linked to specific policies that are under evaluation (e.g., the congestion

price). Finally, even though Sterman (2000) argues that the precise validation and verification of any model is impossible, recent

research Schwandt (2009) has explored the potential use of validation and verification practices that are used in the computer

10 Source: http://tfl.gov.uk.

http://tfl.gov.uk/http://tfl.gov.uk/


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science community in SD modeling. Thus we believe that while implementation will pose numerous challenges this framework

is a first step in a promising research agenda.

Acknowledgements

This research has been supported by NSF Grant #0527252: Collaborative Research Traffic Congestion: Actions and Reac-

tions. This research has also been supported by project211 at Southwestern University of Finance and Economics, Chengdu,

China. The authors would like to express their sincere appreciation to Nasim Sabouchi of Virginia Tech for her data gathering

efforts and subsequent modeling efforts. Any opinions, conclusions, and/or findings are those of the authors and do not nec-

essarily reflect the views of NSF and/or the Southwestern University of Finance and Economics.

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