Transport Policy 47 (2016) 72–83

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Transport Policy journal homepage: www.elsevier.com/locate/tranpol

Trip mode and travel pattern impacts of a Tradable Credits Scheme: A case study of Beijing Meng Xu a,n, Susan Grant-Muller b a b

State Key Laboratory of Rail Trafﬁc Control and Safety, Beijing Jiaotong University, No. 3 of Shangyuan Residence, Haidian District, Beijing 100044, China Institute for Transport Studies, University of Leeds, 34-40 University Road, LS2 9JT Leeds, UK

art ic l e i nf o

a b s t r a c t

Article history: Received 18 August 2015 Received in revised form 15 December 2015 Accepted 25 December 2015

We examine how trip mode and travel pattern of travelers are inﬂuenced by a given Tradable Credits Scheme (TCS). An analysis framework is proposed to investigate the effects of a basic TCS. Using a simulation analysis and case study from the Beijing municipality, we demonstrate that a TCS can achieve a target for reducing the expected car kilometers. The research demonstrates that a TCS will have an effect on travelers’ mode choice. However, it is likely to have only a minor effect on the overall travel pattern in terms of OD movements. & 2015 Elsevier Ltd. All rights reserved.

Keywords: Tradable Credits Scheme (TCS) Transport management policy Mode choice Welfare analysis

1. Introduction Mode choice is a fundamental issue in transport studies and one which has been heavily researched (see, for example, BenAkiva and Lerman, 1985; Dijst et al., 2002; Hensher and Rose, 2007; Van Exel and Rietveld, 2009; Ho and Mulley, 2013; Chidambaram et al., 2014; Habib and Weiss, 2014). However, many of these studies are based on a disaggregate approach and have sought to understand how travelers’ mode choice behavior is affected by a series of factors, based on analysis of past (or anticipated) travel data. Other studies of transport mode choice have been based on a macroscopic network equilibrium approach, e.g., (Shefﬁ, 1985; Jara-Dıaz and Videla, 1989; Oppenheim, 1995; Ortuzar et al., 2001; Xu and Gao, 2009; Can, 2013; Zhao et al., 2013). The notion of the Tradable Credits Scheme (TCS) has evolved over a relatively long period, particularly in relation to pollution control, where it has been well studied and used in practice. In the transport sector, the scheme is a particular case of a wider group of so-called economic instruments that have used pricing or changes to income to inﬂuence travel behavior and transport choices. Economic instruments have a strong, direct leverage on both ﬁxed and variable prices related to travel choices. Fixed price schemes include the use of registration fees and car ownership costs, whilst examples of variable pricing includes public transport (PT) fare n

Corresponding author. E-mail addresses: [email protected] (M. Xu), [email protected] (S. Grant-Muller). http://dx.doi.org/10.1016/j.tranpol.2015.12.007 0967-070X/& 2015 Elsevier Ltd. All rights reserved.

structuring, variable parking charges and toll fees. Other types of economic instruments include positive ‘incentive-based’ policies, taxes and subsidies on vehicle purchase, scrappage incentives, taxes on vehicle use, emission taxes, fuel taxes, vehicle kilometer traveled taxes, congestion charges and pay-as-you-drive insurance. See (e.g. Santos et al., 2010; Ben-Elia and Ettema, 2009; 2011a; 2011b; Potter et al., 2006; Beck et al., 2013). A signiﬁcant tranche of research has also been carried out on alternative transport management policies, largely to understand the role these policies playing in achieving sustainable development of the transport system. Various travel demand management policies have been proposed and analyzed in the context of mitigating trafﬁc congestion, with examples including the use of reward measures (Verhoef et al., 1997; Bliemer and Van Amelsfort, 2010; Ben-Elia and Ettema, 2011b), tradable driving rights (Akamatsu, 2007; Yang and Wang, 2011), road pricing (Yang and Bell, 1997; Yang and Huang, 2005) and rationing (Zhu et al., 2013). Examples of ‘command and control’ policies include controls on car ownership (e.g. a quota system for new vehicle plates in Singapore, Chin and Smith, 1997) and a driving ban scheme in Mexico City (Davis, 2008). Concerning studies of mode choice behavior, the literature reﬂects areas that have had particular attention. Examples include logit-based mode choice analysis under road pricing (Huang, 2002), which provides some discussion of the classical bottleneck model. Tirachini and Hensher (2011) address policies around multimodal transport pricing. Recently, Wu et al. (2012) present optimization model to design equitable and efﬁcient tradable

M. Xu, S. Grant-Muller / Transport Policy 47 (2016) 72–83

credit schemes for general multimodal transportation networks. Tian, Yang and Huang (2013) examine a two-mode problem (auto and transit modes) under a TCS with a bottleneck modal (Arnott, de Palma and Lindsey, 1993) which a physically separated transit mode is parallel to a highway with a bottleneck, and demonstrated that a TCS which emulates the bottleneck congestion pricing and transit subsidy in a revenue-neutral manner. However, further studies are necessary to identify how a TCS may impact on transport mode choice of travelers. TCSs cover a variety of instruments that range from the introduction of ﬂexibility into regulation to the organization of competitive markets for credits (Goddard, 1997). Quantiﬁed physical constraints are set in the form of credits allocated to groups of agents consuming scarce resources, and permission is granted to transfer these quotas between activities, products or places (offsetting), periods of time (banking) or to other agents (trading, hence “tradable credits”). For travel demand management, a tradable credit scheme can reward travel patterns and provide a continuing incentive for travelers to manage their credits, e.g. reducing credit use by carpooling or using PT. Through the design of credit based measure, it is possible to achieve desirable outcomes of travel demand management. In comparison to the case of road pricing and some other economic policies for travel demand management, TCS is a relatively new measure both in theory and in practice. The lack of practical application of this economic measure may be attributable to an undeveloped and incomplete theoretical foundation and particular practical issues that are yet to be resolved (Grant-Muller and Xu, 2014). However, the idea of TCS provides a promising policy approach for mobility management and has received increasing attention in recent years. Section 2 presents a literature review of the art-of-state studies of TCS within the transport ﬁeld, from which it is apparent that most recent studies on TCS have largely focused on macroscopic analysis. A fundamental question is whether a TCS is likely to affect travelers’ mode choice if it were implemented in practice. In the same way that road pricing polices (used in London and Singapore for example) have impacted on demand for private vehicle travel, it is quite possible that a TCS may have a similar effect and reduce the number of vehicle kilometers traveled (VKT). In this study, we examine how travelers’ mode choice preferences may be inﬂuenced by implementing a TCS in an urban setting. The study supposes that the regional authority is responsible for implementing the TCS, the initial credit allocation is free and individuals receive a number of credits (representing vehicle-kilometers) based on a target of reducing the overall total VKT for the urban area. Individuals, in maximizing their utility, must consider their travel mode choice based on their credit allocation. That is, the individual must consider the permitted number of kilometers, the credit price ( pe ) and then determine how many further credits they should purchase if they wish to travel additional kilometers using a private car. To investigate the inﬂuence of a TCS on travel mode choice and different from existing studies i.e. Wu et al. (2012) and Tian et al. (2013), we present a microeconomic quantitative analysis framework to simulate policy scenarios. Travel patterns are compared before and after introduction of a TCS. This study presents a framework which connects a microeconomic analysis (of individual travel mode choice) and a macroscopic network analysis (i.e. the travel pattern for a network) in order to analyze a speciﬁc transport demand management policy (i.e. the TCS). Therefore, a TCS based on VKT for travel demand management is outlined and a new travel demand management policy analysis framework based on a neo-classical microeconomic model is presented. The organization of the paper is as follows. In Section 2, a brief review of TCS and the appropriateness of the Constant Elasticity of

73

Substitution (CES) approach are presented whilst in Section 3, a policy analysis framework for transport mode choice with a TCS is proposed. In Section 4, we develop an estimation model of the individual average vehicle kilometers (based on a neo-classical microeconomic model) with and without a TCS, including the credit equilibrium price and the travel pattern in different zones. In Section 5, the detail of the analysis framework is given, including scenario setting with and without a TCS, input data, and investigation process, based on a small network. We discuss and further compare the effects of a TCS on transport mode choices in Section 6, based on survey data and the presented analysis framework for the case of Beijing municipality. Finally, Section 7 concludes the paper.

2. Problem description and basic considerations 2.1. TCS: a cap-and-trade measure A TCS usually assumes the form of a cap-and-trade system (Dales, 1968). It often targets a certain level of activity (for example, emissions), assigns credits to match the targeted total quantity and allows consumers, organizations and other entities to trade the credits at an endogenously determined price. To the extent that quantity control instruments involve a trading mechanism, they also provide price incentives to the regulated parties (Hepburn, 2006). Although market efﬁciency could be satisﬁed by an auction or other measures and some challenges in policy implication (Sovacool, 2011), the credit allocation mechanism is important. For example in emission control political concerns often favor a proportional allocation based on historical emission records. The credit allocation mechanism has been applied in a variety of different contexts including controlling air pollution, the degradation of wetlands, agricultural pollution, water scarcity and ﬁsheries depletion (OECD, 2004). Examples include an oligopolistic power market model with tradable NOx permits (Chen and Hobbs, 2005), biodiversity conservation with tradable credits (Drechsler and Watzold, 2009), Nitrates control in groundwater (Morgan et al. 2000), regulation of an airline duopoly on a congested airport (Verhoef, 2010), emission reduction from air transport (Carlsson and Hammar, 2002; Mendes and Santos, 2008), incorporating the transport sector into a carbon cap-and-trade program (Ellerman et al., 2006; Millard-Ball, 2008; Jochem, 2008), pollution permits to reduce car ownership in the UK (Walton, 1997) and land use management (Henger and Bizer, 2010). Recent investigations on travel mobility management using tradable credits include a series of studies since the work of Yang and Wang (2011), which has discussed the management of road network mobility with tradable travel credits with a network modeling approach. Continuing this innovative research, there are further series studies on the TCS for travel behavior analysis, see for example, (Wu et al., 2012; Wang and Yang, 2012; Wang et al., 2012; He et al., 2013; Nie and Yin, 2013; Xiao et al., 2013; Tian et al., 2013; Bao et al., 2014; Wang et al., 2014a, 2014b; Zhu et al., 2014; Mamun et al., 2016). Table 1 characterizes existing TCS approaches used in the transport sector for mobility management, along with examples of where such schemes have been adopted. Recent reviews on TCS can refer to Fan and Jiang (2013) and Grant-Muller and Xu (2014), where Fan and Jiang (2013) reviewed a variety of TCSs for roadway capacity allocation focusing on detailed system design and overall functions, and Grant-Muller and Xu (2014) has focused on the TCS roles in road trafﬁc congestion management. In this paper, we discuss how to use a TCS for mobility management and form a comparison with existing studies of TCSs. Supposing that a government authority needs to control the total VKT by private car in an urban area or region, it will need to

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M. Xu, S. Grant-Muller / Transport Policy 47 (2016) 72–83

Table 1 Recent TCS approaches in the transport sector for mobility management. State-of-art studies

Methodology

Approaches

Yang and Wang (2011) Wang and Yang (2012) Wang et al. (2012) Wu et al. (2012)

Mobility management with network equilibrium analysis Mobility management with network equilibrium analysis Mobility management with network equilibrium analysis Effect of income on travelers’ choices on multimodal networks

He et al. (2013)

Mathematical programing Bisection-based trial-and-error method Mathematical programing Mathematical programs with equilibrium constraints Variational inequality

Nie and Yin (2013) Xiao, Qian and Zhang (2013) Tian, Yang and Huang (2013) Bao et al. (2014) Wang et al. (2014a) Wang et al. (2014b) Zhu et al. (2014) Mamun et al. (2016)

Mathematical programing Mathematical programing Mathematical programing Mathematical programing Bilevel programing Bilevel programing Mathematical programing Empirical analysis

calculate the capacity of access roads between different zones and car ownership information for residents in the urban area. The initial credit distribution is assumed to be free and each individual in the zone will receive a certain number of credits for the VKT that they are permitted to travel by car. Each credits holder will then need to consider the amount of kilometers by car permitted by their allocation and the price of credits if they wish to travel further kilometers by car. Those who don't want to travel further kilometers by car will also consider the amount the kilometers they travel, as they can sell excessive credits. The authority sets the credits market, tracking credit prices, the number of credits and transactions in terms of buying and selling credits. With a limited period of validity for credits, the authority can act to adjust the total amount of credits with respect to the target for decreasing total VKT. The mathematical formulation for the TCS studied here will be presented in Section 4.1, following the introduction of the transport analysis framework used in this paper.

Effects on two types of players (Cournot-Nash players and Wardrop-equilibrium players) Bottleneck model for rush hour travel management Bottleneck congestion management Bottleneck congestion management and modal split with heterogeneous users Mobility management with network equilibrium analysis Travel demand management Travel demand management Multiclass trafﬁc network equilibrium analysis Regulating the vehicle miles traveled in Florida, USA

household travel demand and some economic indicators, Kalinowska et al. (2007) described the modiﬁcation of an Austrian computable general equilibrium (CGE) model in order to construct such a model and database for Germany. The transport sector is modeled as comprising car and public transport, using a microeconomic production household possessing a CES and striving to minimize costs per unit of output. The demand functions used in the TRE-part of TREMOVE are nested CES functions. This assumes CES applies at each level of the utility tree, e.g., the elasticity of substitution for the urban areas in the case study for London between private car and public transport is 1.05 in the peak and is 1.95 in the off-peak (The European Commission, Standard & Poor's DRI and K.U. Leuven, 1999). The CES form of utility function allows several situations to be considered, which depend on the elasticity of substitution parameter. It has also used in an individual tradable emission permit scheme for urban motorists (Bulteau, 2012) and the inﬂuence analysis of urban form on energy consumption according to individual consumption behavior (Yin et al., 2013).

2.2. Appropriateness of the CES approach for trip modeling Whilst relatively new to transport practitioners, the constant elasticity of substitution (CES) approach has been widely used in consumer behavior analysis. A consumer is characterized by their preference ordering for the goods obtainable, which is described by a utility function, and by a budget set that is limited by his/her income. The consumer is assumed to choose that bundle of goods in his/her budget set that maximally satisﬁes his/her preferences, i.e., the behavior can be described by utility maximization over the budget set (Varian, 1992). The CES utility function has often been chosen in consumer behavior analysis due to its advantageous properties with respect to ﬂexibility, and its consequences on the assumptions with respect to the existence and uniqueness of equilibrium (Kalinowska et al., 2007). In this paper, we adopt this approach for trips by private car and mass transit modes. The choice of travel mode is determined by the relative costs of different modes and the transport budget. One representative traveler who maximizes his/her utility (maximize his/her mobility) is considered to be representative of all travelers in the study. This rationale has been the basis for some related studies. One example is the European partial equilibrium CAR emissions simulation model (EUCARS 3 model), which was originally developed to study CO2 emission limitation policies in passenger transport. Consumer choices are described in the model by a decision tree (in the consumption block of the model), and the CES approach is used for the consumption of public transport services and private vehicle services (Denis and Koopman, 1998). In order to assess the impact of road pricing measures on

3. Analysis framework Fig. 1 illustrates the policy analysis framework used here to reﬂect mode choice in the context of a TCS, with further details for each component described in Section 4. If a TCS would be implemented, the budget for credits will become an additional resource considered within individuals’ mode choice. The use of a private car beyond the limit of the initial credit allocation will become subject to additional monetary costs. There are various options within the scope of the scheme: people may want to fully use their credits, buy additional credits (where their use of the car exceeds the initial allocation), or save and sell them for ﬁnancial gain. As a result, people not only have to decide on the necessity of the trips they take, but also how they want to manage their budget of allocated credits. Mode choice for a representative individual for each zone will be affected by the individuals’ transport budget, the travel cost according to different modes and the individuals’ attitudes. In choosing a travel mode, the individual is confronted with objective factors such as location, journey duration, departure time, activity type, mode availability and mode characteristics. All these factors, plus others that may be less objective, will affect mode choice. After determining the individuals' average number of trips by mode for a speciﬁed time period, it is possible to estimate the travel pattern (OD matrix) based on the number of trips by different modes. A destination choice model can be used to determine the travel pattern between different zones. This is an

M. Xu, S. Grant-Muller / Transport Policy 47 (2016) 72–83

Travel mode choice for given urban region (Section 4.1)

Representation of individual Transport budget Unit cost for private car/mass transit mode Attitudes (Section 4.1)

75

Regulatory authority Initial credit assignment Credit price Total credit amount (Section 4.3)

Travel OD matrix by modes (Section 4.2)

Destination choice model (Section 4.2)

Policy analysis The effects of the tradable credits scheme The effects of travel cost for different modes (Section 4.1) Fig. 1. Analysis framework for transport mode choice with and without a TCS.

iterative process based on the difference between the new and previous travel patterns, with the pattern ﬁnally determined if that difference is within 5%. A policy analysis can then be undertaken based on the variation in trips.

4. Methodology Based on the analysis framework outlined in Section 3, we present the methodological approach as follows. Firstly we list the notation used in Section 4.1, followed by a presentation of the model formulation in Section 4.2 and determination of the travel pattern in Section 4.3. The calculation of the credit price is described in Section 4.4, whilst the determination of the credits initially distributed to individuals is presented in Section 4.5. Finally, the characteristics of constant elasticity of substitution in the utility function are given in Section 4.6. 4.1. Model formulation Considering a given city or area which is separated into different zones i , i = 1,⋯ , N . We suppose that travelers have a preference to use a private car for their daily trips, but it is feasible to substitute between private car travel and mass transit modes. Considering environmental goals or other priorities, the authority may wish to restraint the number of private cars trips by the number of kilometers traveled (i.e. restraint car trips by VKT) and it is supposed that the authority will implement a tradable credit scheme. Before implementation of the scheme, it is assumed that each individual in zone i maximizes his/her utility by

(

)

( )

(4)

where Ui (x ic , x ib ) represents the utility function for a representative individual in zone i , x ic represents the individual average distance traveled by private car in zone i (unit: vehicle kilometers traveled N (VKT), x c = ∑i = 1 Pi x ic ), x ib represents the individual average distance traveled by mass transit in zone i (unit: vehicle kilometers traveled N (VKT), xb= ∑i = 1 Pi x ib ), and Pi is population in zone i . The variable pv summarizes private car costs per kilometer traveled, representing maintenance costs, fuel and insurance, and pb summarizes the price of mass transit per kilometer traveled. The notation Ii is the individual transport budget devoted to travel in zone i , ai is the allocation parameter for private car use/the proportion of transport income spent on private car use, and ρ is substitution elasticity. When the parameter ρ = 0, the CES utility function is, in fact, in the form of a Cob-Douglas utility function, which shows the car mode and mass transit mode as not being substitutable; when the parameter ρ = 1, it shows the car mode and mass transit mode to be perfect substitutes; when the parameter ρ = − ∞, it shows the car mode and mass transit mode to be complementary. Suppose the regulatory authority then implements a TCS. The initial credit distribution is free and each individual in each zone receives a number of credits that permits travel by car: x¯ ic . The individual then needs to consider the amount of kilometers that are allowed by car and the price of a credit if they wish to travel further more kilometers by car. Under the TCS, the utility maximization problem for each representative individual in zone i can then be formulated as the following:

(1)

s.t.

pv xic +pb xib≤Ii,∀i=1, ⋯,N

(2)

xic ≥0

(3)

1

ρ ρ ρ U 2 : MaxUi xic , xib =⎡⎣ ai ( xic ) + ( 1−ai ) xib ⎤⎦

(

)

( )

(5)

s.t.

pv xic + pe ( xic − x¯ ic ) + pb xib ≤ Ii, ∀ i = 1, ⋯, N

1

ρ ρ ρ U1 : Max Ui xic , xib =⎡⎣ ai ( xic ) + ( 1−ai ) xib ⎤⎦

xib≥0

(6)

(3)-(4) where pe is the price of tradable credits, x¯ ic represents credits received per individual in zone i , e.g., each credit/license entitles the holder to travel one kilometer by car, x¯ summarizes total N number of credits set according to the total VKT, x¯ = ∑i = 1 Pi x¯ ic , and other notations gives as below U1. Generally, travel mode choice is inﬂuenced by different factors and certainly, budget constraint is only one of the key factors. The

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CES method used in consumer behavior analysis generally uses ‘budget’ or ’income’, based on the money budget constraint with ‘goods’. We use the term ‘transport budget’ based on the modeling approach since the ‘goods (transport service)’ consists of car mode travel and mass transit travel under the transport budget constraint without a TCS, Eq. (2), and with TCS, Eq. (6). Eq. (6) represents the transport budget constraint with the car and mass transit travel under the TCS, which means that every individual has a potential ‘transport budget’ for travel during a certain period (e.g., month, day, etc.) before making trips. Comparing Eq. (2) and Eq. (6), we ﬁnd that there exists a balance to be achieved in the working of the credits scheme from the perspective of individuals as follows. Firstly, it brings an increased cost for private car use ( pe ) and secondly, it brings an increase in the individuals’ transport budget ( Ii+pe x¯ ic ) for zone i . This increase could be treated as a transport subsidy ( pe x¯ ic ) paid to an individual if the number of credits x¯ ic is not used. According to the associated Lagrangian, we can derive the following solution for U2 when two modes are used:

⎛ ai ⎞ε Ii + pe x¯ ic ⎟ xic =⎜ ε ⎝ pv + pe ⎠ ai ( pv + pe )1 − ε + ( 1−ai )ε p 1 − ε b

(7)

(8) 1 . 1−ρ

ε ⎛ Pi aiε ( Ii + pe x¯ ic ) N 1 ⎞ ⎟ ∑ x c =⎜ ε 1− ε i=1 ε ⎝ pv + pe ⎠ ai ( pv + pe )1 − ε + ( 1−ai ) pb

Solutions for the

(9)

(10)

4.2. Determination of the travel pattern Different models can be used to determinate travel patterns based on different assumptions, for example, the random utility model (Anderstig and Mattsson, 1991) or the doubly constrained negative exponential gravity model (Wilson, 1970; Boyce and Daskin, 1997; Boyce and Mattsson, 1999; Boyce and Xiong, 2007). Here we use an aggregated logit type model as an approach to determine trip distribution, using two variables reﬂecting the level of employment ( Ej ) and generalized cost by car (Cijc ) or mass transit (Cijb ). Therefore, the number of kilometers with private car Tijc from zone i to zone j can be estimated by

Tijc =Tic

(

exp αEj + βCijc N ∑ j=1

)

(

exp αEj + βCijc

)

(11)

where α , β are parameters, and Tic represents the total private car kilometers in zone i , Tic =Pi x ic , unit: VKT. The number of kilometers by mass transit mode Tijb from zone i to zone j can be estimated by

Tijb=Tib

(

exp αEj + N ∑ j=1

Tib

(

βCijb

exp αEj +

)

βCijb

(13)

or by Eq. (14) without a TCS

Cijc =pv d1ij +γf

( Tijc )

(14)

where d1ij indicates the average distance (kilometers) from zone i to zone j by car, and γ represents the value of time, which converts travel time into generalized monetary travel cost. The f (Tijc ) in Eqs. (13 and 14) is assumed to take the form of a BPR function:

⎡ ⎛ Tijc ⎞φ ⎤ f Tijc =tij0 ⎢ 1 + ϵ ⎜ ⎟ ⎥ ⎢⎣ ⎝ Fij ⎠ ⎥⎦

( )

(15)

where tij0 is the free ﬂow time, Fij represent the general road capacity between zone i to zone j , ϵ = 0.15, φ = 4 . In Eq. (12), the generalize travel cost with mass transit mode Cijb can be written as

( )

model of U1 are also included in Eqs. (7 and 8) by setting pe =0, and x¯ ic =0, ∀ i = 1, ⋯ , N . The equilibrium solution for the total VKT in the zones is given by the following:

ε ⎛ 1 ⎞ε Pi ( 1−ai ) ( Ii + pe x¯ ic ) N xb=⎜ ⎟ ∑ ε 1− ε i=1 ε ⎝ pb ⎠ ai ( pv + pe )1 − ε + ( 1−ai ) pb

( )

Cijc =( pe +pv ) d1ij +γf Tijc

Cijb=pb d2ij +γf Tijb

⎛ 1−ai ⎞ε Ii + pe x¯ ic ⎟ xib=⎜ ε ⎝ pb ⎠ ai ( pv + pe )1 − ε + ( 1−ai )ε p 1 − ε b where ε is an elasticity coefﬁcient, ε =

In Eq. (11), the car generalize travel cost Cijc is either determined by Eq. (13) under a given TCS

(16)

where d2ij is the average distance (kilometers) from zone i to zone j by mass transit, and f (Tijb ) is assumed to take the form of a stepwise function for the generalized trip time between zone i to zone j by mass transit

( )

f Tijb =exp

(∑

K

k=1

δk DTijb

)

(17)

DTijb ,

In Eq. (17), is a dummy variable which is equal to 1 if Tijb falls in the generalized journal time category k and zero otherwise, and δk is the time interval. This type of step function has also been used by Debrezion et al. (2009) as a measure of generalized journey time between railway stations and by Sen (1986). A difference from the more commonly applied type of logit model is that the calculation of the number kilometers by private car, Tijc , and the number of kilometers by mass transit mode, Tijb , is an iterative process here. In Eq. (13) or Eq. (14), the generalized travel cost by car, Cijc is related to Tijc , and in Eq. (16), the generalized travel cost by mass transit, Cijb is related to Tijb . As a result, an iterative solution is necessary to determine the number of kilometers between zones by either private car or mass transit modes. 4.3. Determination of the credit price Here, we further discuss the determination of the credit price and how this will affect the traveler's mode choice. In order for the market to be balanced and consistent with the target for car use (as set by the regulatory authority), the credit price, which is based on the VKT, can be set as

xc = ∑

N

i=1

Pi xic =x¯ = ∑

N

i=1

Pi x¯ ic

(18)

Therefore, N

∑i = 1 Pi ( xic −x¯ ic )=0

(19)

Combining Eqs. (19) and (9), we have the following 1

)

(12)

where represents the total number of kilometers by mass transit in zone i , unit: VKT, Tib=Pi x ib .

⎤ε ⎡ N aiε ( Ii + pe x¯ ic ) ⎥ ⎢ ∑i = 1 ε ( p + p )1 − ε + ( 1 − a )ε p 1 − ε a v e i b ⎥ ⎢ i pe = ⎢ ⎥ − pv N c ¯ ∑ x i i=1 ⎥ ⎢ ⎦ ⎣

(20)

M. Xu, S. Grant-Muller / Transport Policy 47 (2016) 72–83

Deﬁne Fi (pe )=aiε (pv + pe )1 − ε +(1−ai )ε pb1 − ε , then Eq. (20) can be written as

Travel demand by modes with/without a tradable credits scheme (Utility maximum problem: U1/U2)

1

⎡ N aiε ( Ii + pe x¯ ic ) ⎤ ε ⎢ ∑i = 1 F ( p ) ⎥ i e ⎥ − pv pe = ⎢ N ⎥ ⎢ ∑i = 1 x¯ ic ⎦ ⎣

77

Total VKT (21)

Travel OD matrix by modes (Destination choice model)

Eqs. (20) and (21) give an implicit solution for the credit price, which could be solved using an iterative approach given the car costs per kilometer traveled pv , the price of mass transit per kilometer traveled pb , the individual transportation budget in zone i , Ii , the total number of credits sets by the authority x¯ , and related coefﬁcients.

Vehicle Kilometres for each OD No OD consistency

4.4. Determination of the number of credits initially distributed to individuals

Yes Analysis of the effects of the tradable credits

In general there are different ways to determine the number of credits initially received by individuals x¯ ic . We can determine x¯ ic if

Fig. 2. Transport policy analysis framework.

N

the total number of car kilometers ∑i = 1 (Tic +Tib ) is given and from Eqs. (9) and (10), combined with Fi (pe ), we have ε ε ⎛ ¯ ic ) ⎛ 1 ⎞ε N Pi a i ( Ii + pe x 1 ⎞ +⎜ ⎟ ⎜ ⎟ ∑i = 1 Fi ( pe ) ⎝ pv + pe ⎠ ⎝ pb ⎠ N

∑i = 1

ε Pi ( 1−ai ) ( Ii + pe x¯ ic )

Fi ( pe )

N

1

(

= ∑i = 1 Tic +Tib

)

4

3

(22)

2

Speciﬁcally, under the case of an equivalent distribution of initial credits,

Fig. 3. A 4-zone example network.

x¯1c =⋯=x¯ Nc =x̅ C *

(23)

We have ⎡ N ∑ i = 1 T ic + Tib − ⎢ ⎣ C x ̅ *= ⎡ 1 pe ⎢ p + p v e ⎣

(

)

(

ε

ε N Pi a i Ii i = 1 F i ( pe )

ε

+( ) ∑ ( )∑ ( +( ) ∑ )∑ 1 pv + pe

ε

Pi a iε N i = 1 F i ( pe )

1 pb

1 pb

ε

ε ⎤ N Pi 1 − ai Ii ⎥ i =1 F i ( pe ) ⎦

N Pi 1 − a i i = 1 F i ( pe )

(

)

)ε ⎤ ⎥ ⎦

(24)

5. Analysis framework From Sections 2–4, we present here an analysis framework for the investigation of a TCS. This section includes discussion of the scheme features and the assumptions made in the analysis. 5.1. Policy investigation process The research framework for a TCS is based on the main design features described in Sections 2–4 and employs a scenario based approach, as summarized by Fig. 2. 5.2. Numerical example To illustrate the policy simulation framework, we ﬁrstly employ a simple network that includes two origins (zone 1 and zone 2) and two destinations (zone 3 and zone 4), as shown in Fig. 3. Suppose that zone 1 and zone 2 are primarily residential areas, whilst zone 3 and zone 4 are employment zones. Assuming individuals in zone 1 have a preference for car travel with a1 = 5 / 6 whilst individuals in zone 2 have a preference for car travel with a2=2 / 3. It is also assumed that individuals’ budgets for transport in zone 1 and zone 2 are identical, I1=I2=20; the ﬁxed cost per kilometer traveled by car is pv =0.3, and the ﬁxed cost per kilometer traveled by mass transit is pb =0.1. We set the parameter ρ = 0.6 and therefore the elasticity of substitution with a value of ε = 2.5. The population in zones 1 and 2 are identical, P1=P2=1000,

the level of employment in zone 3, E3=1200, and in zone 4, E4=800. From the micro-economic model U1 we can derive the individual average distance in different zones without implementation of the TCS, see Table 2. In this case, the individuals’ average travel pattern is 61 km by car and 17 km by mass transit in zone 1, 35 km by car and 96 km by mass transit in zone 2. Therefore in zone 1, the total distance traveled by private car is 60996.9 km and the total distance traveled by mass transit is 17009.3 km, compared with zone 2, where the total distance traveled by car is 34748.3 km and the total distance traveled by mass transit trips is 95755.1 km. In both zones, the total distance traveled by car is 95745.2 km, the total distance traveled by mass transit is 112764.4 km and the total kilometers traveled by vehicles is 208509.6 km. Now, consider the case where the authority decides to reduce the demand for private car travel by 20.6%, i.e. the expected total number of kilometers by car becomes 76000 km. We can therefore set the total number of credits as x¯ = 76000 km and can consider a design for a TCS that will achieve this target. For the initial credit distribution, there are two general approaches: the ﬁrst is to distribute equally, i.e., we can set x¯1c =x¯2c =38 km in this example; the second approach is to distribute credits in proportion to the number of car kilometers made without a TCS. In this example we would set the number of car kilometers permitted by an individual in zone 1 to be x¯1c =48 km, and in zone 2 to be x¯2c =28 km. Table 2 Vehicle kilometers in different zones without a TCS. Vehicle Kilometers Traveled (VKT)

Zone 1

Zone 2

Total

xic

60.9969

34.7483

–

xib

17.0093

95.7551

–

Tic

60996.9

34748.3

95745.2

Tib

17009.3

95755.1

112764.4

M. Xu, S. Grant-Muller / Transport Policy 47 (2016) 72–83

Initial credit assignment approach

Vehicle Kilometers Traveled (VKT)

Zone 1

Zone 2

Total

Equivalent distribution

xic

51.0764

23.6121

–

xib

31.8637

145.5660

–

Tic

51076.4

23612.1

74688.5

Tib

31863.7

145566.0

177429.7

xic

53.4694

22.5058

–

xib

33.3566

138.7460

–

Tic

53469.4

22505.8

75975.2

Tib

33356.6

138746.0

172102.6

Proportional distribution

According to (20), the credit price can be determined using an iterative process. We set the price of tradable credits to be pe =0.114 . Other parameters in the micro-economic model U2 are as outlined above. We can then derive the number of kilometers in different zones with implementation of the TCS, as indicated in Table 3. It can be seen that the number of car kilometers in zone 1 is more than the number of car kilometers in zone 2, resulting from an initial assumption that the preference of individuals for 5 2 cars in zone 1, a1= 6 , is higher than that in zone 2, a2= 3 . Comparing between Table 2 and Table 3 it can be seen that with the implementation of a TCS, the number of car kilometers in each zone decreases and the number of mass transit kilometers increases. According to this model, the scheme therefore encourages individuals to travel by mass transit. As shown in Table 3, for a TCS with an initial proportional distribution the total number of kilometers by car is 75975.2 whilst the total number of kilometers by mass transit is 172102.5, giving a total distance traveled 248077.8 km. In comparison, with an equal credit distribution scheme, the total car kilometers is 74688.5, the total mass transit kilometers is 177429.7, and the total distance traveled is 252118.2 km. It can therefore be seen that by setting the tradable credits price and according to the approach used for the initial distribution of credits, the TCS can achieve the target of reducing car kilometers by 20.6%. With the implementation of a TCS, it also appears that the effects resulting from different approaches to the distribution of initial credits are different. With an equal initial distribution (the total distance traveled by car is 74688.5 km), the effect in terms of the reduction in car kilometers is stronger than with the use of an initial proportional distribution (the total distance traveled by car is 75975.2 km). However, an equivalent distribution approach also results in more mass transit kilometers (177429.7 km with an equivalent distribution vs 172102.6 km with a proportionate initial distribution). This also brings growth in the total number of kilometers for both zones (252118.2 km with equivalent distribution vs 248077.8 km with initial distribution in proportion). Furthermore, comparing Table 2 and Table 3, we can see that under a TCS, the number of mass transit kilometers in both zones clearly increases. This also causes a substantial increase in the total distance traveled (in comparison with the total distance traveled without a TCS) of 208509.6 km. From the CES model U2 with given TCS, the budget is actually improved with the mode shifting from car to mass transit, and therefore the solutions increase since they are obtained in the manner of maximizing utility. Moreover, the increase in the total number of trips could be caused by shifting mode (i.e., d1 od2) or an increase in frequency (i.e., number of trips), here it was considered to be a result of shifting mode. If it were an increase in frequency, this result would imply that implementing a TCS would cause people to make more trips and/or

increase the mobility freedom. However, overall it cannot be expected that an individuals’ trip frequency would increase by implementing a private-car use management policy (i.e., the TCS). As can be seen from Section 4.4, the determination of the credit price is very important. The credit price can be calculated iteratively, as shown in Eq. (20). Fig. 4 demonstrates the relationship between the total car kilometers and the price of credits for a 4-zone simple network (see Fig. 3). We assume that the TCS is based on an initial equivalent credits distribution approach and has a target goal to reduce the number of kilometers by car by 20.6%. From Fig. 4, in order to achieve this target, there exists a unique solution for the credit price which can be derived using Eq. (20). Under the given TCS, the higher the tradable credits price, the lower the total number of car kilometers and the higher total number of mass transit kilometers. The increase in total mass transit kilometers is generally more rapid than the decrease in total car kilometers. It can therefore be seen that an increase in the tradable credits price causes a growth in the number of total kilometers. From Table 3 we also note that individuals in zone 1 exceed their allocated credits under both initial credit assignment approaches. By way of illustration, using an initial equivalent distribution of credits, an individual in zone 1 traveled about 51 km by car in comparison with the permitted VKT (number of credits) of 38 km. With an initial proportionate distribution, an individual in zone 1 travels about 53 km by car in contrast with the permitted VKT of 48 km. Therefore, individuals in zone 1 have to buy additional credits from the market with a price pe =0.114 . In contrast, individuals in zone 2 have a surplus of credits under both initial tradable credits assignment approaches. With an initial equivalent distribution approach, an individual in zone 2 travels about 24 km by car in comparison with the permitted VKT (number of credits) of 38 km. Alternatively, with an initial proportional distribution of credits, an individual in zone 1 travels about 23 km by car in contrast with a permitted VKT of 28 km. So, in the case of the scheme with an initial equivalent distribution approach for credits there is a credit surplus, whilst with the initial proportional distribution of credits the number of credits sold is equal to the number of credits bought. The difference in credit surplus also explains the difference in total car kilometers according to the different initial credit distribution approach used. It can be seen that the total number of kilometers by car is 74688.5 using an equivalent distribution approach in contrast with a total of 75975.2 km using an initial proportional distribution approach, the latter being closer to the target of 76000 km. The large increase seen in the number of mass transit kilometers under the TCS gives rise to the question of whether to 10

x 10

x 10 8

Total Car Trips Total Car Trips Target Total Mass Transit Trips 8

6

6

4

4

2

2

0 0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

Tradable Credits Price (pe)

Fig. 4. Effects of the tradable credit price on total car kilometers.

1

Total Mass Transit Trips(km)

Table 3 The number of kilometers in different zones with a TCS and according to two different initial distribution measures.

Total Car Trips(km)

78

M. Xu, S. Grant-Muller / Transport Policy 47 (2016) 72–83

attempt to control the total distance traveled. We still assume a TCS is adopted using an initial equivalent credits distribution approach. Now, suppose that the regulatory authority decides to reduce total travel demand by about 20.6% i.e. the expected total distance traveled is about 1.65 × 105 km. According to Eq. (24), Section 4.5, we have the following relationship:

Table 4 Parameter settings for travel pattern estimation. Items

Input matrices

distance matrix by car (km), d1ij

⎧ ⎫ ⎡ ⎛ 5 ⎞2.5 ⎡ ⎛ 1 ⎞2.5 ⎛ 2 ⎞2.5 ⎤ ⎛ 1 ⎞2.5 ⎤ ⎜ ⎟ ⎜ ⎟ ⎪ ⎥ ⎢⎜ ⎟ ⎥⎪ ⎪⎛ ⎪ ⎞2.5 ⎢ ⎝⎜ 6 ⎠⎟ ⎝ ⎠ ⎝ ⎠ 1 ⎥ + 10 2.5 ⎢ ⎝ 6 ⎠ ⎥⎬ ⎟ ⎢ 165 − 20* ⎨ ⎜ + 3 + 3 F 2 ( pe ) ⎥ F 2 ( pe ) ⎥ ⎪ ⎢ F1( pe ) ⎪ ⎝ 0 . 3 + pe ⎠ ⎢ F1( pe ) ⎪ ⎢⎣ ⎥⎦ ⎢⎣ ⎥⎦ ⎪ ⎭ ⎩ x C *= ⎧ ⎫ ⎡ ⎛ 5 ⎞2.5 ⎡ ⎛ 1 ⎞2.5 ⎛ 2 ⎞2.5 ⎤ ⎛ 1 ⎞2.5 ⎤ ⎜ ⎟ ⎜ ⎟ ⎜ ⎟ ⎜ ⎟ ⎪ ⎪ ⎢ ⎥ ⎢ ⎥ 2.5 ⎪⎛ ⎪ ⎞ ⎝ ⎠ ⎝ ⎠ ⎝ ⎠ 1 ⎥ + 10 2.5 ⎢ ⎝ 6 ⎠ ⎥⎬ ⎟ ⎢ 6 pe ⎨ ⎜ + 3 + 3 F 2 ( pe ) ⎥ F 2 ( pe ) ⎥ ⎪ ⎢ F1( pe ) ⎪ ⎝ 0 . 3 + pe ⎠ ⎢ F1( pe ) ⎪ ⎢⎣ ⎥⎦ ⎢⎣ ⎥⎦ ⎪ ⎩ ⎭

distance matrix by mass transit (km), d2ij free ﬂow time (min), tij0 general road capacity (veh/hour), Fij

(25)

where ⎞1.5 ⎛ 1 ⎞2.5 ⎞1.5 ⎛ 1 ⎞2.5 ⎛ 2 ⎞2.5 ⎛ ⎛ 5 ⎞2.5 ⎛ 1 1 ⎜⎜ ⎟⎟ +⎜⎝ 6 ⎟⎠ 101.5, F2 (pe )=⎜⎝ 3 ⎟⎠ ⎜⎜ 0 . 3 + p ⎟⎟ +⎜⎝ 3 ⎟⎠ 101.5. ⎝ 0 . 3 + pe ⎠ ⎝ e⎠

F1 (pe )=⎜⎝ 6 ⎟⎠

There are alternative combinations of the price pe and the number of individual credits distributed xC * in order to satisfy Eq. (25). As a result, for a TCS design in practice we can determine the number of individually distributed credits based initially on the credit price. Fig. 5 demonstrates the effects of the credits price on the total utility of the network. The total utility of the network is deﬁned by the micro-economic model U2 for the case with a TCS in place, and by micro-economic model U1 for the case without a TCS. Assuming an initial distribution of tradable credits, then total utility decreases at the equilibrium tradable credits price ( pe =0.114 ) compared with the case without a credits scheme. Total utility increases quickly with an increase in the credits price and alongside a rapid increase in the number of kilometers by mass transit. The settings for the time parameter, γ = £0. 1 per min, α ¼0.4, β ¼10, and other parameters needed for the estimation of travel patterns were as shown in Table 4. The travel pattern for private car kilometers can be determined iteratively based on Eqs. (11, 13–15), whilst the mass transit travel pattern was estimated based on Eqs. (12, 16–17). In terms of setting the stepwise function for the generalized trip time: 10 categories of generalized journey time were used, with 5 min intervals (K =10, δk=5) and the last category (i.e. the category of Tijb above 50 minutes) was taken as the reference point in the estimation process. The generalized mass transit trip time can b b b b then be calculated based on Eqn. (17): f (T13 ),f (T14 ),f (T23 ),f (T24 ), and further generalize travel costs for the mass transit mode according to b b b b (16), C13 , C14 , and C24 . The private car and mass transit travel , C23 patterns in the case of no TCS and then with a TCS (for each of the two initial credit distribution approaches) are shown in Table 5. 1.5

79

x 10

1.45

1.4

1.35

Zone

3

4

1 2 1 2 1 2 1 2

20 20 15 15 25 15 1500 800

25 25 20 20 10 16 2000 1000

From Table 5 it can be seen that the travel pattern for both private car and mass transit modes are similar with and without implementation of the TCS. Under the scheme, the travel patterns are also seen to be similar according to the two initial credit distribution measures. Compared with the obvious effects on travel mode choice (as shown above), the effects of the scheme on travel patterns overall (i.e. OD matrices) is seen to be minor. This leads to the conclusion that the introduction of a TCS is likely to clearly impact on the distribution of kilometers between different travel modes, but is less likely to affect the overall travel pattern in terms of OD's.

6. Case study for Beijing municipality and discussion Following the illustration of the modeling framework for a simple network in Section 5, here we further investigate the TCS effects for the case of Beijing municipality. The analysis is based on an OD survey between districts in 2000 (China Academy of Urban Planning and Design (CAUPD), 2002). The whole city consists of 10 districts (zones), as shown in Fig. 6. The width of the lines between zones in Fig. 6 shows differences in the average number of trips per person per day according the survey. From the data, a network can be constructed based on 10 zones and from this, a 10 10 OD matrix. It is noted that to apply the policy simulation analysis framework in practice, the model would need to be carefully calibrated using a detailed survey or statistical data. To provide an accurate and true calibration of each parameter in the model for such a large city of Beijing is beyond the scope of this particular paper, which aims instead to illustrate the principles of the method. According to the modeling assumptions outlined in Section 4, private car and mass transit modes act as substitutes and individuals have a preference for car use. We assume this is still the case for travel in Beijing districts, but of course in a real life implementation the local preferences would be investigated and adopted. We further assume that both the population and cars ownership in the city are evenly distributed within the 10 zones, with one private car used by one individual per day. Before describing the trip estimation process,

Total Utility

1.3

Table 5 Travel pattern with/without TCS, unit: VKT.

1.25

Scheme

1.2

1.15

No TCS

1.1

1.05

1 0

0.1

0.2

0.3

0.4 0.5 0.6 Tradable Credits Price (pe)

0.7

0.8

Fig. 5. Effects of the tradable credit prices on total utility.

0.9

1

TCS with an equivalent initial distribution TCS with a proportional distribution

Car travel pattern

Mass transit travel pattern

Zone 3

4

Zone

3

4

1 2 1 2

45748 15637 37796 11098

15249 19111 13280 12515

1 2 1 2

11906 38302 23260 69872

5103 57453 8603 75694

1 2

39567 10578

13902 11928

1 2

24350 66598

9006 72148

80

M. Xu, S. Grant-Muller / Transport Policy 47 (2016) 72–83

6.1. Estimating individual private car kilometers x ic : use of survey data

Fig. 6. Districts of Beijing and average trip distribution. (Source: CAUPD, 2002).

some background data about the Beijing municipality used to illustrate the modeling of the TCS is given. This draws on survey data collected in 2000 and Xu et al. (2010). For the municipality, the average percentage of trips using a private car in 2000 was 23.24%, whilst the average percentage of trips by mass transit (including road surface transit and subway) in 2000 was 26.51%. By the end of 2000, the total population was 13.819 million, and the number of total private cars was 1.578 million. The daily average travel frequency per individual is 2.81 times, the daily average travel frequency per car is 2.49 times, and the average daily distance traveled per car was 24.2 km. In the models given in Section 4.1, there is a need to specify several parameters. The conventional approach (Varian, 1992) is to calibrate functional parameters to benchmark data. Under the assumptions outlined in Section 4 and Section 5 and based on the available travel data (See Section 6.1 for more details.), we set individuals in the ﬁrst 4 zones to have an equal preference for car travel, i.e. a1=a2=a3=a 4=0.8, individuals in zone 5 and zone 6 to have an equal preference for cars with a5=a6=0.77, individuals in zone 7, zone 8 and zone 9 have equal preferences for car travel with a7=a8=a9=0.71 , and ﬁnally, individuals in zone 10 have a strong preference for car travel with a10=0.78. Individuals’ budget for transport are set as follows: zone 1 to zone 4 are identical with I1=I2=I3=I4=1450 yuan (100 yuan ¼16.03 US Dollar), I5=I6=1382 yuan, I7=I8=I9=1350 yuan and ﬁnally for zone 10, I10=1415 yuan. The ﬁxed cost per km traveled by car is pv =20 yuan, whilst the ﬁxed cost per km traveled by mass transit is pb =1 yuan. As we focus on travel mode choice behavior, we assume that the population in each district is the same as the number of vehicles, i.e P1=⋯ = P10=0.1578 million. We set the parameter ρ = 10 with the given substitution assumption of car and mass transit modes. As we have mentioned in Section 4.1, the allocation parameter ai (i = 1, 2, ⋯ , 10) is for private car use / the proportion of transport income spent on private car use in each zone i . In general, the bigger of the parameter ai then the greater the dependence of travelers on private car use in zone i . Using the survey data it is possible to easily estimate daily mass transit kilometers in each zone, however it is far more difﬁcult to estimate the number of daily transit kilometers by car owners. Further survey data, for example from an individual mode choice survey, would be necessary to estimate individual mass transit VKT. This is an issue for further research and outside the scope of this study.

Theoretically there are different ways to estimate individual private car kilometers in each zone based on the survey data. It is possible to estimate individual car kilometers based on a daily OD matrix of total kilometers and for this study, the survey report from the year of 2000 provides the necessary data in the form of total kilometers for a 10 10 OD matrix (the units are per 10,000 kilometers per person per day). To estimate private car kilometers in each zone i.e. x ic as input for individual VKT in the proposed model, it would be possible to apply some basic assumptions in order to transform the total distance traveled in each zone (from the survey data) to individual VKT. The total distance traveled in each zone can be multiplied by the proportionate car mode choice and then divided by the population for each zone. However applying this approach did not produce a satisfactory numerical outcome in practice, particularly when related assumptions in the model were also taken into consideration. As a result an alternative approach was taken in this study as outlined below. Considering that different districts in Beijing have obviously functional differences (i.e concerning land use, employment proﬁle, commercial activity etc.) and the links between different employment types and overall level of travel, in this study we estimate individual private car kilometers in each zone based on daily average travel frequency by level of different employment type/profession, zone 1 to zone 4 are dominated by company employee and government ofﬁcials, zone 5 and zone 6 are dominated by company employees and sole proprietors, zones 7, zone 8 and zone 9 are dominated by teachers, students and scientiﬁc and technology staff, whilst zone 10 is dominated by low grade manual laborers and domestic staff. Based on the survey data, we can then estimate the daily average travel frequency in different zones as shown in Table 6. We can then estimate individual kilometers by private car and mass transit modes in each zone using the daily average travel frequency in each zone, multiplied by the average travel distance per car. 6.2. Estimating individual private car kilometer x ic and mass transit kilometer x ib : a modeling approach Based on the survey data it is possible to estimate a distance matrix based on the location of different zones, free ﬂow travel time and general road capacity (based on the OD matrix and travel time). In the simulation undertaken, 30 categories of generalized journey time were used with 15 min intervals ( K = 20, δk=15). The last category, i.e. the category of Tijb which is above 300 min (or 5 h) was taken to be the reference category in the estimation process. Based on the survey data, the total number of car trips for the year 10 of 2000 is given by ∑i = 1 Tic =1.61*1010 times per year. We suppose that the total number of car trips can be equally allocated across the whole year for each driver. A transformation is then possible to obtain a ﬁgure for the average daily VKT per individual, which is 67.6 km, calculated from (1.61*1010*24.2 / 365*1.578*107). The total VKT per day before the implementation of a TCS is then given by 7.5*108 km ( 67.6*1.578*107). With the introduction of the TCS we now expect that the total number of car kilometers will reduce by 30%. As a result, we can Table 6 Estimated daily average travel frequency, derived from dominant profession in each zone (Unit: times per day). Zone

Z1

Z2

Z3

Z4

Z5

Z6

Z7

Z8

Z9

Z10

Frequency

3.12

3.12

3.12

3.12

2.97

2.97

2.86

2.86

2.86

3.04

M. Xu, S. Grant-Muller / Transport Policy 47 (2016) 72–83

set the total number of credits per day to be x¯ =5.1*108 (67.6*0.7*1.578*107). Based on the scheme assumptions previously outlined, we set the initial distribution of credits using both an equivalent approach and a proportional distribution approach, using the daily average travel frequency in each zone as shown in Table 6. The difference between the two approaches to distributing the initial credits on the allocation to individuals is shown in Table 7. Under the TCS, we set the price of a tradable credit to be pe =10 yuan. With these parameter settings, the estimated kilometers by car and mass transit modes for Beijing municipality are as shown in Table 8. 6.3. Sensitivity analysis As can be seen from the analysis outcomes in Table 8, it is clear that the private car kilometers estimated from the proposed model (I2) and the survey data (I1) as the benchmark data match well, according to the parameters used. To verify the validity and applicability of the proposed model, we can further implement a sensitivity analysis with respect to allocation parameters ai (i = 1, ⋯ , 10). The sensitivity analysis is based on zone 1, as mentioned in Section 6.1, zone 1 is dominated by company employee and government ofﬁcials. The land use characteristics in this zone determine that private car used in this zone is higher than other zones. Fig. 7 demonstrates the impact of the variants of a1 on the car kilometers with/without TCS. As we can see, with the individuals budget ﬁxed for travel I1=1450, the higher the value of a1, the greater the total kilometers for each individual in zone 1. The growth of a1 will bring an increase in mass transit kilometers, and will bring with a small decrease in car kilometers Furthermore, either with/without TCS, and under the case of TCS with proportional initial distribution and equivalent initial distribution, the changes with respect to the car kilometers and mass transit kilometers remain consistent. These characteristics remain with respect to the allocation parameter ai and for the effects of individual car kilometers and mass transit kilometers in other zones.

81

Similarly, we can implement the credits price for the case study in Beijing and the numerical results are similar to those presented in Fig. 5 for the 4-zone example network. Due to space limitations, we have not reported the full set of sensitivity tests. 6.4. Discussion As demonstrated in this Section, the case study presented involves the use of several parameters. These parameters are speciﬁed with relatively few observations, as presented in Section 6.3, The parameters are calibrated using a conventional approach based on the use of benchmark data. The parameter settings for different zones are based on the differences in the main functions of different districts. Although the calibration process is a time consuming process and whilst the speciﬁcation of function coefﬁcients is complicated and error-prone, the sensitivity analysis presented veriﬁes the validity and applicability of the proposed model. In order to extend the sensitivity analysis in Section 6.3, another potential calibration approach is the so-called "calibrated share form", where the cost and demand functions are explicitly incorporated. As introduced by Rutherford (1995), the calibrated share form can be implemented in the GAMS (The General Algebraic Modeling System, www.gams.com). We leave the exploration of the most effective method to set these parameters for further study. The effects of a TCS can be demonstrated by articulating the scheme within the modeling framework described in this paper. The consequences arising from changes in the costs of car travel

Table 7 Distribution of initial number of credits ( x¯ ic ) per individual per zone. Zone

Z1

Z2

Z3

Z4

Z5

Z6

Z7

Z8

Z9

Z10

Equivalent distribution Proportional distribution

47 49

47 49

47 49

47 49

47 46

47 46

47 44

47 44

47 44

47 48 Fig. 7. Impacts of variations in a1 on car kilometers with/without TCS.

Table 8 Kilometers with/without TCS, unit: VKT. Items

Vehicle Kilometers Traveled (VKT)

Z1

Z2

Z3

Z4

Z5

Z6

Z7

Z8

Z9

Z10

I1

xic

69.2

69.2

69.2

69.2

65.9

65.9

63.4

63.4

63.4

67.4

xib

–

–

–

–

–

–

–

–

–

–

xic xib xic xib xic xib

69.1012

69.1012

69.1012

69.1012

65.8662

65.8662

64.3507

64.3507

64.3507

67.4371

67.9756

67.9756

67.9756

67.9756

64.6758

64.6758

62.9862

62.9862

62.9862

66.2571

49.2595

49.2595

49.2595

49.2595

47.5170

47.5170

46.6997

46.6997

46.6997

48.3630

48.1407

48.1407

48.1407

48.1407

46.3536

46.3536

45.4111

45.4111

45.4111

47.2065

49.7726

49.7726

49.7726

49.7726

47.2604

47.2604

45.9299

45.9299

45.9299

48.6196

48.6422

48.6422

48.6422

48.6422

46.1033

46.1033

44.6626

44.6626

44.6626

47.4569

I2 I3 I4

Key: I1 represents kilometers derived from survey; I2 represents kilometers estimated from the model without TCS; I3 refers to kilometers under TCS with an equivalent initial distribution; I4 refers to kilometers under TCS with proportional initial distribution. “Zi” refers to the i’th zone. “ xic ” denotes private car kilometers in the i′th zone. “ xib ”, denotes mass transit kilometers in i′th zone.

82

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alongside the permitted total VKT from the scheme act as a restraint on the pattern of total kilometers, which may be intuitively expected. An iterative process will continue until nobody is willing to make further changes in their travel activities. With the implementation of a TCS, it is therefore possible in principle to reach the target reduction in private car kilometers of 30%. Individuals will adjust their travel patterns differently under the two initial credit distribution approaches. Individuals in zones 1-4 and zone 10 will have to buy credits to support the extra car kilometers over their limit, whilst those in zones 7-9 can sell their credits for ﬁnancial gain. The two alternative approaches to the distribution of initial credits have different effects on the individuals’ travel by car and mass transit modes. From Eq. (24), which shows the relationship between the price of tradable credits and the credits that are individually distributed, the credit price is expected to affect private car kilometers substantially. In order to achieve a target for reductions in VKT traveled by car, the design of the TCS will be crucial, i.e. the choice of credit price and the initial distribution scheme for the tradable credits. A comparison between the travel pattern with and without the TCS for the Beijing study has shown similar ﬁndings to the small network illustration provided in Section 5, i.e. the implementation of a TCS has no obvious effects on the overall travel pattern in terms of OD movements. Furthermore, the travel pattern according to the two different initial credit distribution approaches is also similar.

7. Conclusions TCS has become familiar to environment economists as a pollution control measure. This is in contrast to the case for many transport economists and transport management practitioners, for whom it appears as new and unfamiliar approach. Despite that, researchers in transport economics can see the potential of a TCS for road trafﬁc mobility management, although it is clear that many theoretical and application related issues remain undeveloped. In this paper, we have discussed how a TCS affects travelers’ mode choice based on a simulation framework. The proposed framework will be interesting to policy makers who want to establish sustainable transportation systems. A small scale network and case study for Beijing municipality have been used to illustrate the working of the model proposed using some basic assumptions. These include assumptions on travelers’ preferences across geographic and time spaces and between individuals. Contextual assumptions have also been made for the case of Beijing. As the main goal of the paper has been to illustrate the working of the modeling and analysis framework, it is appreciated that these assumptions would need to be further reﬁned for a more in-depth case study analysis. Outputs from local surveys could supply more accurate data in that case. The main contributions of this paper to the literature are as follows:

A novel analysis framework to investigate the effects of a TCS.

This framework connects individual travel mode choice behavior and travel pattern characteristics in a regional/city trafﬁc network. As a component of the analysis approach, we borrowed consumer behavior analysis methodology and developed a CES approach to modeling the effects of a TCS on daily kilometers, and the choice of travel mode is determined by the relative costs of different modes and the transport budget. We conclude that a TCS provides a promising policy option in reducing private car kilometers. A cap-and-trade measure can achieve the target car trip reduction (as reﬂected by VKT) by

changing travel mode choice behavior. The design of the TCS (including the settings of credit price and initial credit distribution) are discussed. We emphasize that TCS can clearly affect travelers’ mode choice, however, the scheme effects on the travel pattern, as indicated by OD movements overall, is minor. The TCS studied in this paper discourages travelers’ private car use by imposing quantitative restraints and encourages a switch to PT travel. However, the scheme does not consider the time and space factors in this study, and in that respect would be expected to be ineffective in tackling the problem of local road trafﬁc congestion. To deal with current incidents of trafﬁc congestion, new TCSs are needed that are able to consider time and space dependencies, that are able to adjust trafﬁc ﬂow and can make better use the available road capacity. This is an issue for future research, alongside some other key issues as follows:

An in-depth disaggregated analysis of effects of the TCS on

mode choice is necessary in order to explore how this type of scheme can deal with different types of mode choice from different perspectives; Further development of the model is needed to integrate route choice behavior of travelers under a macroscopic transport network equilibrium analysis; Policy packages are now favored by many policy makers as an effective means to introduce behavioral change. Packages can be deﬁned as any combination of one or more economic measures with one or more other types of measures (regulatory, physical, technology). Further research is needed to investigate how a TCS could interact with these other types of measures, e.g., with respect to different transport management measures given in Xu et al. (2015).

Acknowledgments The authors would like to thank Prof. Ronghui Liu (ITS, University of Leeds) for her comments and suggestions that help us to improve the quality of the paper. The work described in this paper was jointly supported by the National Natural Science Foundation of Chin (71422010, 71361130016), the EU Marie Curie IIF (MOPED, 300674), and the National Basic Research Program of China (2012CB725401). The content is solely the responsibility of the authors and does not necessarily represent the views of the funding sources. Any remaining errors or shortcomings are our own. Any views or conclusions expressed in this paper do not represent those of funding sources.

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Transport Policy journal homepage: www.elsevier.com/locate/tranpol

Trip mode and travel pattern impacts of a Tradable Credits Scheme: A case study of Beijing Meng Xu a,n, Susan Grant-Muller b a b

State Key Laboratory of Rail Trafﬁc Control and Safety, Beijing Jiaotong University, No. 3 of Shangyuan Residence, Haidian District, Beijing 100044, China Institute for Transport Studies, University of Leeds, 34-40 University Road, LS2 9JT Leeds, UK

art ic l e i nf o

a b s t r a c t

Article history: Received 18 August 2015 Received in revised form 15 December 2015 Accepted 25 December 2015

We examine how trip mode and travel pattern of travelers are inﬂuenced by a given Tradable Credits Scheme (TCS). An analysis framework is proposed to investigate the effects of a basic TCS. Using a simulation analysis and case study from the Beijing municipality, we demonstrate that a TCS can achieve a target for reducing the expected car kilometers. The research demonstrates that a TCS will have an effect on travelers’ mode choice. However, it is likely to have only a minor effect on the overall travel pattern in terms of OD movements. & 2015 Elsevier Ltd. All rights reserved.

Keywords: Tradable Credits Scheme (TCS) Transport management policy Mode choice Welfare analysis

1. Introduction Mode choice is a fundamental issue in transport studies and one which has been heavily researched (see, for example, BenAkiva and Lerman, 1985; Dijst et al., 2002; Hensher and Rose, 2007; Van Exel and Rietveld, 2009; Ho and Mulley, 2013; Chidambaram et al., 2014; Habib and Weiss, 2014). However, many of these studies are based on a disaggregate approach and have sought to understand how travelers’ mode choice behavior is affected by a series of factors, based on analysis of past (or anticipated) travel data. Other studies of transport mode choice have been based on a macroscopic network equilibrium approach, e.g., (Shefﬁ, 1985; Jara-Dıaz and Videla, 1989; Oppenheim, 1995; Ortuzar et al., 2001; Xu and Gao, 2009; Can, 2013; Zhao et al., 2013). The notion of the Tradable Credits Scheme (TCS) has evolved over a relatively long period, particularly in relation to pollution control, where it has been well studied and used in practice. In the transport sector, the scheme is a particular case of a wider group of so-called economic instruments that have used pricing or changes to income to inﬂuence travel behavior and transport choices. Economic instruments have a strong, direct leverage on both ﬁxed and variable prices related to travel choices. Fixed price schemes include the use of registration fees and car ownership costs, whilst examples of variable pricing includes public transport (PT) fare n

Corresponding author. E-mail addresses: [email protected] (M. Xu), [email protected] (S. Grant-Muller). http://dx.doi.org/10.1016/j.tranpol.2015.12.007 0967-070X/& 2015 Elsevier Ltd. All rights reserved.

structuring, variable parking charges and toll fees. Other types of economic instruments include positive ‘incentive-based’ policies, taxes and subsidies on vehicle purchase, scrappage incentives, taxes on vehicle use, emission taxes, fuel taxes, vehicle kilometer traveled taxes, congestion charges and pay-as-you-drive insurance. See (e.g. Santos et al., 2010; Ben-Elia and Ettema, 2009; 2011a; 2011b; Potter et al., 2006; Beck et al., 2013). A signiﬁcant tranche of research has also been carried out on alternative transport management policies, largely to understand the role these policies playing in achieving sustainable development of the transport system. Various travel demand management policies have been proposed and analyzed in the context of mitigating trafﬁc congestion, with examples including the use of reward measures (Verhoef et al., 1997; Bliemer and Van Amelsfort, 2010; Ben-Elia and Ettema, 2011b), tradable driving rights (Akamatsu, 2007; Yang and Wang, 2011), road pricing (Yang and Bell, 1997; Yang and Huang, 2005) and rationing (Zhu et al., 2013). Examples of ‘command and control’ policies include controls on car ownership (e.g. a quota system for new vehicle plates in Singapore, Chin and Smith, 1997) and a driving ban scheme in Mexico City (Davis, 2008). Concerning studies of mode choice behavior, the literature reﬂects areas that have had particular attention. Examples include logit-based mode choice analysis under road pricing (Huang, 2002), which provides some discussion of the classical bottleneck model. Tirachini and Hensher (2011) address policies around multimodal transport pricing. Recently, Wu et al. (2012) present optimization model to design equitable and efﬁcient tradable

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credit schemes for general multimodal transportation networks. Tian, Yang and Huang (2013) examine a two-mode problem (auto and transit modes) under a TCS with a bottleneck modal (Arnott, de Palma and Lindsey, 1993) which a physically separated transit mode is parallel to a highway with a bottleneck, and demonstrated that a TCS which emulates the bottleneck congestion pricing and transit subsidy in a revenue-neutral manner. However, further studies are necessary to identify how a TCS may impact on transport mode choice of travelers. TCSs cover a variety of instruments that range from the introduction of ﬂexibility into regulation to the organization of competitive markets for credits (Goddard, 1997). Quantiﬁed physical constraints are set in the form of credits allocated to groups of agents consuming scarce resources, and permission is granted to transfer these quotas between activities, products or places (offsetting), periods of time (banking) or to other agents (trading, hence “tradable credits”). For travel demand management, a tradable credit scheme can reward travel patterns and provide a continuing incentive for travelers to manage their credits, e.g. reducing credit use by carpooling or using PT. Through the design of credit based measure, it is possible to achieve desirable outcomes of travel demand management. In comparison to the case of road pricing and some other economic policies for travel demand management, TCS is a relatively new measure both in theory and in practice. The lack of practical application of this economic measure may be attributable to an undeveloped and incomplete theoretical foundation and particular practical issues that are yet to be resolved (Grant-Muller and Xu, 2014). However, the idea of TCS provides a promising policy approach for mobility management and has received increasing attention in recent years. Section 2 presents a literature review of the art-of-state studies of TCS within the transport ﬁeld, from which it is apparent that most recent studies on TCS have largely focused on macroscopic analysis. A fundamental question is whether a TCS is likely to affect travelers’ mode choice if it were implemented in practice. In the same way that road pricing polices (used in London and Singapore for example) have impacted on demand for private vehicle travel, it is quite possible that a TCS may have a similar effect and reduce the number of vehicle kilometers traveled (VKT). In this study, we examine how travelers’ mode choice preferences may be inﬂuenced by implementing a TCS in an urban setting. The study supposes that the regional authority is responsible for implementing the TCS, the initial credit allocation is free and individuals receive a number of credits (representing vehicle-kilometers) based on a target of reducing the overall total VKT for the urban area. Individuals, in maximizing their utility, must consider their travel mode choice based on their credit allocation. That is, the individual must consider the permitted number of kilometers, the credit price ( pe ) and then determine how many further credits they should purchase if they wish to travel additional kilometers using a private car. To investigate the inﬂuence of a TCS on travel mode choice and different from existing studies i.e. Wu et al. (2012) and Tian et al. (2013), we present a microeconomic quantitative analysis framework to simulate policy scenarios. Travel patterns are compared before and after introduction of a TCS. This study presents a framework which connects a microeconomic analysis (of individual travel mode choice) and a macroscopic network analysis (i.e. the travel pattern for a network) in order to analyze a speciﬁc transport demand management policy (i.e. the TCS). Therefore, a TCS based on VKT for travel demand management is outlined and a new travel demand management policy analysis framework based on a neo-classical microeconomic model is presented. The organization of the paper is as follows. In Section 2, a brief review of TCS and the appropriateness of the Constant Elasticity of

73

Substitution (CES) approach are presented whilst in Section 3, a policy analysis framework for transport mode choice with a TCS is proposed. In Section 4, we develop an estimation model of the individual average vehicle kilometers (based on a neo-classical microeconomic model) with and without a TCS, including the credit equilibrium price and the travel pattern in different zones. In Section 5, the detail of the analysis framework is given, including scenario setting with and without a TCS, input data, and investigation process, based on a small network. We discuss and further compare the effects of a TCS on transport mode choices in Section 6, based on survey data and the presented analysis framework for the case of Beijing municipality. Finally, Section 7 concludes the paper.

2. Problem description and basic considerations 2.1. TCS: a cap-and-trade measure A TCS usually assumes the form of a cap-and-trade system (Dales, 1968). It often targets a certain level of activity (for example, emissions), assigns credits to match the targeted total quantity and allows consumers, organizations and other entities to trade the credits at an endogenously determined price. To the extent that quantity control instruments involve a trading mechanism, they also provide price incentives to the regulated parties (Hepburn, 2006). Although market efﬁciency could be satisﬁed by an auction or other measures and some challenges in policy implication (Sovacool, 2011), the credit allocation mechanism is important. For example in emission control political concerns often favor a proportional allocation based on historical emission records. The credit allocation mechanism has been applied in a variety of different contexts including controlling air pollution, the degradation of wetlands, agricultural pollution, water scarcity and ﬁsheries depletion (OECD, 2004). Examples include an oligopolistic power market model with tradable NOx permits (Chen and Hobbs, 2005), biodiversity conservation with tradable credits (Drechsler and Watzold, 2009), Nitrates control in groundwater (Morgan et al. 2000), regulation of an airline duopoly on a congested airport (Verhoef, 2010), emission reduction from air transport (Carlsson and Hammar, 2002; Mendes and Santos, 2008), incorporating the transport sector into a carbon cap-and-trade program (Ellerman et al., 2006; Millard-Ball, 2008; Jochem, 2008), pollution permits to reduce car ownership in the UK (Walton, 1997) and land use management (Henger and Bizer, 2010). Recent investigations on travel mobility management using tradable credits include a series of studies since the work of Yang and Wang (2011), which has discussed the management of road network mobility with tradable travel credits with a network modeling approach. Continuing this innovative research, there are further series studies on the TCS for travel behavior analysis, see for example, (Wu et al., 2012; Wang and Yang, 2012; Wang et al., 2012; He et al., 2013; Nie and Yin, 2013; Xiao et al., 2013; Tian et al., 2013; Bao et al., 2014; Wang et al., 2014a, 2014b; Zhu et al., 2014; Mamun et al., 2016). Table 1 characterizes existing TCS approaches used in the transport sector for mobility management, along with examples of where such schemes have been adopted. Recent reviews on TCS can refer to Fan and Jiang (2013) and Grant-Muller and Xu (2014), where Fan and Jiang (2013) reviewed a variety of TCSs for roadway capacity allocation focusing on detailed system design and overall functions, and Grant-Muller and Xu (2014) has focused on the TCS roles in road trafﬁc congestion management. In this paper, we discuss how to use a TCS for mobility management and form a comparison with existing studies of TCSs. Supposing that a government authority needs to control the total VKT by private car in an urban area or region, it will need to

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Table 1 Recent TCS approaches in the transport sector for mobility management. State-of-art studies

Methodology

Approaches

Yang and Wang (2011) Wang and Yang (2012) Wang et al. (2012) Wu et al. (2012)

Mobility management with network equilibrium analysis Mobility management with network equilibrium analysis Mobility management with network equilibrium analysis Effect of income on travelers’ choices on multimodal networks

He et al. (2013)

Mathematical programing Bisection-based trial-and-error method Mathematical programing Mathematical programs with equilibrium constraints Variational inequality

Nie and Yin (2013) Xiao, Qian and Zhang (2013) Tian, Yang and Huang (2013) Bao et al. (2014) Wang et al. (2014a) Wang et al. (2014b) Zhu et al. (2014) Mamun et al. (2016)

Mathematical programing Mathematical programing Mathematical programing Mathematical programing Bilevel programing Bilevel programing Mathematical programing Empirical analysis

calculate the capacity of access roads between different zones and car ownership information for residents in the urban area. The initial credit distribution is assumed to be free and each individual in the zone will receive a certain number of credits for the VKT that they are permitted to travel by car. Each credits holder will then need to consider the amount of kilometers by car permitted by their allocation and the price of credits if they wish to travel further kilometers by car. Those who don't want to travel further kilometers by car will also consider the amount the kilometers they travel, as they can sell excessive credits. The authority sets the credits market, tracking credit prices, the number of credits and transactions in terms of buying and selling credits. With a limited period of validity for credits, the authority can act to adjust the total amount of credits with respect to the target for decreasing total VKT. The mathematical formulation for the TCS studied here will be presented in Section 4.1, following the introduction of the transport analysis framework used in this paper.

Effects on two types of players (Cournot-Nash players and Wardrop-equilibrium players) Bottleneck model for rush hour travel management Bottleneck congestion management Bottleneck congestion management and modal split with heterogeneous users Mobility management with network equilibrium analysis Travel demand management Travel demand management Multiclass trafﬁc network equilibrium analysis Regulating the vehicle miles traveled in Florida, USA

household travel demand and some economic indicators, Kalinowska et al. (2007) described the modiﬁcation of an Austrian computable general equilibrium (CGE) model in order to construct such a model and database for Germany. The transport sector is modeled as comprising car and public transport, using a microeconomic production household possessing a CES and striving to minimize costs per unit of output. The demand functions used in the TRE-part of TREMOVE are nested CES functions. This assumes CES applies at each level of the utility tree, e.g., the elasticity of substitution for the urban areas in the case study for London between private car and public transport is 1.05 in the peak and is 1.95 in the off-peak (The European Commission, Standard & Poor's DRI and K.U. Leuven, 1999). The CES form of utility function allows several situations to be considered, which depend on the elasticity of substitution parameter. It has also used in an individual tradable emission permit scheme for urban motorists (Bulteau, 2012) and the inﬂuence analysis of urban form on energy consumption according to individual consumption behavior (Yin et al., 2013).

2.2. Appropriateness of the CES approach for trip modeling Whilst relatively new to transport practitioners, the constant elasticity of substitution (CES) approach has been widely used in consumer behavior analysis. A consumer is characterized by their preference ordering for the goods obtainable, which is described by a utility function, and by a budget set that is limited by his/her income. The consumer is assumed to choose that bundle of goods in his/her budget set that maximally satisﬁes his/her preferences, i.e., the behavior can be described by utility maximization over the budget set (Varian, 1992). The CES utility function has often been chosen in consumer behavior analysis due to its advantageous properties with respect to ﬂexibility, and its consequences on the assumptions with respect to the existence and uniqueness of equilibrium (Kalinowska et al., 2007). In this paper, we adopt this approach for trips by private car and mass transit modes. The choice of travel mode is determined by the relative costs of different modes and the transport budget. One representative traveler who maximizes his/her utility (maximize his/her mobility) is considered to be representative of all travelers in the study. This rationale has been the basis for some related studies. One example is the European partial equilibrium CAR emissions simulation model (EUCARS 3 model), which was originally developed to study CO2 emission limitation policies in passenger transport. Consumer choices are described in the model by a decision tree (in the consumption block of the model), and the CES approach is used for the consumption of public transport services and private vehicle services (Denis and Koopman, 1998). In order to assess the impact of road pricing measures on

3. Analysis framework Fig. 1 illustrates the policy analysis framework used here to reﬂect mode choice in the context of a TCS, with further details for each component described in Section 4. If a TCS would be implemented, the budget for credits will become an additional resource considered within individuals’ mode choice. The use of a private car beyond the limit of the initial credit allocation will become subject to additional monetary costs. There are various options within the scope of the scheme: people may want to fully use their credits, buy additional credits (where their use of the car exceeds the initial allocation), or save and sell them for ﬁnancial gain. As a result, people not only have to decide on the necessity of the trips they take, but also how they want to manage their budget of allocated credits. Mode choice for a representative individual for each zone will be affected by the individuals’ transport budget, the travel cost according to different modes and the individuals’ attitudes. In choosing a travel mode, the individual is confronted with objective factors such as location, journey duration, departure time, activity type, mode availability and mode characteristics. All these factors, plus others that may be less objective, will affect mode choice. After determining the individuals' average number of trips by mode for a speciﬁed time period, it is possible to estimate the travel pattern (OD matrix) based on the number of trips by different modes. A destination choice model can be used to determine the travel pattern between different zones. This is an

M. Xu, S. Grant-Muller / Transport Policy 47 (2016) 72–83

Travel mode choice for given urban region (Section 4.1)

Representation of individual Transport budget Unit cost for private car/mass transit mode Attitudes (Section 4.1)

75

Regulatory authority Initial credit assignment Credit price Total credit amount (Section 4.3)

Travel OD matrix by modes (Section 4.2)

Destination choice model (Section 4.2)

Policy analysis The effects of the tradable credits scheme The effects of travel cost for different modes (Section 4.1) Fig. 1. Analysis framework for transport mode choice with and without a TCS.

iterative process based on the difference between the new and previous travel patterns, with the pattern ﬁnally determined if that difference is within 5%. A policy analysis can then be undertaken based on the variation in trips.

4. Methodology Based on the analysis framework outlined in Section 3, we present the methodological approach as follows. Firstly we list the notation used in Section 4.1, followed by a presentation of the model formulation in Section 4.2 and determination of the travel pattern in Section 4.3. The calculation of the credit price is described in Section 4.4, whilst the determination of the credits initially distributed to individuals is presented in Section 4.5. Finally, the characteristics of constant elasticity of substitution in the utility function are given in Section 4.6. 4.1. Model formulation Considering a given city or area which is separated into different zones i , i = 1,⋯ , N . We suppose that travelers have a preference to use a private car for their daily trips, but it is feasible to substitute between private car travel and mass transit modes. Considering environmental goals or other priorities, the authority may wish to restraint the number of private cars trips by the number of kilometers traveled (i.e. restraint car trips by VKT) and it is supposed that the authority will implement a tradable credit scheme. Before implementation of the scheme, it is assumed that each individual in zone i maximizes his/her utility by

(

)

( )

(4)

where Ui (x ic , x ib ) represents the utility function for a representative individual in zone i , x ic represents the individual average distance traveled by private car in zone i (unit: vehicle kilometers traveled N (VKT), x c = ∑i = 1 Pi x ic ), x ib represents the individual average distance traveled by mass transit in zone i (unit: vehicle kilometers traveled N (VKT), xb= ∑i = 1 Pi x ib ), and Pi is population in zone i . The variable pv summarizes private car costs per kilometer traveled, representing maintenance costs, fuel and insurance, and pb summarizes the price of mass transit per kilometer traveled. The notation Ii is the individual transport budget devoted to travel in zone i , ai is the allocation parameter for private car use/the proportion of transport income spent on private car use, and ρ is substitution elasticity. When the parameter ρ = 0, the CES utility function is, in fact, in the form of a Cob-Douglas utility function, which shows the car mode and mass transit mode as not being substitutable; when the parameter ρ = 1, it shows the car mode and mass transit mode to be perfect substitutes; when the parameter ρ = − ∞, it shows the car mode and mass transit mode to be complementary. Suppose the regulatory authority then implements a TCS. The initial credit distribution is free and each individual in each zone receives a number of credits that permits travel by car: x¯ ic . The individual then needs to consider the amount of kilometers that are allowed by car and the price of a credit if they wish to travel further more kilometers by car. Under the TCS, the utility maximization problem for each representative individual in zone i can then be formulated as the following:

(1)

s.t.

pv xic +pb xib≤Ii,∀i=1, ⋯,N

(2)

xic ≥0

(3)

1

ρ ρ ρ U 2 : MaxUi xic , xib =⎡⎣ ai ( xic ) + ( 1−ai ) xib ⎤⎦

(

)

( )

(5)

s.t.

pv xic + pe ( xic − x¯ ic ) + pb xib ≤ Ii, ∀ i = 1, ⋯, N

1

ρ ρ ρ U1 : Max Ui xic , xib =⎡⎣ ai ( xic ) + ( 1−ai ) xib ⎤⎦

xib≥0

(6)

(3)-(4) where pe is the price of tradable credits, x¯ ic represents credits received per individual in zone i , e.g., each credit/license entitles the holder to travel one kilometer by car, x¯ summarizes total N number of credits set according to the total VKT, x¯ = ∑i = 1 Pi x¯ ic , and other notations gives as below U1. Generally, travel mode choice is inﬂuenced by different factors and certainly, budget constraint is only one of the key factors. The

76

M. Xu, S. Grant-Muller / Transport Policy 47 (2016) 72–83

CES method used in consumer behavior analysis generally uses ‘budget’ or ’income’, based on the money budget constraint with ‘goods’. We use the term ‘transport budget’ based on the modeling approach since the ‘goods (transport service)’ consists of car mode travel and mass transit travel under the transport budget constraint without a TCS, Eq. (2), and with TCS, Eq. (6). Eq. (6) represents the transport budget constraint with the car and mass transit travel under the TCS, which means that every individual has a potential ‘transport budget’ for travel during a certain period (e.g., month, day, etc.) before making trips. Comparing Eq. (2) and Eq. (6), we ﬁnd that there exists a balance to be achieved in the working of the credits scheme from the perspective of individuals as follows. Firstly, it brings an increased cost for private car use ( pe ) and secondly, it brings an increase in the individuals’ transport budget ( Ii+pe x¯ ic ) for zone i . This increase could be treated as a transport subsidy ( pe x¯ ic ) paid to an individual if the number of credits x¯ ic is not used. According to the associated Lagrangian, we can derive the following solution for U2 when two modes are used:

⎛ ai ⎞ε Ii + pe x¯ ic ⎟ xic =⎜ ε ⎝ pv + pe ⎠ ai ( pv + pe )1 − ε + ( 1−ai )ε p 1 − ε b

(7)

(8) 1 . 1−ρ

ε ⎛ Pi aiε ( Ii + pe x¯ ic ) N 1 ⎞ ⎟ ∑ x c =⎜ ε 1− ε i=1 ε ⎝ pv + pe ⎠ ai ( pv + pe )1 − ε + ( 1−ai ) pb

Solutions for the

(9)

(10)

4.2. Determination of the travel pattern Different models can be used to determinate travel patterns based on different assumptions, for example, the random utility model (Anderstig and Mattsson, 1991) or the doubly constrained negative exponential gravity model (Wilson, 1970; Boyce and Daskin, 1997; Boyce and Mattsson, 1999; Boyce and Xiong, 2007). Here we use an aggregated logit type model as an approach to determine trip distribution, using two variables reﬂecting the level of employment ( Ej ) and generalized cost by car (Cijc ) or mass transit (Cijb ). Therefore, the number of kilometers with private car Tijc from zone i to zone j can be estimated by

Tijc =Tic

(

exp αEj + βCijc N ∑ j=1

)

(

exp αEj + βCijc

)

(11)

where α , β are parameters, and Tic represents the total private car kilometers in zone i , Tic =Pi x ic , unit: VKT. The number of kilometers by mass transit mode Tijb from zone i to zone j can be estimated by

Tijb=Tib

(

exp αEj + N ∑ j=1

Tib

(

βCijb

exp αEj +

)

βCijb

(13)

or by Eq. (14) without a TCS

Cijc =pv d1ij +γf

( Tijc )

(14)

where d1ij indicates the average distance (kilometers) from zone i to zone j by car, and γ represents the value of time, which converts travel time into generalized monetary travel cost. The f (Tijc ) in Eqs. (13 and 14) is assumed to take the form of a BPR function:

⎡ ⎛ Tijc ⎞φ ⎤ f Tijc =tij0 ⎢ 1 + ϵ ⎜ ⎟ ⎥ ⎢⎣ ⎝ Fij ⎠ ⎥⎦

( )

(15)

where tij0 is the free ﬂow time, Fij represent the general road capacity between zone i to zone j , ϵ = 0.15, φ = 4 . In Eq. (12), the generalize travel cost with mass transit mode Cijb can be written as

( )

model of U1 are also included in Eqs. (7 and 8) by setting pe =0, and x¯ ic =0, ∀ i = 1, ⋯ , N . The equilibrium solution for the total VKT in the zones is given by the following:

ε ⎛ 1 ⎞ε Pi ( 1−ai ) ( Ii + pe x¯ ic ) N xb=⎜ ⎟ ∑ ε 1− ε i=1 ε ⎝ pb ⎠ ai ( pv + pe )1 − ε + ( 1−ai ) pb

( )

Cijc =( pe +pv ) d1ij +γf Tijc

Cijb=pb d2ij +γf Tijb

⎛ 1−ai ⎞ε Ii + pe x¯ ic ⎟ xib=⎜ ε ⎝ pb ⎠ ai ( pv + pe )1 − ε + ( 1−ai )ε p 1 − ε b where ε is an elasticity coefﬁcient, ε =

In Eq. (11), the car generalize travel cost Cijc is either determined by Eq. (13) under a given TCS

(16)

where d2ij is the average distance (kilometers) from zone i to zone j by mass transit, and f (Tijb ) is assumed to take the form of a stepwise function for the generalized trip time between zone i to zone j by mass transit

( )

f Tijb =exp

(∑

K

k=1

δk DTijb

)

(17)

DTijb ,

In Eq. (17), is a dummy variable which is equal to 1 if Tijb falls in the generalized journal time category k and zero otherwise, and δk is the time interval. This type of step function has also been used by Debrezion et al. (2009) as a measure of generalized journey time between railway stations and by Sen (1986). A difference from the more commonly applied type of logit model is that the calculation of the number kilometers by private car, Tijc , and the number of kilometers by mass transit mode, Tijb , is an iterative process here. In Eq. (13) or Eq. (14), the generalized travel cost by car, Cijc is related to Tijc , and in Eq. (16), the generalized travel cost by mass transit, Cijb is related to Tijb . As a result, an iterative solution is necessary to determine the number of kilometers between zones by either private car or mass transit modes. 4.3. Determination of the credit price Here, we further discuss the determination of the credit price and how this will affect the traveler's mode choice. In order for the market to be balanced and consistent with the target for car use (as set by the regulatory authority), the credit price, which is based on the VKT, can be set as

xc = ∑

N

i=1

Pi xic =x¯ = ∑

N

i=1

Pi x¯ ic

(18)

Therefore, N

∑i = 1 Pi ( xic −x¯ ic )=0

(19)

Combining Eqs. (19) and (9), we have the following 1

)

(12)

where represents the total number of kilometers by mass transit in zone i , unit: VKT, Tib=Pi x ib .

⎤ε ⎡ N aiε ( Ii + pe x¯ ic ) ⎥ ⎢ ∑i = 1 ε ( p + p )1 − ε + ( 1 − a )ε p 1 − ε a v e i b ⎥ ⎢ i pe = ⎢ ⎥ − pv N c ¯ ∑ x i i=1 ⎥ ⎢ ⎦ ⎣

(20)

M. Xu, S. Grant-Muller / Transport Policy 47 (2016) 72–83

Deﬁne Fi (pe )=aiε (pv + pe )1 − ε +(1−ai )ε pb1 − ε , then Eq. (20) can be written as

Travel demand by modes with/without a tradable credits scheme (Utility maximum problem: U1/U2)

1

⎡ N aiε ( Ii + pe x¯ ic ) ⎤ ε ⎢ ∑i = 1 F ( p ) ⎥ i e ⎥ − pv pe = ⎢ N ⎥ ⎢ ∑i = 1 x¯ ic ⎦ ⎣

77

Total VKT (21)

Travel OD matrix by modes (Destination choice model)

Eqs. (20) and (21) give an implicit solution for the credit price, which could be solved using an iterative approach given the car costs per kilometer traveled pv , the price of mass transit per kilometer traveled pb , the individual transportation budget in zone i , Ii , the total number of credits sets by the authority x¯ , and related coefﬁcients.

Vehicle Kilometres for each OD No OD consistency

4.4. Determination of the number of credits initially distributed to individuals

Yes Analysis of the effects of the tradable credits

In general there are different ways to determine the number of credits initially received by individuals x¯ ic . We can determine x¯ ic if

Fig. 2. Transport policy analysis framework.

N

the total number of car kilometers ∑i = 1 (Tic +Tib ) is given and from Eqs. (9) and (10), combined with Fi (pe ), we have ε ε ⎛ ¯ ic ) ⎛ 1 ⎞ε N Pi a i ( Ii + pe x 1 ⎞ +⎜ ⎟ ⎜ ⎟ ∑i = 1 Fi ( pe ) ⎝ pv + pe ⎠ ⎝ pb ⎠ N

∑i = 1

ε Pi ( 1−ai ) ( Ii + pe x¯ ic )

Fi ( pe )

N

1

(

= ∑i = 1 Tic +Tib

)

4

3

(22)

2

Speciﬁcally, under the case of an equivalent distribution of initial credits,

Fig. 3. A 4-zone example network.

x¯1c =⋯=x¯ Nc =x̅ C *

(23)

We have ⎡ N ∑ i = 1 T ic + Tib − ⎢ ⎣ C x ̅ *= ⎡ 1 pe ⎢ p + p v e ⎣

(

)

(

ε

ε N Pi a i Ii i = 1 F i ( pe )

ε

+( ) ∑ ( )∑ ( +( ) ∑ )∑ 1 pv + pe

ε

Pi a iε N i = 1 F i ( pe )

1 pb

1 pb

ε

ε ⎤ N Pi 1 − ai Ii ⎥ i =1 F i ( pe ) ⎦

N Pi 1 − a i i = 1 F i ( pe )

(

)

)ε ⎤ ⎥ ⎦

(24)

5. Analysis framework From Sections 2–4, we present here an analysis framework for the investigation of a TCS. This section includes discussion of the scheme features and the assumptions made in the analysis. 5.1. Policy investigation process The research framework for a TCS is based on the main design features described in Sections 2–4 and employs a scenario based approach, as summarized by Fig. 2. 5.2. Numerical example To illustrate the policy simulation framework, we ﬁrstly employ a simple network that includes two origins (zone 1 and zone 2) and two destinations (zone 3 and zone 4), as shown in Fig. 3. Suppose that zone 1 and zone 2 are primarily residential areas, whilst zone 3 and zone 4 are employment zones. Assuming individuals in zone 1 have a preference for car travel with a1 = 5 / 6 whilst individuals in zone 2 have a preference for car travel with a2=2 / 3. It is also assumed that individuals’ budgets for transport in zone 1 and zone 2 are identical, I1=I2=20; the ﬁxed cost per kilometer traveled by car is pv =0.3, and the ﬁxed cost per kilometer traveled by mass transit is pb =0.1. We set the parameter ρ = 0.6 and therefore the elasticity of substitution with a value of ε = 2.5. The population in zones 1 and 2 are identical, P1=P2=1000,

the level of employment in zone 3, E3=1200, and in zone 4, E4=800. From the micro-economic model U1 we can derive the individual average distance in different zones without implementation of the TCS, see Table 2. In this case, the individuals’ average travel pattern is 61 km by car and 17 km by mass transit in zone 1, 35 km by car and 96 km by mass transit in zone 2. Therefore in zone 1, the total distance traveled by private car is 60996.9 km and the total distance traveled by mass transit is 17009.3 km, compared with zone 2, where the total distance traveled by car is 34748.3 km and the total distance traveled by mass transit trips is 95755.1 km. In both zones, the total distance traveled by car is 95745.2 km, the total distance traveled by mass transit is 112764.4 km and the total kilometers traveled by vehicles is 208509.6 km. Now, consider the case where the authority decides to reduce the demand for private car travel by 20.6%, i.e. the expected total number of kilometers by car becomes 76000 km. We can therefore set the total number of credits as x¯ = 76000 km and can consider a design for a TCS that will achieve this target. For the initial credit distribution, there are two general approaches: the ﬁrst is to distribute equally, i.e., we can set x¯1c =x¯2c =38 km in this example; the second approach is to distribute credits in proportion to the number of car kilometers made without a TCS. In this example we would set the number of car kilometers permitted by an individual in zone 1 to be x¯1c =48 km, and in zone 2 to be x¯2c =28 km. Table 2 Vehicle kilometers in different zones without a TCS. Vehicle Kilometers Traveled (VKT)

Zone 1

Zone 2

Total

xic

60.9969

34.7483

–

xib

17.0093

95.7551

–

Tic

60996.9

34748.3

95745.2

Tib

17009.3

95755.1

112764.4

M. Xu, S. Grant-Muller / Transport Policy 47 (2016) 72–83

Initial credit assignment approach

Vehicle Kilometers Traveled (VKT)

Zone 1

Zone 2

Total

Equivalent distribution

xic

51.0764

23.6121

–

xib

31.8637

145.5660

–

Tic

51076.4

23612.1

74688.5

Tib

31863.7

145566.0

177429.7

xic

53.4694

22.5058

–

xib

33.3566

138.7460

–

Tic

53469.4

22505.8

75975.2

Tib

33356.6

138746.0

172102.6

Proportional distribution

According to (20), the credit price can be determined using an iterative process. We set the price of tradable credits to be pe =0.114 . Other parameters in the micro-economic model U2 are as outlined above. We can then derive the number of kilometers in different zones with implementation of the TCS, as indicated in Table 3. It can be seen that the number of car kilometers in zone 1 is more than the number of car kilometers in zone 2, resulting from an initial assumption that the preference of individuals for 5 2 cars in zone 1, a1= 6 , is higher than that in zone 2, a2= 3 . Comparing between Table 2 and Table 3 it can be seen that with the implementation of a TCS, the number of car kilometers in each zone decreases and the number of mass transit kilometers increases. According to this model, the scheme therefore encourages individuals to travel by mass transit. As shown in Table 3, for a TCS with an initial proportional distribution the total number of kilometers by car is 75975.2 whilst the total number of kilometers by mass transit is 172102.5, giving a total distance traveled 248077.8 km. In comparison, with an equal credit distribution scheme, the total car kilometers is 74688.5, the total mass transit kilometers is 177429.7, and the total distance traveled is 252118.2 km. It can therefore be seen that by setting the tradable credits price and according to the approach used for the initial distribution of credits, the TCS can achieve the target of reducing car kilometers by 20.6%. With the implementation of a TCS, it also appears that the effects resulting from different approaches to the distribution of initial credits are different. With an equal initial distribution (the total distance traveled by car is 74688.5 km), the effect in terms of the reduction in car kilometers is stronger than with the use of an initial proportional distribution (the total distance traveled by car is 75975.2 km). However, an equivalent distribution approach also results in more mass transit kilometers (177429.7 km with an equivalent distribution vs 172102.6 km with a proportionate initial distribution). This also brings growth in the total number of kilometers for both zones (252118.2 km with equivalent distribution vs 248077.8 km with initial distribution in proportion). Furthermore, comparing Table 2 and Table 3, we can see that under a TCS, the number of mass transit kilometers in both zones clearly increases. This also causes a substantial increase in the total distance traveled (in comparison with the total distance traveled without a TCS) of 208509.6 km. From the CES model U2 with given TCS, the budget is actually improved with the mode shifting from car to mass transit, and therefore the solutions increase since they are obtained in the manner of maximizing utility. Moreover, the increase in the total number of trips could be caused by shifting mode (i.e., d1 od2) or an increase in frequency (i.e., number of trips), here it was considered to be a result of shifting mode. If it were an increase in frequency, this result would imply that implementing a TCS would cause people to make more trips and/or

increase the mobility freedom. However, overall it cannot be expected that an individuals’ trip frequency would increase by implementing a private-car use management policy (i.e., the TCS). As can be seen from Section 4.4, the determination of the credit price is very important. The credit price can be calculated iteratively, as shown in Eq. (20). Fig. 4 demonstrates the relationship between the total car kilometers and the price of credits for a 4-zone simple network (see Fig. 3). We assume that the TCS is based on an initial equivalent credits distribution approach and has a target goal to reduce the number of kilometers by car by 20.6%. From Fig. 4, in order to achieve this target, there exists a unique solution for the credit price which can be derived using Eq. (20). Under the given TCS, the higher the tradable credits price, the lower the total number of car kilometers and the higher total number of mass transit kilometers. The increase in total mass transit kilometers is generally more rapid than the decrease in total car kilometers. It can therefore be seen that an increase in the tradable credits price causes a growth in the number of total kilometers. From Table 3 we also note that individuals in zone 1 exceed their allocated credits under both initial credit assignment approaches. By way of illustration, using an initial equivalent distribution of credits, an individual in zone 1 traveled about 51 km by car in comparison with the permitted VKT (number of credits) of 38 km. With an initial proportionate distribution, an individual in zone 1 travels about 53 km by car in contrast with the permitted VKT of 48 km. Therefore, individuals in zone 1 have to buy additional credits from the market with a price pe =0.114 . In contrast, individuals in zone 2 have a surplus of credits under both initial tradable credits assignment approaches. With an initial equivalent distribution approach, an individual in zone 2 travels about 24 km by car in comparison with the permitted VKT (number of credits) of 38 km. Alternatively, with an initial proportional distribution of credits, an individual in zone 1 travels about 23 km by car in contrast with a permitted VKT of 28 km. So, in the case of the scheme with an initial equivalent distribution approach for credits there is a credit surplus, whilst with the initial proportional distribution of credits the number of credits sold is equal to the number of credits bought. The difference in credit surplus also explains the difference in total car kilometers according to the different initial credit distribution approach used. It can be seen that the total number of kilometers by car is 74688.5 using an equivalent distribution approach in contrast with a total of 75975.2 km using an initial proportional distribution approach, the latter being closer to the target of 76000 km. The large increase seen in the number of mass transit kilometers under the TCS gives rise to the question of whether to 10

x 10

x 10 8

Total Car Trips Total Car Trips Target Total Mass Transit Trips 8

6

6

4

4

2

2

0 0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

Tradable Credits Price (pe)

Fig. 4. Effects of the tradable credit price on total car kilometers.

1

Total Mass Transit Trips(km)

Table 3 The number of kilometers in different zones with a TCS and according to two different initial distribution measures.

Total Car Trips(km)

78

M. Xu, S. Grant-Muller / Transport Policy 47 (2016) 72–83

attempt to control the total distance traveled. We still assume a TCS is adopted using an initial equivalent credits distribution approach. Now, suppose that the regulatory authority decides to reduce total travel demand by about 20.6% i.e. the expected total distance traveled is about 1.65 × 105 km. According to Eq. (24), Section 4.5, we have the following relationship:

Table 4 Parameter settings for travel pattern estimation. Items

Input matrices

distance matrix by car (km), d1ij

⎧ ⎫ ⎡ ⎛ 5 ⎞2.5 ⎡ ⎛ 1 ⎞2.5 ⎛ 2 ⎞2.5 ⎤ ⎛ 1 ⎞2.5 ⎤ ⎜ ⎟ ⎜ ⎟ ⎪ ⎥ ⎢⎜ ⎟ ⎥⎪ ⎪⎛ ⎪ ⎞2.5 ⎢ ⎝⎜ 6 ⎠⎟ ⎝ ⎠ ⎝ ⎠ 1 ⎥ + 10 2.5 ⎢ ⎝ 6 ⎠ ⎥⎬ ⎟ ⎢ 165 − 20* ⎨ ⎜ + 3 + 3 F 2 ( pe ) ⎥ F 2 ( pe ) ⎥ ⎪ ⎢ F1( pe ) ⎪ ⎝ 0 . 3 + pe ⎠ ⎢ F1( pe ) ⎪ ⎢⎣ ⎥⎦ ⎢⎣ ⎥⎦ ⎪ ⎭ ⎩ x C *= ⎧ ⎫ ⎡ ⎛ 5 ⎞2.5 ⎡ ⎛ 1 ⎞2.5 ⎛ 2 ⎞2.5 ⎤ ⎛ 1 ⎞2.5 ⎤ ⎜ ⎟ ⎜ ⎟ ⎜ ⎟ ⎜ ⎟ ⎪ ⎪ ⎢ ⎥ ⎢ ⎥ 2.5 ⎪⎛ ⎪ ⎞ ⎝ ⎠ ⎝ ⎠ ⎝ ⎠ 1 ⎥ + 10 2.5 ⎢ ⎝ 6 ⎠ ⎥⎬ ⎟ ⎢ 6 pe ⎨ ⎜ + 3 + 3 F 2 ( pe ) ⎥ F 2 ( pe ) ⎥ ⎪ ⎢ F1( pe ) ⎪ ⎝ 0 . 3 + pe ⎠ ⎢ F1( pe ) ⎪ ⎢⎣ ⎥⎦ ⎢⎣ ⎥⎦ ⎪ ⎩ ⎭

distance matrix by mass transit (km), d2ij free ﬂow time (min), tij0 general road capacity (veh/hour), Fij

(25)

where ⎞1.5 ⎛ 1 ⎞2.5 ⎞1.5 ⎛ 1 ⎞2.5 ⎛ 2 ⎞2.5 ⎛ ⎛ 5 ⎞2.5 ⎛ 1 1 ⎜⎜ ⎟⎟ +⎜⎝ 6 ⎟⎠ 101.5, F2 (pe )=⎜⎝ 3 ⎟⎠ ⎜⎜ 0 . 3 + p ⎟⎟ +⎜⎝ 3 ⎟⎠ 101.5. ⎝ 0 . 3 + pe ⎠ ⎝ e⎠

F1 (pe )=⎜⎝ 6 ⎟⎠

There are alternative combinations of the price pe and the number of individual credits distributed xC * in order to satisfy Eq. (25). As a result, for a TCS design in practice we can determine the number of individually distributed credits based initially on the credit price. Fig. 5 demonstrates the effects of the credits price on the total utility of the network. The total utility of the network is deﬁned by the micro-economic model U2 for the case with a TCS in place, and by micro-economic model U1 for the case without a TCS. Assuming an initial distribution of tradable credits, then total utility decreases at the equilibrium tradable credits price ( pe =0.114 ) compared with the case without a credits scheme. Total utility increases quickly with an increase in the credits price and alongside a rapid increase in the number of kilometers by mass transit. The settings for the time parameter, γ = £0. 1 per min, α ¼0.4, β ¼10, and other parameters needed for the estimation of travel patterns were as shown in Table 4. The travel pattern for private car kilometers can be determined iteratively based on Eqs. (11, 13–15), whilst the mass transit travel pattern was estimated based on Eqs. (12, 16–17). In terms of setting the stepwise function for the generalized trip time: 10 categories of generalized journey time were used, with 5 min intervals (K =10, δk=5) and the last category (i.e. the category of Tijb above 50 minutes) was taken as the reference point in the estimation process. The generalized mass transit trip time can b b b b then be calculated based on Eqn. (17): f (T13 ),f (T14 ),f (T23 ),f (T24 ), and further generalize travel costs for the mass transit mode according to b b b b (16), C13 , C14 , and C24 . The private car and mass transit travel , C23 patterns in the case of no TCS and then with a TCS (for each of the two initial credit distribution approaches) are shown in Table 5. 1.5

79

x 10

1.45

1.4

1.35

Zone

3

4

1 2 1 2 1 2 1 2

20 20 15 15 25 15 1500 800

25 25 20 20 10 16 2000 1000

From Table 5 it can be seen that the travel pattern for both private car and mass transit modes are similar with and without implementation of the TCS. Under the scheme, the travel patterns are also seen to be similar according to the two initial credit distribution measures. Compared with the obvious effects on travel mode choice (as shown above), the effects of the scheme on travel patterns overall (i.e. OD matrices) is seen to be minor. This leads to the conclusion that the introduction of a TCS is likely to clearly impact on the distribution of kilometers between different travel modes, but is less likely to affect the overall travel pattern in terms of OD's.

6. Case study for Beijing municipality and discussion Following the illustration of the modeling framework for a simple network in Section 5, here we further investigate the TCS effects for the case of Beijing municipality. The analysis is based on an OD survey between districts in 2000 (China Academy of Urban Planning and Design (CAUPD), 2002). The whole city consists of 10 districts (zones), as shown in Fig. 6. The width of the lines between zones in Fig. 6 shows differences in the average number of trips per person per day according the survey. From the data, a network can be constructed based on 10 zones and from this, a 10 10 OD matrix. It is noted that to apply the policy simulation analysis framework in practice, the model would need to be carefully calibrated using a detailed survey or statistical data. To provide an accurate and true calibration of each parameter in the model for such a large city of Beijing is beyond the scope of this particular paper, which aims instead to illustrate the principles of the method. According to the modeling assumptions outlined in Section 4, private car and mass transit modes act as substitutes and individuals have a preference for car use. We assume this is still the case for travel in Beijing districts, but of course in a real life implementation the local preferences would be investigated and adopted. We further assume that both the population and cars ownership in the city are evenly distributed within the 10 zones, with one private car used by one individual per day. Before describing the trip estimation process,

Total Utility

1.3

Table 5 Travel pattern with/without TCS, unit: VKT.

1.25

Scheme

1.2

1.15

No TCS

1.1

1.05

1 0

0.1

0.2

0.3

0.4 0.5 0.6 Tradable Credits Price (pe)

0.7

0.8

Fig. 5. Effects of the tradable credit prices on total utility.

0.9

1

TCS with an equivalent initial distribution TCS with a proportional distribution

Car travel pattern

Mass transit travel pattern

Zone 3

4

Zone

3

4

1 2 1 2

45748 15637 37796 11098

15249 19111 13280 12515

1 2 1 2

11906 38302 23260 69872

5103 57453 8603 75694

1 2

39567 10578

13902 11928

1 2

24350 66598

9006 72148

80

M. Xu, S. Grant-Muller / Transport Policy 47 (2016) 72–83

6.1. Estimating individual private car kilometers x ic : use of survey data

Fig. 6. Districts of Beijing and average trip distribution. (Source: CAUPD, 2002).

some background data about the Beijing municipality used to illustrate the modeling of the TCS is given. This draws on survey data collected in 2000 and Xu et al. (2010). For the municipality, the average percentage of trips using a private car in 2000 was 23.24%, whilst the average percentage of trips by mass transit (including road surface transit and subway) in 2000 was 26.51%. By the end of 2000, the total population was 13.819 million, and the number of total private cars was 1.578 million. The daily average travel frequency per individual is 2.81 times, the daily average travel frequency per car is 2.49 times, and the average daily distance traveled per car was 24.2 km. In the models given in Section 4.1, there is a need to specify several parameters. The conventional approach (Varian, 1992) is to calibrate functional parameters to benchmark data. Under the assumptions outlined in Section 4 and Section 5 and based on the available travel data (See Section 6.1 for more details.), we set individuals in the ﬁrst 4 zones to have an equal preference for car travel, i.e. a1=a2=a3=a 4=0.8, individuals in zone 5 and zone 6 to have an equal preference for cars with a5=a6=0.77, individuals in zone 7, zone 8 and zone 9 have equal preferences for car travel with a7=a8=a9=0.71 , and ﬁnally, individuals in zone 10 have a strong preference for car travel with a10=0.78. Individuals’ budget for transport are set as follows: zone 1 to zone 4 are identical with I1=I2=I3=I4=1450 yuan (100 yuan ¼16.03 US Dollar), I5=I6=1382 yuan, I7=I8=I9=1350 yuan and ﬁnally for zone 10, I10=1415 yuan. The ﬁxed cost per km traveled by car is pv =20 yuan, whilst the ﬁxed cost per km traveled by mass transit is pb =1 yuan. As we focus on travel mode choice behavior, we assume that the population in each district is the same as the number of vehicles, i.e P1=⋯ = P10=0.1578 million. We set the parameter ρ = 10 with the given substitution assumption of car and mass transit modes. As we have mentioned in Section 4.1, the allocation parameter ai (i = 1, 2, ⋯ , 10) is for private car use / the proportion of transport income spent on private car use in each zone i . In general, the bigger of the parameter ai then the greater the dependence of travelers on private car use in zone i . Using the survey data it is possible to easily estimate daily mass transit kilometers in each zone, however it is far more difﬁcult to estimate the number of daily transit kilometers by car owners. Further survey data, for example from an individual mode choice survey, would be necessary to estimate individual mass transit VKT. This is an issue for further research and outside the scope of this study.

Theoretically there are different ways to estimate individual private car kilometers in each zone based on the survey data. It is possible to estimate individual car kilometers based on a daily OD matrix of total kilometers and for this study, the survey report from the year of 2000 provides the necessary data in the form of total kilometers for a 10 10 OD matrix (the units are per 10,000 kilometers per person per day). To estimate private car kilometers in each zone i.e. x ic as input for individual VKT in the proposed model, it would be possible to apply some basic assumptions in order to transform the total distance traveled in each zone (from the survey data) to individual VKT. The total distance traveled in each zone can be multiplied by the proportionate car mode choice and then divided by the population for each zone. However applying this approach did not produce a satisfactory numerical outcome in practice, particularly when related assumptions in the model were also taken into consideration. As a result an alternative approach was taken in this study as outlined below. Considering that different districts in Beijing have obviously functional differences (i.e concerning land use, employment proﬁle, commercial activity etc.) and the links between different employment types and overall level of travel, in this study we estimate individual private car kilometers in each zone based on daily average travel frequency by level of different employment type/profession, zone 1 to zone 4 are dominated by company employee and government ofﬁcials, zone 5 and zone 6 are dominated by company employees and sole proprietors, zones 7, zone 8 and zone 9 are dominated by teachers, students and scientiﬁc and technology staff, whilst zone 10 is dominated by low grade manual laborers and domestic staff. Based on the survey data, we can then estimate the daily average travel frequency in different zones as shown in Table 6. We can then estimate individual kilometers by private car and mass transit modes in each zone using the daily average travel frequency in each zone, multiplied by the average travel distance per car. 6.2. Estimating individual private car kilometer x ic and mass transit kilometer x ib : a modeling approach Based on the survey data it is possible to estimate a distance matrix based on the location of different zones, free ﬂow travel time and general road capacity (based on the OD matrix and travel time). In the simulation undertaken, 30 categories of generalized journey time were used with 15 min intervals ( K = 20, δk=15). The last category, i.e. the category of Tijb which is above 300 min (or 5 h) was taken to be the reference category in the estimation process. Based on the survey data, the total number of car trips for the year 10 of 2000 is given by ∑i = 1 Tic =1.61*1010 times per year. We suppose that the total number of car trips can be equally allocated across the whole year for each driver. A transformation is then possible to obtain a ﬁgure for the average daily VKT per individual, which is 67.6 km, calculated from (1.61*1010*24.2 / 365*1.578*107). The total VKT per day before the implementation of a TCS is then given by 7.5*108 km ( 67.6*1.578*107). With the introduction of the TCS we now expect that the total number of car kilometers will reduce by 30%. As a result, we can Table 6 Estimated daily average travel frequency, derived from dominant profession in each zone (Unit: times per day). Zone

Z1

Z2

Z3

Z4

Z5

Z6

Z7

Z8

Z9

Z10

Frequency

3.12

3.12

3.12

3.12

2.97

2.97

2.86

2.86

2.86

3.04

M. Xu, S. Grant-Muller / Transport Policy 47 (2016) 72–83

set the total number of credits per day to be x¯ =5.1*108 (67.6*0.7*1.578*107). Based on the scheme assumptions previously outlined, we set the initial distribution of credits using both an equivalent approach and a proportional distribution approach, using the daily average travel frequency in each zone as shown in Table 6. The difference between the two approaches to distributing the initial credits on the allocation to individuals is shown in Table 7. Under the TCS, we set the price of a tradable credit to be pe =10 yuan. With these parameter settings, the estimated kilometers by car and mass transit modes for Beijing municipality are as shown in Table 8. 6.3. Sensitivity analysis As can be seen from the analysis outcomes in Table 8, it is clear that the private car kilometers estimated from the proposed model (I2) and the survey data (I1) as the benchmark data match well, according to the parameters used. To verify the validity and applicability of the proposed model, we can further implement a sensitivity analysis with respect to allocation parameters ai (i = 1, ⋯ , 10). The sensitivity analysis is based on zone 1, as mentioned in Section 6.1, zone 1 is dominated by company employee and government ofﬁcials. The land use characteristics in this zone determine that private car used in this zone is higher than other zones. Fig. 7 demonstrates the impact of the variants of a1 on the car kilometers with/without TCS. As we can see, with the individuals budget ﬁxed for travel I1=1450, the higher the value of a1, the greater the total kilometers for each individual in zone 1. The growth of a1 will bring an increase in mass transit kilometers, and will bring with a small decrease in car kilometers Furthermore, either with/without TCS, and under the case of TCS with proportional initial distribution and equivalent initial distribution, the changes with respect to the car kilometers and mass transit kilometers remain consistent. These characteristics remain with respect to the allocation parameter ai and for the effects of individual car kilometers and mass transit kilometers in other zones.

81

Similarly, we can implement the credits price for the case study in Beijing and the numerical results are similar to those presented in Fig. 5 for the 4-zone example network. Due to space limitations, we have not reported the full set of sensitivity tests. 6.4. Discussion As demonstrated in this Section, the case study presented involves the use of several parameters. These parameters are speciﬁed with relatively few observations, as presented in Section 6.3, The parameters are calibrated using a conventional approach based on the use of benchmark data. The parameter settings for different zones are based on the differences in the main functions of different districts. Although the calibration process is a time consuming process and whilst the speciﬁcation of function coefﬁcients is complicated and error-prone, the sensitivity analysis presented veriﬁes the validity and applicability of the proposed model. In order to extend the sensitivity analysis in Section 6.3, another potential calibration approach is the so-called "calibrated share form", where the cost and demand functions are explicitly incorporated. As introduced by Rutherford (1995), the calibrated share form can be implemented in the GAMS (The General Algebraic Modeling System, www.gams.com). We leave the exploration of the most effective method to set these parameters for further study. The effects of a TCS can be demonstrated by articulating the scheme within the modeling framework described in this paper. The consequences arising from changes in the costs of car travel

Table 7 Distribution of initial number of credits ( x¯ ic ) per individual per zone. Zone

Z1

Z2

Z3

Z4

Z5

Z6

Z7

Z8

Z9

Z10

Equivalent distribution Proportional distribution

47 49

47 49

47 49

47 49

47 46

47 46

47 44

47 44

47 44

47 48 Fig. 7. Impacts of variations in a1 on car kilometers with/without TCS.

Table 8 Kilometers with/without TCS, unit: VKT. Items

Vehicle Kilometers Traveled (VKT)

Z1

Z2

Z3

Z4

Z5

Z6

Z7

Z8

Z9

Z10

I1

xic

69.2

69.2

69.2

69.2

65.9

65.9

63.4

63.4

63.4

67.4

xib

–

–

–

–

–

–

–

–

–

–

xic xib xic xib xic xib

69.1012

69.1012

69.1012

69.1012

65.8662

65.8662

64.3507

64.3507

64.3507

67.4371

67.9756

67.9756

67.9756

67.9756

64.6758

64.6758

62.9862

62.9862

62.9862

66.2571

49.2595

49.2595

49.2595

49.2595

47.5170

47.5170

46.6997

46.6997

46.6997

48.3630

48.1407

48.1407

48.1407

48.1407

46.3536

46.3536

45.4111

45.4111

45.4111

47.2065

49.7726

49.7726

49.7726

49.7726

47.2604

47.2604

45.9299

45.9299

45.9299

48.6196

48.6422

48.6422

48.6422

48.6422

46.1033

46.1033

44.6626

44.6626

44.6626

47.4569

I2 I3 I4

Key: I1 represents kilometers derived from survey; I2 represents kilometers estimated from the model without TCS; I3 refers to kilometers under TCS with an equivalent initial distribution; I4 refers to kilometers under TCS with proportional initial distribution. “Zi” refers to the i’th zone. “ xic ” denotes private car kilometers in the i′th zone. “ xib ”, denotes mass transit kilometers in i′th zone.

82

M. Xu, S. Grant-Muller / Transport Policy 47 (2016) 72–83

alongside the permitted total VKT from the scheme act as a restraint on the pattern of total kilometers, which may be intuitively expected. An iterative process will continue until nobody is willing to make further changes in their travel activities. With the implementation of a TCS, it is therefore possible in principle to reach the target reduction in private car kilometers of 30%. Individuals will adjust their travel patterns differently under the two initial credit distribution approaches. Individuals in zones 1-4 and zone 10 will have to buy credits to support the extra car kilometers over their limit, whilst those in zones 7-9 can sell their credits for ﬁnancial gain. The two alternative approaches to the distribution of initial credits have different effects on the individuals’ travel by car and mass transit modes. From Eq. (24), which shows the relationship between the price of tradable credits and the credits that are individually distributed, the credit price is expected to affect private car kilometers substantially. In order to achieve a target for reductions in VKT traveled by car, the design of the TCS will be crucial, i.e. the choice of credit price and the initial distribution scheme for the tradable credits. A comparison between the travel pattern with and without the TCS for the Beijing study has shown similar ﬁndings to the small network illustration provided in Section 5, i.e. the implementation of a TCS has no obvious effects on the overall travel pattern in terms of OD movements. Furthermore, the travel pattern according to the two different initial credit distribution approaches is also similar.

7. Conclusions TCS has become familiar to environment economists as a pollution control measure. This is in contrast to the case for many transport economists and transport management practitioners, for whom it appears as new and unfamiliar approach. Despite that, researchers in transport economics can see the potential of a TCS for road trafﬁc mobility management, although it is clear that many theoretical and application related issues remain undeveloped. In this paper, we have discussed how a TCS affects travelers’ mode choice based on a simulation framework. The proposed framework will be interesting to policy makers who want to establish sustainable transportation systems. A small scale network and case study for Beijing municipality have been used to illustrate the working of the model proposed using some basic assumptions. These include assumptions on travelers’ preferences across geographic and time spaces and between individuals. Contextual assumptions have also been made for the case of Beijing. As the main goal of the paper has been to illustrate the working of the modeling and analysis framework, it is appreciated that these assumptions would need to be further reﬁned for a more in-depth case study analysis. Outputs from local surveys could supply more accurate data in that case. The main contributions of this paper to the literature are as follows:

A novel analysis framework to investigate the effects of a TCS.

This framework connects individual travel mode choice behavior and travel pattern characteristics in a regional/city trafﬁc network. As a component of the analysis approach, we borrowed consumer behavior analysis methodology and developed a CES approach to modeling the effects of a TCS on daily kilometers, and the choice of travel mode is determined by the relative costs of different modes and the transport budget. We conclude that a TCS provides a promising policy option in reducing private car kilometers. A cap-and-trade measure can achieve the target car trip reduction (as reﬂected by VKT) by

changing travel mode choice behavior. The design of the TCS (including the settings of credit price and initial credit distribution) are discussed. We emphasize that TCS can clearly affect travelers’ mode choice, however, the scheme effects on the travel pattern, as indicated by OD movements overall, is minor. The TCS studied in this paper discourages travelers’ private car use by imposing quantitative restraints and encourages a switch to PT travel. However, the scheme does not consider the time and space factors in this study, and in that respect would be expected to be ineffective in tackling the problem of local road trafﬁc congestion. To deal with current incidents of trafﬁc congestion, new TCSs are needed that are able to consider time and space dependencies, that are able to adjust trafﬁc ﬂow and can make better use the available road capacity. This is an issue for future research, alongside some other key issues as follows:

An in-depth disaggregated analysis of effects of the TCS on

mode choice is necessary in order to explore how this type of scheme can deal with different types of mode choice from different perspectives; Further development of the model is needed to integrate route choice behavior of travelers under a macroscopic transport network equilibrium analysis; Policy packages are now favored by many policy makers as an effective means to introduce behavioral change. Packages can be deﬁned as any combination of one or more economic measures with one or more other types of measures (regulatory, physical, technology). Further research is needed to investigate how a TCS could interact with these other types of measures, e.g., with respect to different transport management measures given in Xu et al. (2015).

Acknowledgments The authors would like to thank Prof. Ronghui Liu (ITS, University of Leeds) for her comments and suggestions that help us to improve the quality of the paper. The work described in this paper was jointly supported by the National Natural Science Foundation of Chin (71422010, 71361130016), the EU Marie Curie IIF (MOPED, 300674), and the National Basic Research Program of China (2012CB725401). The content is solely the responsibility of the authors and does not necessarily represent the views of the funding sources. Any remaining errors or shortcomings are our own. Any views or conclusions expressed in this paper do not represent those of funding sources.

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