Pareto-improving congestion pricing and revenue refunding with multiple user classes

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Abstract

This study investigates Pareto-improving congestion pricing and revenue refunding schemes in general transportation networks, which make every road user better off as compared with the situation without congestion pricing. We consider user heterogeneity in value of time (VOT) by adopting a multiclass user model with fixed origin–destination (OD) demands. We first prove that an OD and class-based Pareto-improving refunding scheme exists if and only if the total system monetary travel disutility is reduced. In view of the practical difficulty in identifying individual user’s VOT, we further investigate class-anonymous refunding schemes that give the same amount of refund to all user classes traveling between the same OD pair regardless of their VOTs. We establish a sufficient condition for the existence of such OD-specific but class-anonymous Pareto-improving refunding schemes, which needs information only on the average toll paid and average travel time for trips between each OD pair.

Introduction

Although congestion pricing has a solid theoretical foundation and nowadays has very advanced technology support for its practical implementation, it has long been viewed as a political issue. In particular, congestion pricing proposals are frequently declined due to public opposition. For examples, the Edinburgh congestion charge plan was rejected by a referendum in 2005, the congestion pricing proposal for the West Midlands in England was rejected by councils in March 2008, and the New York congestion pricing proposal was declined in April 2008 due to public opposition.

There are several reasons for the public unacceptability of congestion pricing. First of all, for the public, congestion pricing is just like another tax collected by the “evil” government. As summarized by Cervero (1998), “middle-class motorists often complain they already pay too much in gasoline taxes and registration fees to drive their cars, and that to pay more during congested periods would add insult to injury. In the United States, few politicians are willing to champion the cause of congestion pricing in fear of reprisal from their constituents”. Indeed, with congestion pricing implemented, users’ surplus is transferred to the government in the form of the toll revenue. Thus users are unhappy even if the society as a whole (including the government and the users) gains. Furthermore, congestion pricing has the well-known social inequity problem, i.e. people with relatively low-income are more likely to be priced out of driving. For this reason, congestion pricing is often considered as an elitist policy, which prices the poor off of roads so that the wealthy can move about unencumbered (Cervero, 1998). In addition, there might be the so-called spatial equity issue, namely congestion pricing may have different impact on people living and working in different places (Yang and Zhang, 2002). For these reasons, congestion pricing as a policy is often faced with public hostility, and its implementation is more like a political issue other than a theoretical or technological problem.

Revenue redistribution has long been considered as a possible way to solve the political issues of congestion pricing. By directly refunding the toll revenue to the users, in an even or uneven manner, all the problems mentioned above that lead to the public unacceptability of congestion pricing could be solved. That is, with proper revenue refunding schemes, congestion pricing no longer makes road users feel like being “exploited” by the government and the potential social and spatial inequity problems can be solved as well. Indeed, various forms of revenue distribution strategies have been proposed and discussed. Goodwin (1989) suggested a combination of revenue uses in order to offset several congestion pricing impacts. Small (1992) proposed a travel allowance for all commuters. Poole (1992) added that it might be possible to introduce off-peak discounts and peak-hour surcharges on a toll road. DeCorla-Souza (1994) proposed a cashing out strategy to induce shift of peak-period travelers to other modes, thus reducing the need for additional infrastructure. Parry and Bento (2001) recommended that income taxes be reduced to offset congestion pricing-related labor supply restriction. Kalmanje and Kockelman, 2004, Kockelman and Kalmanje, 2005 proposed a novel strategy for practical implementation of revenue refunding, the credit-based congestion pricing (CBCP) strategy.

A number of theoretical and quantitative studies have been conducted on road pricing and revenue redistribution.1 Bernstein (1993) examined the possibility of user-neutral congestion pricing with both positive and negative tolls (tolls and subsidies) in the Vickrey bottleneck congestion model (Vickrey, 1969). Arnott et al. (1994) investigated the welfare effects of congestion tolls using the basic bottleneck model with heterogeneous but inelastic commuting demand. They considered the case when the toll revenues are rebated as an equal lump-sum payment to all drivers and analyzed when and how each group of drivers could be made better off with such a uniform rebate. Daganzo (1995) designed a Pareto-improving hybrid strategy between rationing and pricing in the bottleneck congestion model, where a fraction of drivers would be exempt from tolling each day. Nakamura and Kockelman (2002) applied this strategy to the San Francisco Bay Bridge corridor, and concluded that such a Pareto-improving strategy does not exist for that network and it would be difficult to find such a policy in general.

In a network context, Adler and Cetin (2001) discussed a direct distribution approach to congestion pricing, in which the money collected from users on a more desirable route was directly transferred to users on a less desirable route using a two parallel route example with bottleneck congestion. For a single origin–destination (OD) pair connected by a number of parallel routes, Eliasson (2001) showed that a tolling system that reduces aggregate travel time and refunds the toll revenues equally to all users will make everyone better off than before the toll reform. Yang et al. (2004) developed an optimal integrated pricing model in a bi-modal transportation network with explicit consideration of subsidy to transit mode from road congestion pricing revenue. Liu et al. (2009) adopted a continuous value of time (VOT) distribution and examined the existence of Pareto-improving and revenue-neutral pricing scheme in a simple bi-modal network consisting of road and a parallel transit line.

Recently, Lawphongpanich and Yin, 2007, Lawphongpanich and Yin, 2009, Song et al., 2009 studied a class of Pareto-improving pricing schemes without revenue redistribution in networks.2 They formulated the problem of finding Pareto-improving tolls as a mathematical program with complementarity constraints, and proposed a solution algorithm via manifold suboptimization. The existence of the Pareto-improving tolls without revenue redistribution in their study requires that the untolled equilibrium flow pattern be dominated by an alternative feasible flow pattern, under which some users are better off and no user is worse off than in the untolled equilibrium. The dominating flow distribution and the Pareto-improving tolls exist only for certain special networks that exhibit the generalized Braess paradox defined and characterized by Hagstrom and Abrams (2001).

This study investigates Pareto-improving congestion pricing cum revenue refunding (CPRR) schemes in general transportation networks that make every road user better off compared with the untolled case. The key point of the Pareto-improving CPRR scheme is that, compared with the “do-nothing” case, refunding (after tolling) reduces the net travel disutility of each individual user. Such a Pareto-improvement can make congestion pricing as a policy more acceptable to the public, because everyone is a winner under such a policy.3 We consider multiclass users by VOT and fixed demand for each OD pair. This fixed demand model could apply when congestion pricing is introduced during the morning peak-demand period, in which the number of trips taken between each OD pair can be regarded as fixed because a large portion of the trips are work-related and cannot be easily forgone. The fixed demand assumption can be an even milder one for transportation networks with both mass transit and private car modes, because it only requires the combined demand fixed between each OD pair.4 Congestion pricing in this fixed demand case is mainly aimed to rationalize users’ route choices (or mode choices for two-mode networks). In this case, the low-income users are more likely to be forced to change routes (or modes) by congestion charge; it is thus essential to adopt a multiclass user model to capture the effects of user heterogeneity, because our goal is to make everyone better off.

We first show that an OD and class-based Pareto-improving refunding scheme exists if and only if the total system monetary travel disutility is reduced. In view of the practical difficulty in identifying individual user’s VOT, we further investigate class-anonymous refunding schemes that give the same amount of refund to all user classes traveling between the same OD pair regardless of their VOTs.

Our OD-specific but class-anonymous Pareto-improving CPRR scheme takes advantage of users’ utility-maximizing behavior. Specifically, each individual user chooses a route that minimize her travel disutility, taking into account her particular value of time; her generalized travel disutility at equilibrium (including both toll and travel time) will not be larger than that incurred by traveling the OD-average travel time while paying the OD-average toll. With this important observation, we are able to establish a sufficient condition for the existence of a class-anonymous Pareto-improving refunding scheme; namely, the tolling system reduces the average travel time of users between each OD pair on the networks. The actual design and implementation of the class-anonymous Pareto-improving CPRR schemes need only aggregate (or average) information of trips between each OD pair, namely the average toll paid and the average travel time experienced by users between each OD pair. This kind of aggregate (or average) OD-specific information is not difficult to estimate in practice. For example, we can simply estimate these numbers by running a network equilibrium assignment.

An OD-based refunding scheme can be expected with foreseen widespread practical applications of the GPS kind of technology. Currently, drivers’ origins and destinations for regular daily commuting are generally available based on their home and job locations. Also, drivers’ destinations can be obtained from the current parking meters as well. Moreover, our OD-based refunding schemes provide a way to calculate the origin (zone) based refunding scheme, i.e. taking the summation of the OD-based Pareto-improving refund over all destinations for an origin will give (and justify) an (approximate but not necessarily Pareto-improving) amount that should be refunded to all users living in that origin zone.

The remainder of this paper is organized as follows. In next section, we introduce the multiclass user model and the corresponding multiclass system optimization (SO) and user equilibrium (UE) problems. In Section 3, the existence of a Pareto-improving refunding scheme is established in the sense that, if a congestion pricing scheme reduces the total system monetary travel disutility, redistributing the toll revenue to all users in an OD-specific and class-specific manner can make everyone better off. In Section 4, we study the existence and design of OD-specific but class-anonymous Pareto refunding schemes. Finally, some remarks and conclusions are provided in Section 5.

Section snippets

Preliminaries on multiclass user model

Let G(N, A) denote a transportation network, with a set of nodes N and a set of links A, together with a set of OD pairs W. We consider separable link travel time function ta(va),aA, i.e. travel time on a link depends on the flow on that link only. The link travel time function ta(va),aA, is assumed to be monotonically increasing with va. We consider a discrete set of user classes corresponding to the groups of users with different socio-economic characteristics, such as income level. Let M

Existence of Pareto-improving refunding schemes

Now we move on to investigate revenue redistribution. We first consider a class and OD-based refunding scheme Φ={Φwm,wW,mM}, where Φwm is the amount of refund to be equally refunded to the dwm users of class mM between OD pair wW. In spite of its practical difficulty for implementation, the class-specific refunding scheme is introduced here to serve as a theoretical benchmark, more practical refunding schemes will be considered later.

Definition 1

A refunding scheme Φ={Φwm,wW,mM} is said to be

Anonymous Pareto-improving refunding schemes

Although the aggregate VOT distribution among the population can be estimated, the VOT of each individual user is in general unobservable. This makes it unrealistic to implement refunding scheme ϕwm by user class. Therefore, we introduce anonymous OD-based refunding schemes, which give the same amount of refund to users of all classes between the same OD pair. An anonymous OD-based refunding scheme is denoted by Φ={Φw,wW}, where Φw is the total amount of refund to be equally refunded to users

Conclusions

In this paper we studied Pareto-improving CPRR schemes for the fixed demand case with multiclass users. We proved that, an OD and class-based Pareto-improving refunding scheme exists if and only if the total system travel cost is reduced. In this context our results highlight the importance of system cost other than system time, while the latter has long been accepted as a standard index of transportation system performance.

We then studied the existence and design of more plausible

Acknowledgements

The authors wish to express their thanks to Robin Lindsey and two anonymous reviewers for their very useful comments on an earlier version of the paper. The work described in this paper was supported by a Grant from the Research Grants Council of the Hong Kong Special Administrative Region, China (Project No. HKUST 6215/06E).

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