طراحی عوارض مبتنی بر سرعت برای باجه های عوارض مناطق پر تراکم Speed-based toll design for cordon-based congestion pricing scheme

The toll design problem for congestion pricing schemes refers to the determination of the optimal toll charge according to one or more objectives, based on given charging locations. Two congestion pricing schemes have received much attention and been comprehensively investigated: first-best (Pigouvian) and second-best pricing (see the monograph by Lewis, 1993; Yang and Huang, 2005; Lawphongpanich et al., 2006; Small and Verhoef, 2007; and a recent review by de Palma and Lindsey, 2011). Some system-wide objectives are usually adopted for the toll design of these two schemes, for instance, the total social benefit, total travel time and toll revenue. However, compared with these system-wide objectives, government and network authorities are usually more concerned about the traffic conditions in a central business district (CBD), the commercial heart of a city, where traffic congestion is likely to cause greater economic losses and worse impacts on a city’s image. Thus, regarding the practical implementation of congestion pricing schemes, mitigating traffic congestion in the CBD is usually taken as a primary target. A cordon-based congestion pricing scheme is advantageous for improving the traffic condition in a CBD as it defines a pricing cordon, encircling a certain area (usually the CBD), and charges each incoming vehicle; the total inbound volume is thus limited and traffic congestion in this area significantly ameliorated. Additionally, area-wide cordon-based pricing schemes are more convenient in terms of operation and supervision, compared with first-best and second-best pricing, which aims to optimize a system-wide objective. Until now, most applications of congestion pricing are cordon-based, for instance the Area Licensing Scheme (ALS) in Singapore (Phang and Toh, 1997; Li, 1999) that was upgraded in 1998 to the Electronic Road Pricing (ERP) system (Olszewski and Xie, 2005), the London Congestion Charging Scheme (Santos, 2008), and a more recent trial in Stockholm (Eliasson, 2009). It should be pointed out that the Stockholm congestion charge scheme also levies tolls on vehicles leaving the charging area. Average travel speed is an ideal measure of the traffic conditions in an area guarded by a pricing cordon (called a cordon area hereafter), in that it is much easier to observe than traffic column or density (Li, 2002) and is also a better representative of the commuter’s driving experience. In the cordon-based ERP system in Singapore, the objective is to keep the average speed of vehicles in the cordon area within a target range: [20, 30] km/h, which is achieved by adjusting the toll charges (Olszewski and Xie, 2005). Note that the lower-bound of this range guarantees a reasonably rapid travel. The upper-bound on travel speed is a concern about traffic safety, and it also avoids a waste of the road resources by ensuring that sufficient vehicles are traveling in the cordon area. Herein, the search for a toll charge pattern that will keep the average travel speed of vehicles in the cordon area within a predetermined target range is named the speed-based toll design problem. Despite its practical significance, the problem is still an open question, since few of the existing studies of toll design problems have taken the traffic conditions in the CBD as an objective or used travel speed as a criterion for network performance. Modeling the toll design problem requires an analysis of the commuters’ route choice problem, and a simple assumption is made here that the commuters will select the path with minimal travel cost based on their pre-trip perceived travel times. The probit-based stochastic user equilibrium (SUE) principle is adopted as a framework for the route choice problem, in view of its better suitability to realistic conditions compared with the deterministic user equilibrium (DUE) and logit-based SUE cases (Sheffi, 1985, p. 318). The commuters’ travel costs consist of two components: travel time cost and toll charge, which are expressed in different units. The value-of-time (VOT) is needed to convert the toll charges into time units for the analysis (e.g., Lam and Small, 2001; Yang et al., 2001; Small et al., 2005). The VOT is largely influenced by the commuters’ level of income and trip emergency, thus it can vary significantly among commuters. It is difficult to find two commuters on the network with identical VOT values, thus at an aggregate level, it is more suitable to define the VOT as a continuously distributed random variable. The probit-based SUE principle and continuously distributed VOT both increase the challenges involved in modeling and solving the speed-based toll design problem, which are the aims of this paper.