This paper discusses an on-line, trail-and-error implementation of marginal-cost pricing for networks with users whose values of travel time vary, whose demand functions are unknown, and whose route choices conform to random-utility maximization. It is an extension of calculations of optimal congestion tolls with homogenous travelers and shortest-path choices. The numerical example on an actual, large-scale network suggests the heuristic iterative procedure does converge in searching for optimal tolls. Key Words: Marginal cost pricing, congestion pricing, toll roads, value of travel time 2
INTRODUCTIONRoad tolls based on marginal social delay costs have long been considered an economically efficient solution to highway congestion (Vickrey 1969). In most markets, goods should not be allocated beyond the point where marginal gains equal the marginal cost (MC) to furnish the good. And in certain, imperfect markets, the presence of unpriced externalities stymies this relationship. Such is the case of road use, where travelers are generally oblivious to the delays imposed on those following them during dense traffic conditions, and consider only the average travel time, or average cost (AC), they experience directly. A marginal-cost-pricing (MCP) strategy charges the user any difference between average cost and marginal costs, theoretically driving the market to a level of flow where marginal costs and benefits equate.Knowing demand for travel across a network, one can iteratively solve for the set of prices that equate MC and marginal benefits (MB) on all links. In practice, however, demand functions are unknown. Li (2002) initiated and Yang et al (2004) expanded a trail-and-error implementation of MCP on a network without knowledge of demand functions but with known link performance functions, observed flows, and observed responses to pricing decisions. The procedure they propose assumes a single value of time for all users and computes the optimal prices at any demonstrated flow levels. It then relies on a diminishing fraction of the difference in optimal and current toll values, in order to adjust current tolls.Yang et al's calculations are based on some important assumptions, including user equilibrium (UE) or shortest-path route choices and a single, known value of travel time (VOTT) for all vehicles. The UE assumption requires full information of roadway conditions (and prices) on the part of all drivers and a focus on travel time (rather than other elements of travel, such as number of stops, reliability, and route aesthetics). A more realistic network assignment assumption is believed to be stochastic user equilibrium (SUE), where each user may perceive different path costs or benefits, and random variation in route and/or traveler characteristics results in a distribution of route choices, for the same origin-destination (O-D) pair at the same time of day. In addition, travelers value their time differently, depending on the purpose of their trip and their willingness and/or ability to pay. To rela...
