Road pricing has an established history in the literature of transport economics, and its use as a theoretical and practical means of traffic restraint and management has attracted considerable interest for more than half a century. The theory of road pricing asserts that the optimal price should be the one that reflects the full cost of making an additional trip. Evidently, the magnitude of such a congestion toll varies over time and space. However, a review of some practical applications of road pricing in different countries reveals that no policy has as yet been implemented which aims to charge road users directly in relation to the congestion they actually cause and the time delay they impose on others. Therefore, the aim of this study is to model such a time-varying pricing scheme,t en-ned:T ime-DependentR oad Pricing, TDRP, and evaluate its various impacts on a single bottleneck as well as a traffic network. The TDRP function is derived basedo n the solution of the time-dependentq ueuesa nd delays problem at traffic junctions. The derived function is demonstrated to lead to a very unstable user equilibrium for a single bottleneck. Therefore, two different approaches are adopted to modifý this function: first, by considering the schedule delay changes imposed by vehicles on one another; and second, by using the day-to-day adjustment process. The former approach is demonstrated to eliminate queues completely and thus lead to system optimal SO for a single traffic bottleneck. Besides, the simulation solution demonstrates that TDRP, modified by the second approach, could lead to a stable equilibrium, and although it does not lead to SO it results in a very substantial reduction in queuing delay and travel time. To evaluate the stability of the results and the different impacts of TDRP on a traffic network, a traffic assigrunent model is developed. This model embraces route choices, departure time choices and the TDRP function, and it has the ability to evaluate the road network under different charging systems. Before evaluating the different impacts of TDRP on a traffic network, the importance of the phenomenon of interaction between nodes and its impacts on the value of TDRP are discussed. A general solution under specific traffic conditions as well as different TDRP scenarios are suggested. A set of numerical simulation experiments using the assignment model and a typical traffic network for urban areas is conducted. The results demonstrate that although TDRP does not eliminate the queues completely, it leads to a very substantial saving in travel time and queuing delay for all movements throughout the network under different levels of congestion. On the other hand, exempting some nodes (or links) from tile charges, would lead to a very substantial fall in the benefit obtained. The comparative analysis demonstrates that 7, DRP is a superioi charging system compared with other charging systems. It Is also concluded that TDRP docý' not represent the optimal charging system for a traffic network sliicc otlict cliirt-nin, nictliods could lead to a better performance under very high levels of charge Finally, the sensitivity of the results to work start time flexibility and the shadoN%va lues of the schedule delay function is investigated, and at the end, directions for further research arc proposed
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