Minimal revenue network tolling: system optimisation under stochastic assignment with elastic demand.

Stewart, Kathryn; Maher, Mike

Abstract

The classical road tolling problem is to toll network links such that, under the principles of Wardropian User Equilibrium (UE) assignment, a System Optimising (SO) flow pattern is obtained. Such toll sets are however non-unique, and further optimisation is possible: for example, minimal revenue tolls create the desired SO flow pattern at minimal additional cost to the users. In the case of deterministic assignment, the minimal revenue toll problem is capable of solution by various methods, such as linear programming [BHR97] and heuristically by reduction to a multi-commodity max-flow problem [Dia00]. However, it is generally accepted that deterministic models are less realistic than stochastic, and thus it is of interest to investigate the principles of tolling under stochastic modelling conditions. This paper develops methodologies to examine the minimal revenue toll problem in the case of Stochastic User Equilibrium. Tolling solutions for both ‘true’ System Optimum and Stochastic System Optimum under SUE are derived, using both logit and probit assignment methods.

Citation

Stewart, K., & Maher, M. (2006). Minimal revenue network tolling: system optimisation under stochastic assignment with elastic demand. In S. Lawphongpanich, D. Hearn, & M. Smith (Eds.), Mathematics in transport : selected proceedings of the 4th IMA International Conference on Mathematics in Transport : in honour of Richard Allsop (201-218). Boston, MA: Springer. https://doi.org/10.1007/0-387-29645-X_9

• Start Date: Sep 7, 2007
• End Date: Sep 9, 2007
• Publication Date: 2006
• Deposit Date: Jun 13, 2008
• Publisher: Springer
• Peer Reviewed: Peer Reviewed
• Pages: 201-218
• Series Title: Applied Optimization
• Series Number: 101
• Book Title: Mathematics in transport : selected proceedings of the 4th IMA International Conference on Mathematics in Transport : in honour of Richard Allsop
• ISBN: 9780387296449
• DOI: https://doi.org/10.1007/0-387-29645-X_9
• Keywords: Traffic assignment; Stochastic user equilibrium; Probit model; Logit model; Optimal tolls; Marginal social costs
• Public URL: http://researchrepository.napier.ac.uk/id/eprint/1968