Research Output

Minimal revenue network tolling: system optimisation under stochastic assignment.

  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.

  • Type:

    Book Chapter

  • Date:

    16 February 2006

  • Publication Status:


  • Publisher


  • DOI:



Stewart, K. & Maher, M. (2006). Minimal revenue network tolling: system optimisation under stochastic assignment. In Hearn, D. W., Smith, M. J. & Lawphongpanich, S. (Eds.). Mathematical and Computational Models for Congestion Charging, 201-218. Springer. doi:10.1007/0-387-29645-X_9. ISBN 978-0-387-29644-9



Road traffic tolls; Traffic charging; System optimisation; Random variable; Statistical analysis;

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