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Modelling Impacts of Tolling Systems with Multiple User Classes. (2009)
Book Chapter
Stewart, K. (2009). Modelling Impacts of Tolling Systems with Multiple User Classes. In W. Saleh (Ed.), Travel Demand Management and Road User Pricing (73-88). Ashgate Publishing

This paper extends the formulation for SSO to include MUCs (where the different groups of drivers are assigned different generalised cost functions), such that total perceived network travel costs for all classes are minimised and presents an objecti... Read More about Modelling Impacts of Tolling Systems with Multiple User Classes..

Tolling traffic links under stochastic assignment: Modelling the relationship between the number and price level of tolled links and optimal traffic flows (2007)
Journal Article
Stewart, K. (2007). Tolling traffic links under stochastic assignment: Modelling the relationship between the number and price level of tolled links and optimal traffic flows. Transportation Research Part A: Policy and Practice, 41(7), 644-654. https://do

The classical road-tolling problem is to toll network links such that under the principles of Wardropian User Equilibrium Assignment a System Optimising (SO) flow pattern is obtained. Stochastic assignment methods are accepted to be more realistic th... Read More about Tolling traffic links under stochastic assignment: Modelling the relationship between the number and price level of tolled links and optimal traffic flows.

Minimal revenue network tolling: system optimisation under stochastic assignment with elastic demand. (2006)
Book Chapter
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 Intern

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 optimisa... Read More about Minimal revenue network tolling: system optimisation under stochastic assignment with elastic demand..

Modelling the effects of road pricing (2006)
Thesis
Stewart, K. Modelling the effects of road pricing. (Thesis). Napier University. Retrieved from http://researchrepository.napier.ac.uk/Output/2254692

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 optimisati... Read More about Modelling the effects of road pricing.

Stochastic social optimum traffic assignment (2005)
Journal Article
Maher, M., Stewart, K., & Rosa, A. (2005). Stochastic social optimum traffic assignment. Transportation Research Part B: Methodological, 39(8), 753-767. https://doi.org/10.1016/j.trb.2004.10.001

This paper formulates a Stochastic Social Optimum (SSO) that relates to the Stochastic User Equilibrium (SUE) in the same way as the Social Optimum (SO) relates to the User Equilibrium (UE) in a deterministic environment. At the SSO solution, the tot... Read More about Stochastic social optimum traffic assignment.