Traffic equilibrium

Traffic equilibrium, in its static version, is a well researched field of transportation theory. Basically, an equilibrium can be characterized as the solution of a finite-dimensional variational inequality defined over a multicommodity transportation network. In theory, any VI algorithm can find a traffic equilbirum. In this presentation, I will briefly introduce the basic formulation, its main properties and an algorithmic framework. I will then proceed to the study of variants and extensions that pose challenges, both from the modelling and computational points of view. They are:
1. Multi-attribute models, where the perception of travel disutility varies across the poputlation.
2. Strategic models where users adapt their path to changing traffic conditions.
3. Optimization under equilibrium constraints. In particular I will discuss the choice of optimal tolls, according to criteria such as revenue or welfare maximization.

Patrice Marcotte is professor in the department of computer science and operations research of the University of Montreal. He has published more than sixty papers on traffic equilibrium, variational inequalities, bilevel programming and badminton. He is associate editor of several journals, among which Operations Research Letters, Operations Research and Transportation Science. His main area of research is currently the application of bilevel programming to revenue management problems.