Robust congestion pricing under boundedly rational user equilibrium

This paper investigates congestion pricing strategies in static networks with boundedly rational route choice behavior. Under such behavior, users do not necessarily choose a shortest or cheapest route when doing so does not reduce their travel times by a significant amount. A general path-based definition and a more restrictive link-based representation of boundedly rational user equilibrium (BRUE) are presented. The set of BRUE flow distributions is generally non-convex and non-empty. The problems of finding best- and worst-case BRUE flow distributions are formulated and solved as mathematical programs with complementarity constraints. Because alternative tolled BRUE flow distributions exist, our congestion pricing models seek a toll vector or pattern that minimizes the system travel time of the worst-case tolled BRUE flow distribution. As formulated, the models are generalized semi-infinite min-max problems and we propose a heuristic algorithm based on penalization and a cutting-plane scheme to solve them. Numerical examples are presented to illustrate key concepts and results.