A Bilevel Optimization Program with Equilibrium Constraints for an Urban Network Dependent on Time

There is a gap between theoretical and practical developments on time-dependent traffic assignment problems. In order to contribute to bridge this gap, we propose a bilevel formulation and the inclusion of the queue length variable in the objective function of the upper level. The objective of this paper is to propose an alternative to approach to the traffic assignment problem with time dependent user equilibrium by means a traffic network design problem. The mathematical program arises as a non-cooperative Stackelberg game and is formulated as a combination of bilevel network design problems, time dependent user equilibrium assignment and suitable link performance functions. We are setting up a time-dependent bilevel traffic assignment model, expressed and treated as a mathematical program with equilibrium constraints. In addition, we suggest an objective function to minimize the total travelled time on the network, which depends on link flow and arc queue length, that recognizes the Wardrop user equilibrium, where travel time is dependent on both flow and queue length on the arc.