A link based quasi-variational inequality model for dynamic user equilibria, towards real time traffic operations

We propose a link based quasi-variational inequality formulation for the deterministic dynamic user equilibrium problem with single-user-class and fixed demands. The solution existence and boundedness condition for the proposed model is established using a newly developed theory for a group of quasi-variational inequality problems. The model can be solved by the damped Newton approach based on two observations: a) the sub-problem can be reformulated as a nonlinear complementarity problem which can be solved very efficiently by existing solution techniques, and b) the step size of the algorithm can be calculated using an approximate merit function developed in this paper, which is more rigorous than existing heuristic approaches. Some promising results are shown through two case studies, one of which is on a relatively large transportation network. Also, the results obtained can be further applied for real time traffic operations purposes.