Retarded weighted quasi‐variational inequalities for traffic equilibrium problems

The aim of the paper is to consider user equilibrium problems in transportation networks in the most complete and realistic situations. In fact, the presented model allows, for the dependence of data on time, the presence of elastic travel demands, the capacity restrictions and delay effects. Moreover, the weights give the possibility to study the problem in the presence of congestion. The equilibrium conditions for such a model are given and the equivalent formulation in terms of a weighted quasi‐variational inequality is discussed. Then, a theorem for the existence of solutions is shown. Moreover, by using the set convergence in Kuratowski’s sense, a continuity result for equilibrium solutions is obtained. At last, a numerical example is provided.