Quasi-variational inequalities in transportation networks

This paper aims 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. The equilibrium conditions for such a model are given and the equivalent formulation in terms of a quasi-variational inequality is discussed. Moreover, a theorem for the existence of solutions is shown and a numerical example is provided. Finally, some questions of stability are studied.