A variational inequality formulation of the dynamic network user equilibrium problem

In the present paper the authors are concerned with developing more realistic dynamic models of route choice and departure time decisions of transportation network users than have been proposed in the literature heretofore. They briefly review one class of models that is a dynamic generalization of the static Wardropian user equilibrium, the so-called Boston traffic equilibrium. In contrast, the authors then propose a new class of models that is also a dynamic generalization of the static Wardropian user equilibrium. In particular, they show for the first time that there is a variational inequality formulation of dynamic user equilibrium with simultaneous route choice and departure time decisions which, when appropriate regularity conditions hold, preserves the first in, first out queue discipline.