Convex programming,variational inequalities,and applications to the traffic equilibrium problem

The problem of determining the equilibrium distribution of the traffic flow in a city network is studied when the traffic demands on a set of given routes are known. The problem is formulated in terms of a nonlinear variational inequality over a polyhedron and a solving procedure, different from those shown in 1], 3], 4], is exhibited. This procedure is based on a very simple, necessary, and sufficient condition for a solution of the variational inequality to lie on a face of the polyhedron. Moreover, it is also compared, by means of numerical examples, with the procedures formulated in 1], 3], and 4] (see expressions (1.2) and (3.5) for a significant valuation).