Mixed behavior network equilibria and quasi-variational inequalities

Abstract

In the modeling of competition on networks it is usually assumedthat users either behave following the Wardropian user equilibrium or thesystem optimum concept. Nevertheless, in several equilibriumsituations, for instance in urban traffic flows, intercity freightflows and telecommunication networks, a mixed behavior is observed.This paper presents a time-dependent network-based model shared by twotypes of users: generalized Nash players anduser equilibrium players. Generalized Nash players have a significant impact onthe load of the network, whereas user equilibrium players have a negligibleimpact. Both classes of players choose the paths to send their flows soas to minimize their own costs, but they apply different optimizationcriteria. Players interact via some implicit balance constraintswhich depend on the equilibriumsolution. Thus, the equilibrium distribution is proved to be equivalent to the solutionof a time-dependent quasi-variational inequality problem.Results on existence of solutions are discussed as well as a numerical example.