Stability and Wardrop Equilibria of Noncooperative Routing With Time-Varying Load

Noncooperative or selfish routing problems emerge in several applications of network control theory. Considering a multicommodity setting subject to time-varying traffic demands, this article studies the convergence properties of a family of noncooperative routing control laws, originally developed in the literature for constant traffic demands. By employing results from hybrid systems theory and set stability, this article identifies the minimum time between bounded load variations to assure the convergence of the controlled system toward a set of approximated Wardrop equilibria. Numerical simulations validate the results on a test scenario.