Stability and Wardrop Equilibria of Non-Cooperative Routing With Time-Varying Load

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