On the performance of averaged optimal routing

Traffic uncertainty makes designing optimal routing protocols for many networks a difficult problem. A good way to capture uncertainty is via an uncertainty set - a collection of traffic matrices with associated probabilities of occurrence. Averaged optimal routing, where the performance metric is averaged over the potential traffic matrices, allows us to incorporate an uncertainty set into an optimization framework. We derive bounds on the performance of averaged optimal routing where the objective is to minimize maximum channel load, a commonly used metric. Furthermore, we provide examples of networks and uncertainty sets where the bounds are tight. These bounds can be used to quickly check whether averaged optimal routing is an effective routing protocol for a given network and uncertainty set. Numerical evaluations of the performance of the bounds for uncertainty sets drawn from random graphs are presented and some interesting trends are noted. Also, simulations performed on a cycle level on-chip network simulator demonstrate that averaged optimal routing outperforms general-purpose routing algorithms.