Optimal routing for minimizing the maximal link congestion

A lot of attention has been devoted to flow routing in networks by the past. Usually, each commodity to be routed is characterized by a single deterministic traffic value. However, many real-life application contexts require to consider stochastic flows. This is the case, for instance, in telecommunication networks. The current paper revisits usual network routing and dimensioning models, in considering that traffic amounts to be routed are random variables. This leads naturally to probabilistic constraints. Some mathematical properties of the stochastic models introduced are described. A special focus is made on the relations between these stochastic models and usual deterministic approaches.