Speeding Up the Estimation of the Expected Value of Maximum Flow Through Reliable Networks

A common measure of performance of a reliable network, i.e., a network in which elements are failure prone, is the expected value of the maximum s-t flow between a pre-specified source node s and a pre-specified terminal node t in the network. The problem of determining the expected value of maximum s-t flow is computationally hard. Therefore, for practical sized networks, it is estimated through Monte Carlo based simulation methods which estimate the measure by evaluating the maximum flows in a large sample of network states. Such methods are computationally expensive. In this paper, we present an algorithm which speeds up the process of evaluating maximum flows in the sampled states by a factor of three on two difficult classes of randomly generated networks. This speed-up allows us to compute the measure for larger networks than is currently possible. It also allows us to obtain more accurate estimates on similar sized problems within similar execution times.