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

Abstract

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 flow between a pre-specified source node and a pre-specified terminal node in the network. The problem of determining the expected value of maximum 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. Index Terms-Expected value of maximumflow, Monte Carlo simulation, network flows.

Efficient routing through discretization of overlapped road segments in VANETs

“…A reliable network is one in which each arc has a certain probability of being functional [19]. Reliable networks are observed in different states, where each state is a conventional network defined on a subset of arcs in the reliable network, which are functional at the point of interest.…”