Refinements of a path-based efficient algorithm for network relia- bility estimation in the rare event case

This paper presents some refinements of a rare event simulation algorithm developped in [1] for estimating the probability of connection of two nodes s and t in an undirected graph G representing a communication network where nodes are perfect but links can fail. The method proposed in [1] makes use of disjoint paths (that is, with no common link) and samples a geometric variable representing the first time independent replications of a graph result in a configuration with at least one failed link in each path of a predetermined set. Generating such a random variable allows therefore to save a lot of computational time (but does not reduce variance) by avoiding the generation of all graphs. We propose here to investigate the variance reduction that can be obtained by replacing the geometric random variable by its expected value (conditional Monte Carlo). We also discuss how the set of disjoint paths can be determined and the robustness properties of the resulting estimator.