Static Network Reliability Estimation via Generalized Splitting

Authors:
Zdravko I. Botev;Pierre L'Ecuyer;Gerardo Rubino;Richard Simard;Bruno Tuffin
Affiliations:
School of Mathematics and Statistics, University of New South Wales, Sydney 2052, Australia;DIRO, Université de Montreal, Montréal, Québec, H3C 3J7, Canada;INRIA Rennes Bretagne Atlantique, Campus Universitaire de Beaulieu, 35042 Rennes Cedex, France;DIRO, Université de Montreal, Montréal, Québec, H3C 3J7, Canada;INRIA Rennes Bretagne Atlantique, Campus Universitaire de Beaulieu, 35042 Rennes Cedex, France
Venue:
INFORMS Journal on Computing
Year:
2013

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Abstract

We propose a novel simulation-based method that exploits a generalized splitting GS algorithm to estimate the reliability of a graph or network, defined here as the probability that a given set of nodes are connected, when each link of the graph fails with a given small probability. For large graphs, in general, computing the exact reliability is an intractable problem and estimating it by standard Monte Carlo methods poses serious difficulties, because the unreliability one minus the reliability is often a rare-event probability. We show that the proposed GS algorithm can accurately estimate extremely small unreliabilities and we exhibit large examples where it performs much better than existing approaches. It is also flexible enough to dispense with the frequently made assumption of independent edge failures.