Combination of conditional Monte Carlo and approximate zero-variance importance sampling for network reliability estimation

Abstract

We study the combination of two efficient rare event Monte Carlo simulation techniques for the estimation of the connectivity probability of a given set of nodes in a graph when links can fail: approximate zero-variance importance sampling and a conditional Monte Carlo method which conditions on the event that a prespecified set of disjoint minpaths linking the set of nodes fails. Those two methods have been applied separately. Here we show how their combination can be defined and implemented, we derive asymptotic robustness properties of the resulting estimator when reliabilities of individual links go arbitrarily close to one, and we illustrate numerically the efficiency gain that can be obtained.

Static Network Reliability Estimation via Generalized Splitting

“…Several variance reduction methods have been proposed for this problem. Among the most prominent ones, we find conditional Monte Carlo approaches (Cancela and El Khadiri, 2003;Cancela et al, 2009b;Elperin et al, 1991;Gertsbakh and Shpungin, 2010;Lomonosov and Shpungin, 1999), methods that change the sampling distribution (usually by concentrating the sampling in subsets of the sample space where there is more uncertainty, using paths and cuts to determine those subsets) (Fishman, 1986;Manzi et al, 2001;Zenklusen and Laumanns, 2011), approximate zero-variance importance sampling (L'Ecuyer et al, 2011), and combinations of those (Cancela et al, 2010). There are many more.…”

Some Recent Results in Rare Event Estimation

“…As a last remark, this IS technique can be combined with other existing variance reduction techniques or graph reduction techniques, for an additional efficiency improvement [11,29].…”

“…For many numerical illustrations of the efficiency of the methods, we advise the reader to go to [11,28,29].…”

Monte Carlo estimation of diameter-constrained network reliability conditioned by pathsets and cutsets

“…Surveys on simulation schemes that have been devised for estimating RðG; KÞ in the CLR context can be found in [14,12]. More recent works include [15][16][17][18][19]. The existing methods for the CLR can be adapted to the DCR context.…”