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In this paper we consider the evaluation of the well known K -network unreliability parameter by means of a new RVR Monte-Carlo method. This method is based on series-parallel reductions and a partitioning procedure using pathsets and cutsets for recursively changing the original problem into similar ones on smaller networks. By means of several experimental results, we show that the proposed method has good performances in rare event cases and offers significant gains over other state-of-the-art variance reduction techniques.

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Exact evaluation of static network reliability parameters belongs to the NP-hard family, and Monte Carlo simulation is therefore a relevant tool to provide their estimations. The first goal of this work is to review a Recursive Variance Reduction (RVR) estimator, which approaches the unreliability by recursively reducing the graph from the random choice of the first working link on selected cuts. We show that the method does not verify the bounded relative error (BRE) property as reliability of individual links goes to one-that is, that the estimator is not robust in general to high reliability of links. We then propose to use the decomposition ideas of the RVR estimator in conjunction with the importance sampling technique. Two new estimators are presented: the first one-the Balanced Recursive Decomposition estimator-chooses the first working link on cuts uniformly, whereas the second-the Zero-Variance Approximation Recursive Decomposition estimator-tries to mimic the estimator with variance zero for this technique. We show that in both cases the BRE property is verified and, moreover, that a vanishing relative error (VRE) property can be obtained for the Zero-Variance Approximation RVR under specific sufficient conditions. A numerical illustration of the power of the methods is provided on several benchmark networks.