A simple and efficient importance sampling scheme for stochastic network unreliability estimation

Direct simulation for estimating unreliability of a highly reliable stochastic network often requires huge sample size to obtain statistically significant results. In this paper, a simple and efficient importance sampling estimator, based on the capacity of the minimum cut, for estimating network unreliability is proposed. Under mild conditions, the proposed estimator guarantees the variance reduction and an upperbound on the relative error of the proposed estimator is derived for the case when the network edges have common functioning probabilities. Empirical results show that the proposed importance sampling estimator achieves significant variance reduction, especially for highly reliable networks.