The cross-entropy method for network reliability estimation

Consider a network of unreliable links, modelling for example a communication network. Estimating the reliability of the network – expressed as the probability that certain nodes in the network are connected – is a computationally difficult task. In this paper we study how the Cross-Entropy method can be used to obtain more efficient network reliability estimation procedures. Three techniques of estimation are considered: Crude Monte Carlo and the more sophisticated Permutation Monte Carlo and Merge Process. We show that the Cross-Entropy method yields a speed-up over all three techniques.