Reliability of stochastic flow networks with continuous link capacities

We consider the problem of estimating the unreliability of a stochastic flow network, defined as the probability that the maximum flow value from a source node to a terminal node in a directed network with stochastic link capacities, is less than a specified demand level. The link capacities are assumed to be continuous random variables with a known joint distribution. We are interested in the situation where the unreliability is very small, in which case a crude Monte Carlo is not viable. We show how a Monte Carlo splitting algorithm can be adapted to handle this problem effectively.