Monte Carlo methods for reliability analysis of stochastic flow networks

This thesis describes an efficient Monte Carlo sampling plan for estimating the probability that the maximal s-t flow in a stochastic flow network greater than or equal to d;The paper first describes a method to derive lower and upper bounds on the probability. Using this information on bounds, the paper describes how to replace the sampling distribution with a distribution that concentrates sampling in a specialize region to obtain an unbiased estimator with smaller variance than crude Monte Carlo sampling allows. The paper also presents a method for estimating variation in system performance in response to variation performances using the sampling data accumulated to estimate the probability be interested.