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Evaluating reliability of stochastic flow networks. (English) Zbl 1134.90326
Summary: This paper describes a highly efficient Monte Carlo sampling plan for evaluating the probability that the flow value in a stochastic flow network is greater than or equal to a prespecified level \(d\). A stochastic flow network can characterize communication, transportation, and water or oil distribution systems. The paper first derives lower and upper bounds on the probability of interest and then describes how one can concentrate sampling in a specialized region’ of the arc capacity state space to increase the statistical efficiency of the resulting estimate. The paper also gives expressions for worst-case sample sizes needed to meet specified bounds on variances and coefficients of variation and-illustrates the proposed sampling plan with an example.
MSC:
90B15 Stochastic network models in operations research
90B25 Reliability, availability, maintenance, inspection in operations research
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