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A new importance sampling Monte Carlo method for a flow network reliability problem. (English) Zbl 1142.90332
Summary: The exact evaluation of the probability that the maximum st-flow is greater than or equal to a fixed demand in a stochastic flow network is an NP-hard problem. This limitation leads one to consider Monte Carlo alternatives. In this paper, we propose a new importance sampling Monte Carlo method. It is based on a recursive use of the state space decomposition methodology of Doulliez and Jamoulle during the simulation process. We show theoretically that the resulting estimator belongs to the variance-reduction family and we give an upper bound on its variance. As shown by experimental tests, the new sampling principle offers, in many cases, substantial speedups with respect to a previous importance sampling based on the same decomposition procedure and its best performances are obtained when highly reliable networks are analyzed.

MSC:
90B15 Stochastic network models in operations research
90B35 Deterministic scheduling theory in operations research
62N05 Reliability and life testing
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