A new importance sampling Monte Carlo method for a flow network reliability problem.

*(English)*Zbl 1142.90332Summary: 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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\textit{S. Bulteau} and \textit{M. El Khadiri}, Nav. Res. Logist. 49, No. 2, 204--228 (2002; Zbl 1142.90332)

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