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

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  • Stéphane Bulteau
  • Mohamed El Khadiri

Abstract

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. © 2002 Wiley Periodicals, Inc. Naval Research Logistics 49: 204–228, 2002; DOI 10.1002/nav.10004

Suggested Citation

  • Stéphane Bulteau & Mohamed El Khadiri, 2002. "A new importance sampling Monte Carlo method for a flow network reliability problem," Naval Research Logistics (NRL), John Wiley & Sons, vol. 49(2), pages 204-228, March.
    • Handle: RePEc:wly:navres:v:49:y:2002:i:2:p:204-228
    DOI: 10.1002/nav.10004
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    References listed on IDEAS

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    1. Sheldon M. Ross, 1994. "A new simulation estimator of system reliability," International Journal of Stochastic Analysis, Hindawi, vol. 7, pages 1-6, January.
    2. George S. Fishman, 1989. "Monte Carlo estimation of the maximal flow distribution with discrete stochastic arc capacity levels," Naval Research Logistics (NRL), John Wiley & Sons, vol. 36(6), pages 829-849, December.
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    Cited by:

    1. Chan, Jianpeng & Papaioannou, Iason & Straub, Daniel, 2022. "An adaptive subset simulation algorithm for system reliability analysis with discontinuous limit states," Reliability Engineering and System Safety, Elsevier, vol. 225(C).
    2. Qiyun Pan & Eunshin Byon & Young Myoung Ko & Henry Lam, 2020. "Adaptive importance sampling for extreme quantile estimation with stochastic black box computer models," Naval Research Logistics (NRL), John Wiley & Sons, vol. 67(7), pages 524-547, October.

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