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Monte Carlo estimation of the maximal flow distribution with discrete stochastic arc capacity levels

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  • George S. Fishman

Abstract

This article describes a highly efficient Monte Carolo sampling plan for estimating ordinates of the complementary distribution function of the maximal s‐t flow in a directed network with source node s, terminal node t and whose arcs assume random capacities. Communication, electric power, transportation, and water distribution systems fit this representation. The article derives point estimates and interval estimates that hold for finite sample sizes, and shows the extent to which the proposed technique saves time, as compared to crude Monte Carlo sampling, in achieving a specified accuracy.

Suggested Citation

  • 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.
    • Handle: RePEc:wly:navres:v:36:y:1989:i:6:p:829-849
    DOI: 10.1002/1520-6750(198912)36:63.0.CO;2-4
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    References listed on IDEAS

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    1. George S. Fishman, 1986. "A Monte Carlo Sampling Plan for Estimating Network Reliability," Operations Research, INFORMS, vol. 34(4), pages 581-594, August.
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    Cited by:

    1. 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.
    2. 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).

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