A Monte Carlo Estimator Based on a State Space Decomposition Methodology for Flow Network Reliability

  • Stéphane Bulteau
  • Mohamed El Khadiri
Part of the Lecture Notes in Statistics book series (LNS, volume 127)


The exact evaluation of the probability that the maximum st-flow is greater than or equal to a fixed value d in a stochastic flow network is an NP-hard problem. This limitation leads to consider Monte Carlo alternatives. In this paper, we show how to exploit the state space decomposition methodology of Doulliez and Jamoulle for deriving a Monte Carlo simulation algorithm. We show that the resulting Monte Carlo estimator belongs to the variance-reduction family and we give a worst-case bound on the variance-reduction ratio that can be expected when compared with the standard sampling. We illustrate by numerical comparisons that the proposed simulation algorithm allows substantial variance-reduction with respect to the standard one and it is competitive when compared to a previous work in this context.


Monte Carlo Estimator Recursive Call Exact Evaluation Lower Vector Level Confidence Interval 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


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Copyright information

© Springer Science+Business Media New York 1998

Authors and Affiliations

  • Stéphane Bulteau
    • 1
  • Mohamed El Khadiri
    • 2
  1. 1.IrisaCampus de BeaulieuRennes CédexFrance
  2. 2.C.E.R.L., I.U.T.Saint NazaireFrance

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