On Monte Carlo Estimates in Network Reliability

M. Lomonosov

Research output: Contribution to journalArticlepeer-review

26 Scopus citations

Abstract

The paper considers representations of network reliability measures as the mean value of a random variable defined on the trajectories of a certain Markov process and investigates utility of such formulae for Monte Carlo (MC) estimating. Such an MC estimator is called (ε, δ)-polynomial if its relative error is less than e with probability >1—δ, for any sample size equal to or greater than a polynomial of ε-1, δ—1, and the size of the network. One of the main results: The suggested MC estimator for the disconnectedness probability of a multiterminal network is (ε, δ)-polynomial, under a certain natural condition on the edge failure probabilities. The method applies also to estimating the percolation critical point and certain equilibrium characteristics of renewal networks.

Original languageEnglish
Pages (from-to)245-264
Number of pages20
JournalProbability in the Engineering and Informational Sciences
Volume8
Issue number2
DOIs
StatePublished - 1 Jan 1994

ASJC Scopus subject areas

  • Statistics and Probability
  • Statistics, Probability and Uncertainty
  • Management Science and Operations Research
  • Industrial and Manufacturing Engineering

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