## 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 language | English |
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Pages (from-to) | 245-264 |

Number of pages | 20 |

Journal | Probability in the Engineering and Informational Sciences |

Volume | 8 |

Issue number | 2 |

DOIs | |

State | Published - 1 Jan 1994 |

## ASJC Scopus subject areas

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