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On Monte Carlo Estimates in Network Reliability

Published online by Cambridge University Press:  27 July 2009

M. Lomonosov
M. Lomonosov
Affiliation:
Department of Mathematics & Computer Science, Ben-Gurion University of the Negev, Beer-Sheva, 84105, Israel, and ARTEMIS, IMAG, Univ. J. Fourier BP 53X, 38041 Grenoble cedex, France
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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 ε 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.

Type
Research Article
Information
Probability in the Engineering and Informational Sciences , Volume 8 , Issue 2 , April 1994 , pp. 245 - 264
Copyright
Copyright © Cambridge University Press 1994

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