On Monte Carlo Estimates in Network Reliability

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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.

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