On Monte Carlo Estimates in Network Reliability

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.