Splitting sequential Monte Carlo for efficient unreliability estimation of highly reliable networks

Abstract Assessing the reliability of complex technological systems such as communication networks, transportation grids, and bridge networks is a difficult task. From a mathematical point of view, the problem of estimating network reliability belongs to the #P complexity class. As a consequence, no analytical solution for solving this problem in a reasonable time is known to exist and one has to rely on approximation techniques. In this paper we focus on a well-known sequential Monte Carlo algorithm — Lomonosov’s turnip method. Despite the fact that this method was shown to be efficient under some mild conditions, it is known to be inadequate for a stable estimation of the network reliability in a rare-event setting. To overcome this obstacle, we suggest a quite general combination of sequential Monte Carlo and multilevel splitting. The proposed method is shown to bring a significant variance reduction as compared to the turnip algorithm, is easy to implement and parallelize, and has a proven performance guarantee for certain network topologies.

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