Fast simulation of Markovian reliability/availability models with general repair policies

Abstract

Markovian models of highly reliable systems are considered. An importance sampling based variance reduction technique known as failure biasing has been found to be very useful in the fast Monte Carlo simulation of such systems. The authors show by examples that existing failure biasing heuristics break down for systems which involve more general repair/recovery policies that are common in practice. This motivated a detailed look at the theory of failure biasing from a different perspective than what has been done before, i.e., the effect of failure biasing on sample paths of the Markov chain that involve cycles. This cycling perspective is used to give a much simpler proof of the established fact that existing failure biasing heuristics produce an order of magnitude increase in simulation efficiency over standard simulation, for a class of Markovian systems with simple repair policies. This approach allows the development of theory and efficient heuristics for systems with the more general repair policies.