Efficient Simulation via Cross-Entropy

Abstract

The performance of modern systems, such as coherent reliability systems, inventory systems, insurance risk, storage systems, computer networks and telecommunication networks is often characterized by probabilities of rare events and is frequently studied through simulation. Analytical solutions or accurate approximations for such rare-event probabilities are only available for a very restricted class of systems. Consequently, one often has to resort to simulation. However, estimation of rare-event probabilities with crude Monte Carlo techniques requires a prohibitively large numbers of trials, as illustrated in Example 1.3. Thus, new techniques are required for this type of problem. Two methods, called splitting/RESTART and importance sampling (IS) have been extensively investigated by the simulation community in the last decade.