The theory of direct probability redistribution and its application to rare event simulation

Estimating rare event probabilities in communication systems using Monte Carlo simulation can require a prohibitively large number of trials for acceptable accuracy. We develop and present a technique in this paper that provides large speedup factors over conventional Monte Carlo simulation based on the theory of "direct probability redistribution" (DPR). We show that DPR can be viewed as a type of importance sampling (IS), albeit "nontraditional", which requires little additional effort to apply. The theory of DPR is presented for systems that can be described as a discrete time Markov chain (DTMC). We show that the RESTART technique is an important special case of direct probability redistribution. An efficient simulation technique based on DPR is less restrictive than RESTART, and is much less problem specific than traditional IS techniques. We demonstrate how to use DPR to speedup Monte Carlo simulation of non-trivial systems by applying the technique to two examples: A 64/spl times/64 three-stage ATM switch, and an ATM multiplexer with internal flow control. For these systems we estimate small cell loss probabilities and show that the improvement is nearly inversely proportional to the probability estimate.