Rare Event Simulation Techniques for Queueing Models(<Special Topics>Applied Mathematics in Queueing)

Abstract

This paper gives an overview of importance sampling simulation techniques for queueing models with rare events. The importance sampling technique is known to be effective in estimating the probability to occur rare events: simulate a modified probability distribution so as to generate more "rare" events and estimate the true value by multiplying the likelihood ratio to correct the bias. The key to the success of this technique is how to select appropriate modified distributions. The large deviation principle provides the powerful tool to this problem. This paper discusses about the exponential twisting distribution transform based on the large deviation principle. Dynamic distribution transform technique is also discussed, which is effective for the steady state simulation.