Nonparametric Adaptive Importance Sampling for Rare Event Simulation

Simulating rare events in telecommunication networks such as estimation for cell loss probability in Asynchronous Transfer Mode (ATM) networks requires a major simulation effort due to the slight chance of buffer overflow. Importance Sampling (IS) is applied to accelerate the occurrence of rare events. Importance Sampling depends on a biasing scheme to make the estimator from IS unbiased. Adaptive Importance Sampling (AIS) employs an estimated sampling distribution of IS to the system of interest during the course of simulation. In this study, we propose a Nonparametric Adaptive Importance Sampling (NAIS) technique, a non-parametrically modified version of AIS, and estimate the probability of rare event occurrence in an M/M/1 queueing model. Compared with classical Monte Carlo simulation and AIS, the computational efficiency and variance reductions gained via NAIS are reasonable. A possible extension of NAIS with regards to random number generation is also discussed.