Improving Adaptive Importance Sampling Simulation of Markovian Queueing Models using Non-parametric Smoothing

Previous work on state-dependent adaptive importance sampling techniques for the simulation of rare events in Markovian queueing models used either no smoothing or a parametric smoothing technique, which was known to be non-optimal. In this paper, we introduce the use of kernel smoothing in this context. We derive eXpressions for the smoothed transition probabilities, compare several variations of the technique, and explore the choice of kernel width. We provide some examples, demonstrating that the technique significantly improves convergence and estimator variance.