Fast simulation of tandem networks using importance sampling and stochastic gradient techniques

To obtain large speed-up factors in Monte Carlo simulation using importance sampling (IS), the modification, or bias of the underlying probability measures must be carefully chosen. In this paper, we utilize the stochastic gradient descent (SGD) algorithm, which uses stochastic gradient optimization techniques, to arrive at favorable IS bias parameter settings for the simulation of tandem queues with bursty traffic, geometric service times and a finite buffer. We describe in detail the experimental method associated with applying the SGD algorithm. Speed-up factors of 1 to 8 orders of magnitude over conventional Monte Carlo estimation of the cell loss probability are achieved for the examples presented