Stochastic gradient techniques for the efficient simulation of high-speed networks using importance sampling

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. Analytical optimization techniques are generally ineffective, especially for queueing networks with bursty traffic. The authors present two stochastic gradient optimization techniques that lead to favorable IS parameter settings in the simulation of queueing networks, including queues with bursty traffic. Namely, they motivate and describe the stochastic gradient descent (SGD) algorithm, and the stochastic (important event) frequency ascent (SFA) algorithm. They demonstrate the effectiveness of their algorithms by applying them to the problem of estimating the blocking probability for a queue with two arrival streams, a modified interrupted Bernoulli stream and a Markov modulated Bernoulli stream with batch arrivals, deterministic service times, and finite capacity K (denoted by M-IBP+MMBBP/D/1/K). Speed-up factors of 1 to 6 orders of magnitude over conventional Monte Carlo simulation are achieved for the examples presented