On Conditional Monte Carlo Estimation of Busy Period Probabilities in Gaussian Queues
Олег Лукашенко, Evsey V. Morozov, Michele Pagano · Communications in computer and information science · 2016
Due to the self-similar nature of broadband traffic, the arrival rate can persist on relatively high values for a considerable amount of time. Such a behavior, closely related to the duration of busy periods, has a deep impact on queueing performance in terms of loss probability and distribution of losses. In the paper we consider the probability that the normalized cumulative workload grows at least as the length T of the considered interval in case of Gaussian input traffic. As T increases, the event becomes rare and standard Monte Carlo simulation would require a large number of generated sample paths to get an accurate estimate. To cope with this problem, we propose a variant of the well-known conditional Monte Carlo method, in which conditioning is expressed in terms of the bridge process. We derive the analytical expression of the estimator and verify its effectiveness through simulations.