Asymptotically Optimal Importance Sampling for Product-Form Queuing Networks

Monte Carlo integration M apphed to the integral representation of the normalization constant for a famdy of product-form multiclass queuing networks These networks are closed with single-server, fixed-rate stations and at least one infinite-server station. Letting the population for each class go to infinity, the asymptotically optimal importance-samphng distributions are derived for estimates of the normalization constant and of the utilizations. In the normal-usage regime, in which the asymptotic utilizations at the single-server stations are strictly less than one, independent exponential samphng is asymptotically optimal for estimating the normalization constant. In the same regime, the asymptotically optimal sampling dmtrlbution for estimatmg utilization is complex and dependent across single-server stations. In the critical-usage regime, m which the asymptotic utlhzatlons at the single-server stations are equal to one, truncated multivarlate normal sampling is asymptotically optimal for estimating the normalization constant.