Hybrid analysis of response time distributions in queueing networks

A hybrid analytic/simulation methodology is formulated for evaluating end-to-end response time distributions in closed product-form queueing networks. The method combines Markov-Monte-Carlo simulation with analytical results pertaining to uniformized Markov chains and product-form queuing networks. A stratified sampling plan is incorporated as a variance reduction technique. The concept of importance sampling is used to reduce the computational requirements of the plan and make it realizable in practice. The most important consequence of applying uniformization is that it enables the characterization of the response time distribution as an infinite mixture of Erlangian distributions. An estimate of the entire response time distribution may then be obtained in each simulation trial. This circumvents the practical problems associated with estimating tail probabilities. A numerical example is provided to illustrate the theory