Random number generation and quasi-Monte Carlo methods
Random number generation and quasi-Monte Carlo methods
Asymptotically optimal importance sampling for product-form queuing networks
ACM Transactions on Modeling and Computer Simulation (TOMACS)
Monte Carlo summation and integration applied to multiclass queuing networks
Journal of the ACM (JACM)
Implementation of Monte Carlo integration for the analysis of product-form queueing networks
Performance Evaluation
Open, Closed, and Mixed Networks of Queues with Different Classes of Customers
Journal of the ACM (JACM)
Computational algorithms for closed queueing networks with exponential servers
Communications of the ACM
Some current issues in quasi-Monte Carlo methods
Journal of Complexity
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Performance of product-form multiclass queuing networks can be determined from normalization constants. For large models, the evaluation of these performance metrics is not possible because of the required amount of computer resources (either by using normalization constants or by using MVA approaches). Such large models can be evaluated with Monte Carlo summation and integration methods. This article proposes two cluster sampling Monte Carlo techniques to deal with such models. First, for a particular type of network, we propose a variance reduction technique based on antithetic variates. It leads to an improvement of Ross, Tsang and Wang's algorithm which is designed to analyze the same family of models. Second, for a more general class of models, we use a mixture of Monte Carlo and quasi-Monte Carlo methods to improve the estimate with respect to Monte Carlo alone.