Filtered and Setwise Gibbs Samplers for Teletraffic Analysis

The Gibbs sampler is a very simple yet efficient method for the performance evaluation of product form loss networks. This paper introduces the setwise Gibbs sampler as a flexible technique for analysing closed BCMP networks, which model telecommunication networks using window flow control. The efficiency of another variant, the filtered Gibbs sampler (FGS), is also investigated. It is shown that the FGS is considerably more efficient than the standard Gibbs sampler. It is also shown that traditional estimates of the accuracy of FGS can be excessively optimistic, and a more conservative estimator is presented. Keywords— Product form; Queueing networks; Gibbs Sampler; Markov chain Monte Carlo

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