Perfect Sampling of Phase-Type Servers using Bounding Envelopes

Bruno Gaujal 1 Gorgo Gaël 1 Jean-Marc Vincent 1
1 MESCAL - Middleware efficiently scalable
Inria Grenoble - Rhône-Alpes, LIG - Laboratoire d'Informatique de Grenoble
Abstract : Perfect sampling, or coupling from the past enables one to compute unbiased samples of the stationary distribution of Markov chains. An efficient method consists in computing a set of extremal envelopes which bound all trajectories. When the chain is not monotone, these envelopes are upper and lower bounds. The main drawback of this method is that envelopes may not couple or their coupling time may be too large. However, envelopes have already proved very efficient on several examples: negative customers, forks and joins, batch arrivals. In this research report, we construct the envelopes for phase-type servers and we show that this is another example where the envelope approach for perfect sampling is very efficient.
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Bruno Gaujal, Gorgo Gaël, Jean-Marc Vincent. Perfect Sampling of Phase-Type Servers using Bounding Envelopes. [Research Report] RR-7460, INRIA. 2010, pp.20. 〈inria-00540967〉

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