Perfect Sampling of Networks with Finite and Infinite Capacity Queues

Ana Busic 1 Bruno Gaujal 2 Florence Perronnin 3
1 TREC - Theory of networks and communications
DI-ENS - Département d'informatique de l'École normale supérieure, Inria Paris-Rocquencourt
2 MESCAL - Middleware efficiently scalable
Inria Grenoble - Rhône-Alpes, LIG - Laboratoire d'Informatique de Grenoble
3 MESCAL - Middleware efficiently scalable
ID-IMAG - Informatique et Distribution, Inria Grenoble - Rhône-Alpes
Abstract : We consider open Jackson queueing networks with mixed finite and infinite buffers and analyze the efficiency of sampling from their exact stationary distribution. We show that perfect sampling is possible, although the underlying Markov chain has a large or even infinite state space. The main idea is to use a Jackson network with infinite buffers (that has a product form stationary distribution) to bound the number of initial conditions to be considered in the coupling from the past scheme. We also provide bounds on the sampling time of this new perfect sampling algorithm under hyper-stability conditions (to be defined in the paper) for each queue. These bounds show that the new algorithm is considerably more efficient than existing perfect samplers even in the case where all queues are finite. We illustrate this efficiency through numerical experiments.
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https://hal.inria.fr/hal-00788003
Contributor : Arnaud Legrand <>
Submitted on : Wednesday, February 13, 2013 - 2:57:30 PM
Last modification on : Thursday, October 11, 2018 - 8:48:02 AM

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Ana Busic, Bruno Gaujal, Florence Perronnin. Perfect Sampling of Networks with Finite and Infinite Capacity Queues. 19th International Conference on Analytical and Stochastic Modelling Techniques and Applications (ASMTA) 2012, 2012, Grenoble, France. pp.136-149, ⟨10.1007/978-3-642-30782-9_10⟩. ⟨hal-00788003⟩

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