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Perfect Sampling of Networks with Finite and Infinite Capacity Queues

  • Ana Bušić
  • Bruno Gaujal
  • Florence Perronnin
Part of the Lecture Notes in Computer Science book series (LNCS, volume 7314)

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.

Keywords

Markov Chain Stationary Distribution Queueing Network Coalescence Time Jackson Network 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© Springer-Verlag Berlin Heidelberg 2012

Authors and Affiliations

  • Ana Bušić
    • 1
  • Bruno Gaujal
    • 2
  • Florence Perronnin
    • 3
  1. 1.INRIA - ENSParisFrance
  2. 2.INRIA Grenoble - Rhône-AlpesMontbonnotFrance
  3. 3.Joseph Fourier UniversityGrenobleFrance

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