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Conference Papers Year : 2008

Perfect Simulation and Non-monotone Markovian Systems

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Ana Bušić
Bruno Gaujal
Jean-Marc Vincent

Abstract

Perfect simulation, or coupling from the past, is an efficient technique for sampling the steady state of monotone discrete time Markov chains. Indeed, one only needs to consider two trajectories corresponding to minimal and maximal state in the system. We show here that even for non-monotone systems one only needs to compute two trajectories: an infimum and supremum envelope. Since the sequence of states obtained by taking infimum (resp. supremum) at each time step does not correspond to a feasible trajectory of the system, envelopes and not feasible trajectories. We show that the envelope approach is efficient for some classes of non-monotone queuing networks, such as networks of queues with batch arrivals, queues with fork and join nodes and/or with negative customers.
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Dates and versions

hal-00953624 , version 1 (28-02-2014)

Identifiers

  • HAL Id : hal-00953624 , version 1

Cite

Ana Bušić, Bruno Gaujal, Jean-Marc Vincent. Perfect Simulation and Non-monotone Markovian Systems. 3rd International Conference Valuetools'08, 2008, Athens, Greece. ⟨hal-00953624⟩
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