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Stationary Analysis of a Fluid Queue Driven by Some Countable State Space Markov Chain

Author

Listed:
  • Fabrice Guillemin

    (France Telecom)

  • Bruno Sericola

    (IRISA-INRIA, Campus de Beaulieu)

Abstract

Motivated by queueing systems playing a key role in the performance evaluation of telecommunication networks, we analyze in this paper the stationary behavior of a fluid queue, when the instantaneous input rate is driven by a continuous-time Markov chain with finite or infinite state space. In the case of an infinite state space and for particular classes of Markov chains with a countable state space, such as quasi birth and death processes or Markov chains of the G/M/1 type, we develop an algorithm to compute the stationary probability distribution function of the buffer level in the fluid queue. This algorithm relies on simple recurrence relations satisfied by key characteristics of an auxiliary queueing system with normalized input rates.

Suggested Citation

  • Fabrice Guillemin & Bruno Sericola, 2007. "Stationary Analysis of a Fluid Queue Driven by Some Countable State Space Markov Chain," Methodology and Computing in Applied Probability, Springer, vol. 9(4), pages 521-540, December.
    • Handle: RePEc:spr:metcap:v:9:y:2007:i:4:d:10.1007_s11009-006-9007-1
    DOI: 10.1007/s11009-006-9007-1
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    Cited by:

    1. Bruno Sericola & Marie-Ange Remiche, 2011. "Maximum Level and Hitting Probabilities in Stochastic Fluid Flows Using Matrix Differential Riccati Equations," Methodology and Computing in Applied Probability, Springer, vol. 13(2), pages 307-328, June.

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