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

Fabrice Guillemin () and Bruno Sericola ()
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Fabrice Guillemin: France Telecom
Bruno Sericola: IRISA-INRIA, Campus de Beaulieu

Methodology and Computing in Applied Probability, 2007, vol. 9, issue 4, 521-540

Abstract: 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.

Keywords: fluid queues; Markov chains; uniformization; stationary regime; numerical algorithm; Primary 60K25; Secondary 60J27 (search for similar items in EconPapers)
Date: 2007
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Citations: View citations in EconPapers (1)

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DOI: 10.1007/s11009-006-9007-1

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