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Steady-state probabilities of the PH/PH/1 queue

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Abstract

It is proven that the steady-state probability of the PH/PH/1 queue is a linear combination of product forms. The method of linear combination of product forms is introduced, and simple formulae are obtained.

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References

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    P.P. Socharov and V.A. Naumov, Matrix geometric stationary distribution for the PH/PH/1/r queue, Rapport de Recherche no. 304, INRIA, Mai 1984.

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    J.Y. Le Boudec, Analyse quantitative de réseaux de files d'attente markoviens, Thèse de 3è cycle, Rennes, juin 1984.

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    M. Neuts, Matrix geometric solutions in stochastic models, Johns Hopkins, 1981.

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    E. Seneta,Non-negative Matrices and Markov Chains (Springer-Verlag, 1980).

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    A.H.A. van de Liefvort, An algebraic approach to the steady-state solution of G/G/1//N type loops, Ph D dissertation, University of Nebraska, March 1982.

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Le Boudec, J. Steady-state probabilities of the PH/PH/1 queue. Queueing Syst 3, 73–87 (1988). https://doi.org/10.1007/BF01159088

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Keywords

  • Single server queue
  • matrix-geometric solution
  • product form
  • phase type distribution