Skip to main content
Log in

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

  • Contributed Paper
  • Published:
Queueing Systems Aims and scope Submit manuscript

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.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Similar content being viewed by others

References

  1. 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.

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

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

  4. G. Rubino, Etude de la file FIFO multiclasse, Congresso dos matematicos de espressáo latina, Coimora, Set. 1984.

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

  6. 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.

Download references

Author information

Authors and Affiliations

Authors

Rights and permissions

Reprints and permissions

About this article

Cite this article

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

Download citation

  • Received:

  • Revised:

  • Issue Date:

  • DOI: https://doi.org/10.1007/BF01159088

Keywords

Navigation