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

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