Detailed state probability distribution of infinite servers queues with phase-type distributed service times

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Ivan Mura

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ONTARE. REVISTA DE INVESTIGACIÓN DE LA FACULTAD DE INGENIERÍA


We present a detailed analysis of the M/PH/ queue, which allows determining an analytic form for both the transient and the steady-state probability distribution of customers at the various phases of the service. The analysis is based on the correspondence that can be found between the stochastic process representing the number of customers in service at the various phases of the PH distribution, and a stochastic process that represents the evolution of the number of customers in the nodes of a Jackson’s network where all service centers are M/M/ queues.

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