Archive

Volume 1, Number 2 / August issue 2015
Manuel Alberto M. Ferreira
A differential equation occurring in the M|M|∞ queue parameters study using a Markov renewal process
Abstract

This work main objective is to present a process to compute the Markov renewal matrix R(t) for Markov renewal processes with infinite countable states space, which semi-Markov matrixes Q(t) are immigration and death type and assume a tridiagonal form. These processes occur often in practical applications. And the difficulty in obtaining friendly results for R(t) is a great obstacle to its application in practical cases modelling. It is exemplified the application to the M|M ∞ queue particular case. The work presented in (5) is resumed but now the emphasis is put in the determination of a pfaffian solution that must be considered in this example.
Keywords: Markov renewal process, tridiagonal matrix, M|M ∞ queue, pfaffian, exact differential equation

Cite this article:
Manuel Alberto M. Ferreira. A differential equation occurring in the M|M|∞ queue parameters study using a Markov renewal process. Acta Scientiae et Intellectus, 1(2), 10-15.


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