A differential equation occurring in the M/M/oo 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 coutable 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/oo queue particular case. The work presented in (5) is resumed but now the emphasis is put in the determination of pfaffian solutionthat must be considered in this example.