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 M(M) for Markov renewal processes with infinite countable states
space, which semi-Markov matrixes M(M) 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 M(M)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.