Some notes on a semi-Markov matrix occurring in the M|M|∞ queue parameters study

The main objective of this work is to present a process to compute the Markov renewal matrix R(t) for Markov renewal processes with countable infinite spaces, 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 considered the application to the M|M|∞ queue particular case