  The main objective of this work is to present a process to compute the Markov
renewal matrix for Markov renewal processes with countable infinite spaces,
which semi-Markov matrixes 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 that matrix is a great
obstacle to its application in practical cases modelling. It is considered the
application to the MMinf queue particular case.
