Some notes on a semi-Markov matrix occurring in the MMinf queue parameters study

TL;DR

This paper introduces a method to compute the semi-Markov matrix for Markov renewal processes with infinite state spaces, focusing on immigration and death types, and applies it to the MMinf queue model.

Contribution

It presents a novel process for calculating semi-Markov matrices with a tridiagonal form in infinite state spaces, aiding practical applications.

Findings

Successfully computes semi-Markov matrices for infinite state processes.

Provides a practical approach for MMinf queue modeling.

Facilitates application of semi-Markov processes in real-world systems.

Abstract

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.