About ergodicity and polynomial convergence rate of Generalized Markov modulated Poisson processes

TL;DR

This paper develops a method to derive convergence rate bounds for generalized Markov modulated Poisson processes, enhancing tools for analyzing complex stochastic models in reliability and queuing theory.

Contribution

It introduces a novel approach to establish ergodicity and polynomial convergence rates for generalized MMPP models, extending existing inequalities.

Findings

Provides bounds on convergence rates for generalized MMPP

Applicable to reliability and queuing systems

Enhances understanding of stochastic process convergence

Abstract

Generalization of the Lorden's inequality is an excellent tool for obtaining strong upper bounds for the convergence rate for various complicated stochastic models. This paper demonstrates a method for obtaining such bounds for some generalization of the Markov modulated Poisson process (MMPP). The proposed method can be applied to reliability and queuing theory.