Bounds on the rate on convergence for Markovian queueing models with catastrophes

TL;DR

This paper develops a general method to analyze the convergence rates of non-stationary Markov chains with catastrophes, providing estimates for their limiting behavior and illustrating with a specific queuing model example.

Contribution

It introduces a novel approach for bounding convergence rates in Markovian queueing models with catastrophes, advancing understanding of their limiting regimes.

Findings

Derived bounds on convergence rates for Markovian queues with catastrophes

Provided estimates for the limiting regime of such queues

Illustrated the approach with a specific queuing model example

Abstract

In this note, a general approach to the study of non-stationary Markov chains with catastrophes and the corresponding queuing models is considered, as well as to obtain estimates of the limiting regime itself. As an illustration, an example of a queuing model is studied.