On strong bounds of rate of convergence for regenerative processes

TL;DR

This paper establishes strong bounds on how quickly regenerative processes converge to their stationary distribution using coupling methods, with applications to queueing systems.

Contribution

It introduces a coupling-based approach to derive convergence bounds specifically for queueing regenerative processes, advancing theoretical understanding.

Findings

Derived explicit bounds for convergence rates in total variation

Applied coupling method to queueing regenerative processes

Enhanced theoretical tools for analyzing stochastic process convergence

Abstract

We give strong bounds for the rate of convergence of the regenerative process distribution to the stationary distribution in the total variation metric. These bounds are obtained by using coupling method. We propose this method for obtaining such bounds for the queueing regenerative processes.