Lorden's inequality and coupling method for backward renewal process

TL;DR

This paper introduces a coupling-based scheme to derive strong convergence bounds for the backward renewal process's distribution, applicable to various regenerative processes in queuing theory.

Contribution

It presents a novel coupling method scheme for obtaining convergence bounds in backward renewal processes, expanding analytical tools in regenerative process analysis.

Findings

Provides a coupling scheme for convergence bounds

Applicable to a wide class of regenerative processes

Enhances analysis of backward renewal process convergence

Abstract

We give a scheme of using the coupling method to obtain strong bounds for the convergence rate of the distribution of the backward renewal process in the total variation distance. This scheme can be applied to a wide class of regenerative processes in queuing theory.