On coupling epoch for renewal times

TL;DR

This paper presents a general approach to using the coupling method for regenerative processes, enabling estimation of convergence rates in queuing theory and related fields, covering both polynomial and exponential cases.

Contribution

It introduces a unified framework for applying the coupling method to regenerative processes, improving convergence rate estimations.

Findings

Applicable to polynomial and exponential convergence rates

Provides a general approach for regenerative process analysis

Enhances estimation accuracy of convergence times

Abstract

The ability to estimate the rate of convergence for the distributions of regenerative processes is in great demand. These processes are often encountered in queuing theory and in related problems. In some papers on regenerative processes, the coupling method and subsequent estimation of the convergence rate is used. In the presented small publication, we describe a general approach to using the coupling method for regenerative processes - both in the case of a polynomial and an exponential rate of convergence.