Two-sided bounds on the rate of convergence for continuous-time finite inhomogeneous Markov chains

TL;DR

This paper introduces a method for deriving two-sided bounds on the convergence rate of various continuous-time Markov chains using weighted norms, applicable to models like birth-death processes and queueing systems.

Contribution

It provides a novel approach to estimate convergence rates with explicit bounds for a broad class of inhomogeneous Markov chains.

Findings

Derived two-sided bounds for convergence rates

Applicable to birth-death, queueing, and absorption processes

Enhanced understanding of convergence behavior in complex Markov models

Abstract

We suggest an approach to obtaining general two-sided bounds on the rate of convergence in terms of special "weighted" norms related to total variation. Some important classes of continuous-time Markov chains are considered: birth-death-catastrophes processes, queueing models with batch arrivals and group services, chains with absorption in zero.