Two approaches to the construction of perturbation bounds for continuous-time Markov chains

TL;DR

This paper reviews two main methods for deriving perturbation bounds in continuous-time Markov chains, applies them to queuing models, and calculates specific bounds for various models.

Contribution

It introduces an approach to construct perturbation estimates for five classes of continuous-time Markov chains related to queuing models and provides explicit bounds for specific cases.

Findings

Derived perturbation bounds for five classes of Markov chains

Applied methods to queuing models with explicit calculations

Compared stability and perturbation estimates for different models

Abstract

The paper is largely of a review nature. It considers two main methods used to study stability and obtain appropriate quantitative estimates of perturbations of (inhomogeneous) Markov chains with continuous time and a finite or countable state space. An approach is described to the construction of perturbation estimates for the main five classes of such chains associated with queuing models. Several specific models are considered for which the limit characteristics and perturbation bounds for admissible "perturbed" processes are calculated.