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

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.