Abstract
This paper is largely a review. It considers two main methods used to study stability and to 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.
Highlights
Some topics are considered that are related to the stability of both homogeneous and non-homogeneous continuous-time Markov chains with respect to the perturbation of their intensities
It is assumed that the evolution of the system under consideration is described by a Markov chain with the known state space, and it is the infinitesimal matrix that is given inexactly
Since the 1980s, the problems related to the estimation of stability of Markov chains with respect to perturbations of their characteristics have been thoroughly studied by Kartashov for homogeneous discrete-time chains with general state space and, in parallel, by Zeifman for inhomogeneous continuous-time chains within the seminar mentioned above
Summary
Some topics are considered that are related to the stability of both homogeneous and non-homogeneous continuous-time Markov chains with respect to the perturbation of their intensities (infinitesimal characteristics). Since the 1980s, the problems related to the estimation of stability of Markov chains with respect to perturbations of their characteristics have been thoroughly studied by Kartashov for homogeneous discrete-time chains with general state space and, in parallel, by Zeifman for inhomogeneous continuous-time chains within the seminar mentioned above (see [7,8,9]). Following the ideas of Kartashov (see a detailed description in [24]), most authors use the probability methods to study ergodicity and perturbation bounds of stationary chains (with a finite, countable, or general state space) in various norms [13,25,26]. In the works of the authors of the present paper, perturbation bounds for non-stationary finite or infinite continuous-time chains were studied by other methods.
Sign-in/Register to view highlights & summary Sign-in/Register to access full text options 
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a callDisclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.
