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Two Approaches to the Construction of Perturbation Bounds for Continuous-Time Markov Chains

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Department of Applied Mathematics, Vologda State University, 160000 Vologda, Russia
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Institute of Informatics Problems of the Federal Research Center “Computer Science and Control”, Russian Academy of Sciences, 119333 Moscow, Russia
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Vologda Research Center of the Russian Academy of Sciences, 160014 Vologda, Russia
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Faculty of Computational Mathematics and Cybernetics, Moscow State University, 119991 Moscow, Russia
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Department of Mathematics, School of Science, Hangzhou Dianzi University, Hangzhou 310018, China
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Author to whom correspondence should be addressed.
Mathematics 2020, 8(2), 253; https://doi.org/10.3390/math8020253
Received: 20 January 2020 / Revised: 10 February 2020 / Accepted: 11 February 2020 / Published: 14 February 2020
(This article belongs to the Special Issue Stability Problems for Stochastic Models: Theory and Applications)
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.
Keywords: continuous-time Markov chains; non-stationary Markovian queueing model; stability; perturbation bounds; forward Kolmogorov system continuous-time Markov chains; non-stationary Markovian queueing model; stability; perturbation bounds; forward Kolmogorov system
MDPI and ACS Style

Zeifman, A.; Korolev, V.; Satin, A.Y. Two Approaches to the Construction of Perturbation Bounds for Continuous-Time Markov Chains. Mathematics 2020, 8, 253.

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