Abstract
We consider inhomogeneous continuous-time Markov chains with vanishing perturbations. It is proved that, under some natural conditions, the limiting regimes of the initial and perturbed chains coincide. We obtain explicit estimates, which allow construction of the limiting regime of the perturbed chain, and show how these results can be used in the analysis of several known classes of queuing systems.
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Funding
This work was supported by the Ministry of Science and Higher Education of the Russian Federation, project no. 075-15-2020-799.
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Translated by I. Ruzanova
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Zeifman, A.I., Korolev, V.Y., Razumchik, R.V. et al. Limiting Characteristics of Queueing Systems with Vanishing Perturbations. Dokl. Math. 106, 375–379 (2022). https://doi.org/10.1134/S1064562422050209
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DOI: https://doi.org/10.1134/S1064562422050209