Bounds on the Rate of Convergence for M t X / M t X /1 Queueing Models

Alexander Zeifman, Yacov Satin and Alexander Sipin
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Alexander Zeifman: Department of Applied Mathematics, Vologda State University, Lenina 15, 160000 Vologda, Russia
Yacov Satin: Department of Applied Mathematics, Vologda State University, Lenina 15, 160000 Vologda, Russia
Alexander Sipin: Department of Applied Mathematics, Vologda State University, Lenina 15, 160000 Vologda, Russia

Mathematics, 2021, vol. 9, issue 15, 1-11

Abstract: We apply the method of differential inequalities for the computation of upper bounds for the rate of convergence to the limiting regime for one specific class of (in)homogeneous continuous-time Markov chains. Such an approach seems very general; the corresponding description and bounds were considered earlier for finite Markov chains with analytical in time intensity functions. Now we generalize this method to locally integrable intensity functions. Special attention is paid to the situation of a countable Markov chain. To obtain these estimates, we investigate the corresponding forward system of Kolmogorov differential equations as a differential equation in the space of sequences l 1 .

Keywords: inhomogeneous continuous-time Markov chain; weak ergodicity; rate of convergence; sharp bounds; differential inequalities; forward Kolmogorov system (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2021
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