Informatics and Applications
2020, Volume 14, Issue 2, pp 39
ON APPROACHES TO CONSTRUCTING LIMITING REGIMES FOR SOME QUEUING MODELS
 Ya. A. Satin
 A. I. Zeifman
 G. N. Shilova
Abstract
The authors consider nonstationary queuing models, the number of customers in which is described by finite Markov chains with periodic intensities. For many classes of such models, the methods of obtaining upper bounds on the rate of convergence to the limiting regime were developed in previous papers of the authors. Using these methods, one can find the main limiting characteristics of the system, study their stability with respect to small perturbations of the arrival and service intensities, and receive information on how current characteristics of the system differ from the limiting characteristics at each moment of time. In the present paper, the authors study a different situation, namely, it is assumed that explicit estimates of the rate of convergence to the limiting regime cannot be obtained. The methods for constructing the limiting regimes of such systems and for obtaining information on the rate of convergence to them are considered. As an example, the authors consider a simple model of a nonstationary system with a rather slow rate of convergence to the limiting regime.
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[+] About this article
Title
ON APPROACHES TO CONSTRUCTING LIMITING REGIMES FOR SOME QUEUING MODELS
Journal
Informatics and Applications
2020, Volume 14, Issue 2, pp 39
Cover Date
20200630
DOI
10.14357/19922264200201
Print ISSN
19922264
Publisher
Institute of Informatics Problems, Russian Academy of Sciences
Additional Links
Key words
queuing system; finite Markov chains; periodic intensities; limiting characteristics; rate of convergence
Authors
Ya. A. Satin , A. I. Zeifman , , , and G. N. Shilova
Author Affiliations
Vologda State University, 15 Lenin Str., Vologda 160000, Russian Federation
Institute of Informatics Problems, Federal Research Center "Computer Science and Control" of the Russian Academy of Sciences, 442 Vavilov Str., Moscow 119333, Russian Federation
Vologda Research Center of the Russian Academy of Sciences, 56A Gorky Str., Vologda 160014, Russian Federation
