Informatics and Applications
2022, Volume 16, Issue 3, pp 75-82
ON AN APPROACH FOR ESTIMATING THE RATE OF CONVERGENCE FOR NONSTATIONARY MARKOV MODELS OF QUEUEING SYSTEMS
- I. A. Kovalev
- Y. A. Satin
- A. V. Sinitcina
- A. I. Zeifman
Abstract
The transformation of the forward Kolmogorov system is considered which allows one to obtain simple estimates on the rate of convergence for Markov chains with continuous time describing queuing systems. In addition, the concept of the logarithmic norm of the operator function and the associated estimates of the norm of the Cauchy matrix are used. The results obtained make it possible to estimate the rate of convergence for new classes of models in which the matrix is not significantly nonnegative and the use of the logarithmic norm method does not guarantee the possibility of obtaining estimates of the rate of convergence. Previously, a rather laborious more general method of inequalities was used for such situations. A theorem is formulated on obtaining the rate of convergence when the intensities of the matrix change. An estimate was obtained for the process of birth and death with constant intensities. As an example, a special nonstationary model with group service of requirements (service in pairs) is investigated.
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[+] About this article
Title
ON AN APPROACH FOR ESTIMATING THE RATE OF CONVERGENCE FOR NONSTATIONARY MARKOV MODELS OF QUEUEING SYSTEMS
Journal
Informatics and Applications
2022, Volume 16, Issue 3, pp 75-82
Cover Date
2022-10-10
DOI
10.14357/19922264220310
Print ISSN
1992-2264
Publisher
Institute of Informatics Problems, Russian Academy of Sciences
Additional Links
Key words
rate of convergence; ergodicity bounds; logarithmic norm; queuing systems
Authors
I. A. Kovalev  ,  , Y. A. Satin , A. V. Sinitcina  , and A. I. Zeifman , , , 
Author Affiliations
Department of Applied Mathematics, Vologda State University, 15 Lenin Str., Vologda 160000, Russian Federation
Moscow Center for Fundamental and Applied Mathematics, M.V. Lomonosov Moscow State University, 1-52 Leninskie Gory, GSP-1, Moscow 119991, Russian Federation
P. G. Demidov Yaroslavl State University, 14 Sovetskaya Str., Yaroslavl 150003, Russian Federation
Federal Research Center "Computer Science and Control" of the Russian Academy of Sciences, 44-2 Vavilov Str., Moscow 119333, Russian Federation
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