Informatics and Applications
2023, Volume 17, Issue 3, pp 49-57
ON THE RATE OF CONVERGENCE AND LIMITING CHARACTERISTICS FOR ONE QUASI-BIRTH-DEATH PROCESS
- I. A. Usov
- Y. A. Satin
- A. I. Zeifman
Abstract
A queuing system with one server and different repair and failure options is considered, the number of requirements in which is described by a quasi-birth-death process. To reasonably find the limiting probabilistic characteristics of the system, the rate of convergence to them is studied (that is, the rate at which the initial conditions of the system are "forgotten"). To study the rate of convergence to the limiting regime, a recently developed version of the approach based on the concept of the logarithmic norm of the operator function corresponding to the estimate of the norm of the Cauchy matrix as well as a modernized special transformation of the forward Kolmogorov system was applied. A numerical example is considered for which the estimation of the rate of convergence is shown in detail as well as the construction of some limiting characteristics of the model based on these estimates.
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[+] About this article
Title
ON THE RATE OF CONVERGENCE AND LIMITING CHARACTERISTICS FOR ONE QUASI-BIRTH-DEATH PROCESS
Journal
Informatics and Applications
2023, Volume 17, Issue 3, pp 49-57
Cover Date
2023-10-10
DOI
10.14357/19922264230307
Print ISSN
1992-2264
Publisher
Institute of Informatics Problems, Russian Academy of Sciences
Additional Links
Key words
quasi-birth-death processes; rate of convergence; ergodicity bounds; logarithmic norm; queuing systems
Authors
I. A. Usov  , Y. A. Satin , and A. I. Zeifman ,  ,  , 
Author Affiliations
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
Federal Research Center "Computer Science and Control" of the Russian Academy of Sciences, 44-2 Vavilov Str., Moscow 119333, Russian Federation
Vologda Research Center of the Russian Academy of Sciences, 56A Gorky Str., Vologda 160014, Russian Federation
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