Systems and Means of Informatics
2022, Volume 32, Issue 4, pp 21-31
CONVERGENCE RATE AND STABILITY ESTIMATES FOR A CLASS OF NONSTATIONARY MARKOV MODELS OF QUEUES WITH IMPATIENT CUSTOMERS
- I. A. Kovalev
- Y. A. Satin
- A. I. Zeifman
Abstract
A nonstationary queuing system with S servers and impatient customers is considered, i. e., the arrival intensities decrease with the growth of the queue. The process X (t) describing the number of customers in such a system is considered, the existence of a limiting mode of the probability distribution of states and a limiting mean for X (t) is proved, and the estimates of the rate of convergence to the limiting mode and the limiting mean are obtained. Also, the
perturbation estimates are obtained. The authors apply an approach based on the concept of the logarithmic norm of the operator function. As an example, a simple model of a nonstationary system is considered in which potential customers are discouraged by queue length.
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[+] About this article
Title
CONVERGENCE RATE AND STABILITY ESTIMATES FOR A CLASS OF NONSTATIONARY MARKOV MODELS OF QUEUES WITH IMPATIENT CUSTOMERS
Journal
Systems and Means of Informatics
Volume 32, Issue 4, pp 21-31
Cover Date
2022-30-11
DOI
10.14357/08696527220403
Print ISSN
0869-6527
Publisher
Institute of Informatics Problems, Russian Academy of Sciences
Additional Links
Key words
rate of convergence; ergodicity bounds; logarithmic norm; perturbation; queuing systems
Authors
I. A. Kovalev  ,  , Y. A. Satin , 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
Federal Research Center "Computer Science and Control", 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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