Informatics and Applications
2021, Volume 15, Issue 2, pp 20-25
ON ONE NONSTATIONARY SERVICE MODEL WITH CATASTROPHES AND HEAVY TAILS
- A. I. Zeifman
- Ya. A. Satin
- I. A. Kovalev
Abstract
The paper considers the nonstationary queuing system with catastrophes, one server, and special group arrivals of requests. The intensities of increasing groups of requests can decrease rather slowly. The process X(t), which describes the number of requirements in such system, is considered, the existence of a limiting regime of the probability distribution of states and a limiting average for X(t) is proved, and estimates of the rate of convergence to the limiting regime and the limiting average are obtained. Approximation estimates are obtained using truncations by finite processes. As an example, the authors consider a simple model of a nonstationary system with a rather slow rate of decrease in the arrival rates of customer groups when the group size grows.
[+] References (5)
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[+] About this article
Title
ON ONE NONSTATIONARY SERVICE MODEL WITH CATASTROPHES AND HEAVY TAILS
Journal
Informatics and Applications
2021, Volume 15, Issue 2, pp 20-25
Cover Date
2021-06-30
DOI
10.14357/19922264210203
Print ISSN
1992-2264
Publisher
Institute of Informatics Problems, Russian Academy of Sciences
Additional Links
Key words
nonstationary queuing system; countable Markov chains; limiting characteristics; rate of convergence; approximation
Authors
A. I. Zeifman  ,  ,  and Ya. A. Satin , and I. A. Kovalev
Author Affiliations
Department of Applied Mathematics, 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, 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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