Systems and Means of Informatics
2021, Volume 31, Issue 1, pp 28-36
ON APPROXIMATION WITH TRUNCATIONS FOR THE NONSTATIONARY QUEUING MODEL
Abstract
The author deals with a nonstationary queuing model Mt/Mt/1 with one server. It is assumed here that the customers arrive with the intensity Ë^) but are served in pairs (that is, in this case, yu(t) is the service rate of a group of two customers). For the considered model, the limiting characteristics are constructed using the method of truncating the state space of the system. A numerical example with exact given values of intensities showing the application of the studied approach is constructed and corresponding graphic illustrations are provided. The author uses the general algorithm to build graphs, it is associated with solving the Cauchy problem for the forward Kolmogorov system on the corresponding interval which has already been used by the author in previous papers.
[+] References (4)
- Satin, Y., A. Zeifman, and A. Kryukova. 2019. On the rate of convergence and limiting characteristics for a nonstationary queueing model. Mathematics 7(8):678. 11 p.
- Zeifman, A. I., A. V. Korotysheva, V. Yu. Korolev, and Ya. A. Satin. 2016. Truncation bounds for approximations of inhomogeneous continuous-time Markov chains. Theor. Probab. Appl. 61 (3):513-520.
- Arns, M., P. Buchholz, and A. Panchenko. 2010. On the numerical analysis of inhomogeneous continuous-time Markov chains. Informs J. Comput. 22:416-432.
- Andreychenko, A., W. Sandmann, and V. Wolf. 2018. Approximate adaptive uni- formization of continuous-time Markov chains. Appl. Math. Model. 61:561-576.
[+] About this article
Title
ON APPROXIMATION WITH TRUNCATIONS FOR THE NONSTATIONARY QUEUING MODEL
Journal
Systems and Means of Informatics
Volume 31, Issue 1, pp 28-36
Cover Date
2021-04-20
DOI
10.14357/08696527210103
Print ISSN
0869-6527
Publisher
Institute of Informatics Problems, Russian Academy of Sciences
Additional Links
Key words
queuing systems; Mt/Mt/1 queue; nonstationary queuing model; approximation; limiting characteristics; rate of convergence; truncation of the state space
Authors
Ya. A. Satin 
Author Affiliations
Department of Applied Mathematics, Vologda State University, 15 Lenin Str., Vologda 160000, Russian Federation
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