Systems and Means of Informatics
2021, Volume 31, Issue 1, pp 17-27
ON THE BOUNDS OF THE RATE OF CONVERGENCE FOR Mt/Mt/1 MODEL WITH TWO DIFFERENT TYPES OF REQUESTS
Abstract
The author deals with a nonstationary queuing model Mt/Mt/1 with one server and two different types of requests. For this model, the author obtains a one-dimensional birth and death process that describes the number of requirements in the original system. By applying the standard method of the logarithmic norm of the operator of a linear function, corresponding estimates for the rate of convergence and ergodicity are obtained. 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 authors in previous papers.
[+] References (4)
- Zeifman, A., Y. Satin, K. Kiseleva, and V. Korolev. 2019. On the rate of convergence for a characteristic of multidimensional birth-death process. Mathematics 7(5):477. 10 p. doi: 10.3390/math7050477.
- Zeifman, A. I. 1995. On the estimation of probabilities for birth and death processes. J. Appl. Probab. 32(3):623-634.
- Granovsky, B., and A. Zeifman. 2004. Nonstationary queues: Estimation of the rate of convergence. Queueing Syst. 46:363-388.
- Adan, I., B. Hathaway, and V. G. Kulkarni. 2019. On first-come, first-served queues with two classes of impatient customers. Queueing Syst. 91:113-142. doi: 10.1007/ s11134-018-9592-z.
[+] About this article
Title
ON THE BOUNDS OF THE RATE OF CONVERGENCE FOR Mt/Mt/1 MODEL WITH TWO DIFFERENT TYPES OF REQUESTS
Journal
Systems and Means of Informatics
Volume 31, Issue 1, pp 17-27
Cover Date
2021-04-20
DOI
10.14357/08696527210102
Print ISSN
0869-6527
Publisher
Institute of Informatics Problems, Russian Academy of Sciences
Additional Links
Key words
queuing systems; nonstationary queuing model; one-dimensional birth-death process; rate of convergence; ergodicity bounds; logarithmic norm; Mt/Mt/1 queue
Authors
Ya. A. Satin 
Author Affiliations
Department of Applied Mathematics, Vologda State University, 15 Lenin Str., Vologda 160000, Russian Federation
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