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Article

Vacation Queueing Model for Performance Evaluation of Multiple Access Information Transmission Systems without Transmission Interruption

1
Department of Applied Mathematics and Computer Science, Belarusian State University, 4, Nezavisimosti Ave., 220030 Minsk, Belarus
2
Applied Mathematics and Communications Technology Institute, Peoples’ Friendship University of Russia (RUDN University), 6 Miklukho-Maklaya St, 117198 Moscow, Russia
*
Author to whom correspondence should be addressed.
Academic Editor: Manuel Alberto M. Ferreira
Mathematics 2021, 9(13), 1508; https://doi.org/10.3390/math9131508
Received: 10 June 2021 / Revised: 22 June 2021 / Accepted: 23 June 2021 / Published: 28 June 2021
(This article belongs to the Special Issue Applications of Mathematical Analysis in Telecommunications)
We consider a MAP/PH/1-type queueing system with server vacations as a model that is useful for the analysis of multiple access systems with polling discipline without transmission interruption. Vacation of the server corresponds to the service providing competitive information flows to the polling system. In this paper, we consider a vacation queueing model under pretty general assumptions about the probabilistic distributions describing the behavior of the system and the realistic assumption, in many real-world systems, that ongoing service cannot be terminated ahead of schedule. We derive the criterion of the stable operation of the system and the stationary distributions of the system states and the waiting time. An illustrative numerical example is presented. View Full-Text
Keywords: queueing model; random multiple access; time-limited service; polling system; stability queueing model; random multiple access; time-limited service; polling system; stability
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MDPI and ACS Style

Dudin, A.; Dudin, S.; Klimenok, V.; Gaidamaka, Y. Vacation Queueing Model for Performance Evaluation of Multiple Access Information Transmission Systems without Transmission Interruption. Mathematics 2021, 9, 1508. https://doi.org/10.3390/math9131508

AMA Style

Dudin A, Dudin S, Klimenok V, Gaidamaka Y. Vacation Queueing Model for Performance Evaluation of Multiple Access Information Transmission Systems without Transmission Interruption. Mathematics. 2021; 9(13):1508. https://doi.org/10.3390/math9131508

Chicago/Turabian Style

Dudin, Alexander, Sergei Dudin, Valentina Klimenok, and Yuliya Gaidamaka. 2021. "Vacation Queueing Model for Performance Evaluation of Multiple Access Information Transmission Systems without Transmission Interruption" Mathematics 9, no. 13: 1508. https://doi.org/10.3390/math9131508

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