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

Alexander Dudin, Sergei Dudin, Valentina Klimenok and Yuliya Gaidamaka
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Alexander Dudin: Department of Applied Mathematics and Computer Science, Belarusian State University, 4, Nezavisimosti Ave., 220030 Minsk, Belarus
Sergei Dudin: Department of Applied Mathematics and Computer Science, Belarusian State University, 4, Nezavisimosti Ave., 220030 Minsk, Belarus
Valentina Klimenok: Department of Applied Mathematics and Computer Science, Belarusian State University, 4, Nezavisimosti Ave., 220030 Minsk, Belarus
Yuliya Gaidamaka: Applied Mathematics and Communications Technology Institute, Peoples’ Friendship University of Russia (RUDN University), 6 Miklukho-Maklaya St, 117198 Moscow, Russia

Mathematics, 2021, vol. 9, issue 13, 1-15

Abstract: We consider a M A P / P H / 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.

Keywords: queueing model; random multiple access; time-limited service; polling system; stability (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2021
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