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Article information
2017 , Volume 22, ¹ 1, p.55-66
Nazarov A.A., Sonkin M.A.
The single-server queueing model with vacations and exhaustive service
Single-line queueing systems with server vacations are common mathematical models of telecommunication systems. In real systems “vacations” are considered as a temporal suspension of service to perform any other operation of the device, or its breakdown or repair. Queueing system with server vacations is one of the known methods for research of cyclic or polling systems. Let us review the queueing system with one service device and a queue with unlimited number of waiting seats. The system receives Poisson process of customers with intensity 𝜆. Device operation mode consists of two consecutive intervals. During first interval customers are handled at the device, distributed by function 𝐵(𝑥). The device serves the customers who have collected in queue until it does not turn out empty. When this interval ends, the server goes on a vacation. During vacations, all requests coming into the system are gathered in the queue and are waiting for device to return to the operating mode. Duration of this interval is random and determined by distribution function 𝑇 (𝑥). We have found generating function distribution of probabilities for a number of customers in the queue and the characteristic function of waiting time in the single-line queueing systems with server vacations and exhaustive service.
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Keywords: queueing system with server vacations, exhaustive service, polling, waiting time
Author(s):
Nazarov Anatoly Andreevich
Dr. , Professor
Position: Head of Chair
Office: National Research Tomsk State University
Address: 634050, Russia, Tomsk, 36, Lenina Avenue
Phone Office: (3822) 42 60 99
E-mail: nazarov.tsu@gmail.com
SPIN-code: 1341-6014Sonkin Mikhail Arkadievich
Position: Director
Address: Russia, Tomsk, Tomsk, 36, Lenina Avenue
Phone Office: (3822) 51 75 30
E-mail: sonkin@cc.tpu.edu.ru
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Bibliography link:
Nazarov A.A., Sonkin M.A. The single-server queueing model with vacations and exhaustive service // Computational technologies. 2017. V. 22. ¹ 1. P. 55-66
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