Analysis of an M/G/1 Stochastic Clearing Queue in a 3-Phase Environment

Zhang Xiaoyan (), Liu Liwei () and Jiang Tao ()
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Zhang Xiaoyan: School of Science, Nanjing University of Science and Technology, Nanjing210094, China
Liu Liwei: School of Science, Nanjing University of Science and Technology, Nanjing210094, China
Jiang Tao: School of Science, Nanjing University of Science and Technology, Nanjing210094, China

Journal of Systems Science and Information, 2015, vol. 3, issue 4, 374-384

Abstract: This paper studies a single server M/G/1 stochastic clearing queue operating in a 3-phase environment, where the time length of the first and third phase are assumed to follow exponential distributions, and the time length of the second phase is a constant value. At the completion of phase 1, the system moves to phase 2, and after a fixed time length, the system turns to phase 3. At the end of phase 3, all present customers in the system are forced to leave the system, then the system moves to phase 1 and restarts a new service cycle. Using the supplementary variable technique, we obtain the distribution for the stationary queue at an arbitrary epoch. We also derive the sojourn time distribution and the length of the server’s working time in a cycle.

Keywords: M/G/1 queue; fixed time length; supplementary variable technique; sojourn time distribution (search for similar items in EconPapers)
Date: 2015
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Persistent link: https://EconPapers.repec.org/RePEc:bpj:jossai:v:3:y:2015:i:4:p:374-384:n:8

DOI: 10.1515/JSSI-2015-0374

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