Analysis of a Single-Sever Queue with Disasters and Repairs Under Bernoulli Vacation Schedule

Ye Jingjing (), Liu Liwei () and Jiang Tao ()
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Ye Jingjing: 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, 2016, vol. 4, issue 6, 547-559

Abstract: This paper studies a single-sever queue with disasters and repairs, in which after each service completion the server may take a vacation with probability q(0 ≤q≤ 1), or begin to serve the next customer, if any, with probability p(= 1 − q). The disaster only affects the system when the server is in operation, and once it occurs, all customers present are eliminated from the system. We obtain the stationary probability generating functions (PGFs) of the number of customers in the system by solving the balance equations of the system. Some performance measures such as the mean system length, the probability that the server is in different states, the rate at which disasters occur and the rate of initiations of busy period are determined. We also derive the sojourn time distribution and the mean sojourn time. In addition, some numerical examples are presented to show the effect of the parameters on the mean system length.

Keywords: Bernoulli vacation schedule; disasters; strong Markov property; sojourn time (search for similar items in EconPapers)
Date: 2016
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Persistent link: https://EconPapers.repec.org/RePEc:bpj:jossai:v:4:y:2016:i:6:p:547-559:n:5

DOI: 10.21078/JSSI-2016-547-13

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