Transient Analysis of a Two-Heterogeneous Severs Queue with Impatient Behaviour and Multiple Vacations

Xu Jia (), Liu Liwei () and Zhu Taozeng ()
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Xu Jia: School of Science, Nanjing University of Science and Technology, Nanjing, 210094, China
Liu Liwei: School of Science, Nanjing University of Science and Technology, Nanjing, 210094, China
Zhu Taozeng: School of Management, University of Science and Technology of China, Hefei, 230026, China

Journal of Systems Science and Information, 2018, vol. 6, issue 1, 69-84

Abstract: We consider an M/M/2 queueing system with two-heterogeneous servers and multiple vacations. Customers arrive according to a Poisson process. However, customers become impatient when the system is on vacation. We obtain explicit expressions for the time dependent probabilities, mean and variance of the system size at time t by employing probability generating functions, continued fractions and properties of the modified Bessel functions. Finally, two special cases are provided.

Keywords: M/M/2 queueing system; multiple vacations; probability generating functions; continued fractions; modified Bessel functions (search for similar items in EconPapers)
Date: 2018
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Persistent link: https://EconPapers.repec.org/RePEc:bpj:jossai:v:6:y:2018:i:1:p:69-84:n:5

DOI: 10.21078/JSSI-2018-069-16

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