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

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Listed:
  • Xu Jia
  • 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)

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.

Suggested Citation

  • Xu Jia & Liu Liwei & Zhu Taozeng, 2018. "Transient Analysis of a Two-Heterogeneous Severs Queue with Impatient Behaviour and Multiple Vacations," Journal of Systems Science and Information, De Gruyter, vol. 6(1), pages 69-84, February.
    • Handle: 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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    References listed on IDEAS

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    4. Ward Whitt, 1983. "Untold Horrors of the Waiting Room: What the Equilibrium Distribution Will Never Tell About the Queue-Length Process," Management Science, INFORMS, vol. 29(4), pages 395-408, April.
    5. Naishuo Tian & Zhe George Zhang, 2006. "Applications of Vacation Models," International Series in Operations Research & Management Science, in: Vacation Queueing Models Theory and Applications, chapter 0, pages 343-358, Springer.
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