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Analysis of an M/M/c Queueing System with Impatient Customers and Synchronous Vacations

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  • Dequan Yue
  • Wuyi Yue
  • Guoxi Zhao

Abstract

We consider an M/M/c queueing system with impatient customers and a synchronous vacation policy, where customer impatience is due to the servers’ vacation. Whenever a system becomes empty, all the servers take a vacation. If the system is still empty, when the vacation ends, all the servers take another vacation; otherwise, they return to serve the queue. We develop the balance equations for the steady‐state probabilities and solve the equations by using the probability generating function method. We obtain explicit expressions of some important performance measures by means of the two indexes. Based on these, we obtain some results about limiting behavior for some performance measures. We derive closed‐form expressions of some important performance measures for two special cases. Finally, some numerical results are also presented.

Suggested Citation

  • Dequan Yue & Wuyi Yue & Guoxi Zhao, 2014. "Analysis of an M/M/c Queueing System with Impatient Customers and Synchronous Vacations," Journal of Applied Mathematics, John Wiley & Sons, vol. 2014(1).
    • Handle: RePEc:wly:jnljam:v:2014:y:2014:i:1:n:893094
    DOI: 10.1155/2014/893094
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    References listed on IDEAS

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    1. Saif Benjaafar & Mohsen ElHafsi & Tingliang Huang, 2010. "Optimal control of a production‐inventory system with both backorders and lost sales," Naval Research Logistics (NRL), John Wiley & Sons, vol. 57(3), pages 252-265, April.
    2. Naishuo Tian & Zhe George Zhang, 2006. "Vacation Queueing Models Theory and Applications," International Series in Operations Research and Management Science, Springer, number 978-0-387-33723-4, June.
    3. Chao, Xiuli & Zhao, Yiqiang Q., 1998. "Analysis of multi-server queues with station and server vacations," European Journal of Operational Research, Elsevier, vol. 110(2), pages 392-406, October.
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