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An M/G/1 Retrial Queue With General Retrial Times, Working Vacations And Vacation Interruption

Author

Listed:
  • SHAN GAO

    (Department of Mathematics, Beijing Jiaotong University, Beijing 100044, P. R. China;
    Department of Mathematics, Fuyang Normal College, Fuyang 236037, P. R.China)

  • JINTING WANG

    (Department of Mathematics, Beijing Jiaotong University, Beijing 100044, P. R. China)

  • WEI WAYNE LI

    (Department of Computer Science, Texas Southern University, Houston, TX 77004, USA)

Abstract

We consider an M/G/1 retrial queue with general retrial times, and introduce working vacations and vacation interruption policy into the retrial queue. During the working vacation period, customers can be served at a lower rate. If there are customers in the system at a service completion instant, the vacation will be interrupted and the server will come back to the normal working level. Using supplementary variable method, we obtain the stationary probability distribution and some performance measures. Furthermore, we carry out the waiting time distribution and prove the conditional stochastic decomposition for the queue length in orbit. Finally, some numerical examples are presented.

Suggested Citation

  • Shan Gao & Jinting Wang & Wei Wayne Li, 2014. "An M/G/1 Retrial Queue With General Retrial Times, Working Vacations And Vacation Interruption," Asia-Pacific Journal of Operational Research (APJOR), World Scientific Publishing Co. Pte. Ltd., vol. 31(02), pages 1-25.
    • Handle: RePEc:wsi:apjorx:v:31:y:2014:i:02:n:s0217595914400065
    DOI: 10.1142/S0217595914400065
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    Citations

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    Cited by:

    1. Madhu Jain & Sandeep Kaur & Parminder Singh, 2021. "Supplementary variable technique (SVT) for non-Markovian single server queue with service interruption (QSI)," Operational Research, Springer, vol. 21(4), pages 2203-2246, December.
    2. Liu, Baoliang & Cui, Lirong & Wen, Yanqing & Shen, Jingyuan, 2015. "A cold standby repairable system with working vacations and vacation interruption following Markovian arrival process," Reliability Engineering and System Safety, Elsevier, vol. 142(C), pages 1-8.
    3. Lee, Doo Ho & Kim, Bo Keun, 2015. "A note on the sojourn time distribution of an M/G/1 queue with a single working vacation and vacation interruption," Operations Research Perspectives, Elsevier, vol. 2(C), pages 57-61.

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