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Discrete-Time Gix/Geo/1/N Queue With Working Vacations And Vacation Interruption

Author

Listed:
  • SHAN GAO

    (School of Mathematics, Central South University, Changsha 410075, P. R. China;
    Department of Mathematics, Fuyang Normal College, Fuyang 236037, P. R. China)

  • ZAIMING LIU

    (School of Mathematics, Central South University, Changsha 410075, P. R. China)

  • QIWEN DU

    (Information and Electrical Engineering, Shandong University of Science and Technology, Qingdao 266400, P. R. China)

Abstract

In this paper, we study a discrete-time finite buffer batch arrival queue with multiple geometric working vacations and vacation interruption: the server serves the customers at the lower rate rather than completely stopping during the vacation period and can come back to the normal working level once there are customers after a service completion during the vacation period, i.e., a vacation interruption happens. The service times during a service period, service times during a vacation period and vacation times are geometrically distributed. The queue is analyzed using the supplementary variable and the imbedded Markov-chain techniques. We obtain steady-state system length distributions at pre-arrival, arbitrary and outside observer's observation epochs. We also present probability generation function (p.g.f.) of actual waiting-time distribution in the system and some performance measures.

Suggested Citation

  • Shan Gao & Zaiming Liu & Qiwen Du, 2014. "Discrete-Time Gix/Geo/1/N Queue With Working Vacations And Vacation Interruption," Asia-Pacific Journal of Operational Research (APJOR), World Scientific Publishing Co. Pte. Ltd., vol. 31(01), pages 1-22.
    • Handle: RePEc:wsi:apjorx:v:31:y:2014:i:01:n:s0217595914500031
    DOI: 10.1142/S0217595914500031
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    References listed on IDEAS

    as
    1. 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, December.
    2. 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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    Cited by:

    1. 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.
    2. 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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