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A Lévy-Driven Stochastic Queueing System with Server Breakdowns and Vacations

Author

Listed:
  • Yi Peng

    (School of Mathematical Science, Changsha Normal University, Changsha 410100, China)

  • Jinbiao Wu

    (School of Mathematics and Statistics, Central South University, Changsha 410083, China)

Abstract

Motivated by modelling the data transmission in computer communication networks, we study a Lévy-driven stochastic fluid queueing system where the server may subject to breakdowns and repairs. In addition, the server will leave for a vacation each time when the system is empty. We cast the workload process as a Lévy process modified to have random jumps at two classes of stopping times. By using the properties of Lévy processes and Kella–Whitt martingale method, we derive the limiting distribution of the workload process. Moreover, we investigate the busy period and the correlation structure. Finally, we prove that the stochastic decomposition properties also hold for fluid queues with Lévy input.

Suggested Citation

  • Yi Peng & Jinbiao Wu, 2020. "A Lévy-Driven Stochastic Queueing System with Server Breakdowns and Vacations," Mathematics, MDPI, vol. 8(8), pages 1-12, July.
    • Handle: RePEc:gam:jmathe:v:8:y:2020:i:8:p:1239-:d:391568
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    References listed on IDEAS

    as
    1. Jau-Chuan Ke, 2003. "Optimal strategy policy in batch arrival queue with server breakdowns and multiple vacations," Mathematical Methods of Operations Research, Springer;Gesellschaft für Operations Research (GOR);Nederlands Genootschap voor Besliskunde (NGB), vol. 58(1), pages 41-56, September.
    2. S. W. Fuhrmann & Robert B. Cooper, 1985. "Stochastic Decompositions in the M / G /1 Queue with Generalized Vacations," Operations Research, INFORMS, vol. 33(5), pages 1117-1129, October.
    3. 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, September.
    4. 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.
    Full references (including those not matched with items on IDEAS)

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