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Discrete-time modified number- and time-limited vacation queues

Author

Listed:
  • Dieter Claeys

    (Ghent University
    Flanders Make)

  • Stijn De Vuyst

    (Ghent University)

Abstract

A vast amount of literature has appeared on vacation queues. In the well-known number- and time-limited vacation policies, the server goes on vacation if the number of customers, respectively, work (time slots) served since the previous vacation reaches a specified value, or if the system becomes empty, whichever occurs first. However, in practice, the server does not always go on vacation when the system is empty if the number of customers/work to be served has not yet reached the specified amount. Therefore, we study modified number- and time-limited vacation policies, where we account for this feature. We complement our recent work on these vacation policies by considering a discrete time, instead of a continuous-time, setting. We therefore adopt a different analysis approach, which enables us to obtain similar as well as new results as compared to our previous work. The results in this paper are valid for a memoryless distribution, but also for distributions with finite support, and a mixture of geometric distributions.

Suggested Citation

  • Dieter Claeys & Stijn De Vuyst, 2019. "Discrete-time modified number- and time-limited vacation queues," Queueing Systems: Theory and Applications, Springer, vol. 91(3), pages 297-318, April.
    • Handle: RePEc:spr:queues:v:91:y:2019:i:3:d:10.1007_s11134-018-9596-8
    DOI: 10.1007/s11134-018-9596-8
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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. Si, Xiao-Sheng & Wang, Wenbin & Hu, Chang-Hua & Zhou, Dong-Hua, 2011. "Remaining useful life estimation - A review on the statistical data driven approaches," European Journal of Operational Research, Elsevier, vol. 213(1), pages 1-14, August.
    3. Wang, Hongzhou, 2002. "A survey of maintenance policies of deteriorating systems," European Journal of Operational Research, Elsevier, vol. 139(3), pages 469-489, June.
    4. A. Krishnamoorthy & P. Pramod & S. Chakravarthy, 2014. "Queues with interruptions: a survey," TOP: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 22(1), pages 290-320, April.
    5. Onno Boxma & Dieter Claeys & Lennart Gulikers & Offer Kella, 2015. "A queueing system with vacations after N services," Naval Research Logistics (NRL), John Wiley & Sons, vol. 62(8), pages 646-658, December.
    6. Nam K. Kim & Kyung C. Chae & Mohan L. Chaudhry, 2004. "An Invariance Relation and a Unified Method to Derive Stationary Queue-Length Distributions," Operations Research, INFORMS, vol. 52(5), pages 756-764, October.
    7. Claeys, Dieter & Adan, Ivo & Boxma, Onno, 2016. "Stochastic bounds for order flow times in parts-to-picker warehouses with remotely located order-picking workstations," European Journal of Operational Research, Elsevier, vol. 254(3), pages 895-906.
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