IDEAS home Printed from https://ideas.repec.org/a/spr/queues/v91y2019i3d10.1007_s11134-018-9596-8.html
   My bibliography  Save this article

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
    as

    Download full text from publisher

    File URL: http://link.springer.com/10.1007/s11134-018-9596-8
    File Function: Abstract
    Download Restriction: Access to the full text of the articles in this series is restricted.
    File URL: https://libkey.io/10.1007/s11134-018-9596-8?utm_source=ideas
    LibKey link: if access is restricted and if your library uses this service, LibKey will redirect you to where you can use your library subscription to access this item
    ---><---

    As the access to this document is restricted, you may want to search for a different version of it.

    References listed on IDEAS

    as
    1. 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.
    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, March.
    3. 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.
    4. Wang, Hongzhou, 2002. "A survey of maintenance policies of deteriorating systems," European Journal of Operational Research, Elsevier, vol. 139(3), pages 469-489, June.
    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. 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.
    7. 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.
    Full references (including those not matched with items on IDEAS)

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Zhengxin Zhang & Xiaosheng Si & Changhua Hu & Xiangyu Kong, 2015. "Degradation modeling–based remaining useful life estimation: A review on approaches for systems with heterogeneity," Journal of Risk and Reliability, , vol. 229(4), pages 343-355, August.
    2. 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.
    3. Si, Xiao-Sheng & Chen, Mao-Yin & Wang, Wenbin & Hu, Chang-Hua & Zhou, Dong-Hua, 2013. "Specifying measurement errors for required lifetime estimation performance," European Journal of Operational Research, Elsevier, vol. 231(3), pages 631-644.
    4. Alaswad, Suzan & Xiang, Yisha, 2017. "A review on condition-based maintenance optimization models for stochastically deteriorating system," Reliability Engineering and System Safety, Elsevier, vol. 157(C), pages 54-63.
    5. Badía, F.G. & Berrade, M.D. & Cha, Ji Hwan & Lee, Hyunju, 2018. "Optimal replacement policy under a general failure and repair model: Minimal versus worse than old repair," Reliability Engineering and System Safety, Elsevier, vol. 180(C), pages 362-372.
    6. Guo, Chiming & Wang, Wenbin & Guo, Bo & Si, Xiaosheng, 2013. "A maintenance optimization model for mission-oriented systems based on Wiener degradation," Reliability Engineering and System Safety, Elsevier, vol. 111(C), pages 183-194.
    7. Compare, Michele & Antonello, Federico & Pinciroli, Luca & Zio, Enrico, 2022. "A general model for life-cycle cost analysis of Condition-Based Maintenance enabled by PHM capabilities," Reliability Engineering and System Safety, Elsevier, vol. 224(C).
    8. Berrade, M.D. & Scarf, P.A. & Cavalcante, C.A.V., 2018. "Conditional inspection and maintenance of a system with two interacting components," European Journal of Operational Research, Elsevier, vol. 268(2), pages 533-544.
    9. Lee, Juseong & Mitici, Mihaela, 2020. "An integrated assessment of safety and efficiency of aircraft maintenance strategies using agent-based modelling and stochastic Petri nets," Reliability Engineering and System Safety, Elsevier, vol. 202(C).
    10. Wang, Xiaolin & Balakrishnan, Narayanaswamy & Guo, Bo, 2014. "Residual life estimation based on a generalized Wiener degradation process," Reliability Engineering and System Safety, Elsevier, vol. 124(C), pages 13-23.
    11. Barlow, E. & Bedford, T. & Revie, M. & Tan, J. & Walls, L., 2021. "A performance-centred approach to optimising maintenance of complex systems," European Journal of Operational Research, Elsevier, vol. 292(2), pages 579-595.
    12. Fauriat, William & Zio, Enrico, 2020. "Optimization of an aperiodic sequential inspection and condition-based maintenance policy driven by value of information," Reliability Engineering and System Safety, Elsevier, vol. 204(C).
    13. B. Krishna Kumar & R. Rukmani & A. Thanikachalam & V. Kanakasabapathi, 2018. "Performance analysis of retrial queue with server subject to two types of breakdowns and repairs," Operational Research, Springer, vol. 18(2), pages 521-559, July.
    14. Michele Compare & Luca Bellani & Enrico Zio, 2017. "Availability Model of a PHM-Equipped Component," Post-Print hal-01652232, HAL.
    15. Zhang, Zhengxin & Si, Xiaosheng & Hu, Changhua & Lei, Yaguo, 2018. "Degradation data analysis and remaining useful life estimation: A review on Wiener-process-based methods," European Journal of Operational Research, Elsevier, vol. 271(3), pages 775-796.
    16. Ece Zeliha Demirci & Joachim Arts & Geert-Jan Van Houtum, 2022. "A restless bandit approach for capacitated condition based maintenance scheduling," DEM Discussion Paper Series 22-01, Department of Economics at the University of Luxembourg.
    17. Lee, Juseong & Mitici, Mihaela, 2022. "Multi-objective design of aircraft maintenance using Gaussian process learning and adaptive sampling," Reliability Engineering and System Safety, Elsevier, vol. 218(PA).
    18. Tang, Diyin & Makis, Viliam & Jafari, Leila & Yu, Jinsong, 2015. "Optimal maintenance policy and residual life estimation for a slowly degrading system subject to condition monitoring," Reliability Engineering and System Safety, Elsevier, vol. 134(C), pages 198-207.
    19. Alexander Dudin & Olga Dudina & Sergei Dudin & Konstantin Samouylov, 2021. "Analysis of Multi-Server Queue with Self-Sustained Servers," Mathematics, MDPI, vol. 9(17), pages 1-18, September.
    20. Huynh, K.T. & Grall, A. & Bérenguer, C., 2017. "Assessment of diagnostic and prognostic condition indices for efficient and robust maintenance decision-making of systems subject to stress corrosion cracking," Reliability Engineering and System Safety, Elsevier, vol. 159(C), pages 237-254.

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:spr:queues:v:91:y:2019:i:3:d:10.1007_s11134-018-9596-8. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Sonal Shukla or Springer Nature Abstracting and Indexing (email available below). General contact details of provider: http://www.springer.com .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.