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Queueing systems with vacation: an overview

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  • Shweta Upadhyaya

Abstract

Vacation models deal with a very important class of real life congestion situations encountered in day-to-day as well as in industrial scenario. A vacation in queueing context is the period when the server is not attending to a particularly targeted queue. The server may be under repair, attending to other queues, or simply forced to stop serving. Queueing systems with vacations have wide applications in the performance evaluation and dimensioning of computer networks, telecommunications, manufacturing systems, etc. The present survey article is devoted to the overview, methodology, some key aspects and ramifications concerning queueing systems with vacation. The related literature is classified based on modelling and methodological concepts. We present the review of the related work starting from the advent of vacation queueing systems up to the recent contributions. We illustrate how the seemingly diverse mix of problems is closely related in structure and can be understood in a common framework. Moreover, some general decomposition results and various techniques used to obtain performance indices for various vacation models in different frameworks are presented.

Suggested Citation

  • Shweta Upadhyaya, 2016. "Queueing systems with vacation: an overview," International Journal of Mathematics in Operational Research, Inderscience Enterprises Ltd, vol. 9(2), pages 167-213.
    • Handle: RePEc:ids:ijmore:v:9:y:2016:i:2:p:167-213
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    Citations

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    Cited by:

    1. Lotfi Tadj, 2017. "An Unreliable Quorum Queueing System with Single and Multiple Vacations," Asia-Pacific Journal of Operational Research (APJOR), World Scientific Publishing Co. Pte. Ltd., vol. 34(06), pages 1-16, December.
    2. Shweta Upadhyaya & Richa Sharma & Divya Agarwal & Geetika Malik, 2023. "Convexity analysis and cost optimization of a retrial queue with Bernoulli vacation and delayed phase mending," International Journal of System Assurance Engineering and Management, Springer;The Society for Reliability, Engineering Quality and Operations Management (SREQOM),India, and Division of Operation and Maintenance, Lulea University of Technology, Sweden, vol. 14(5), pages 1671-1690, October.
    3. Manickam Vadivukarasi & Kaliappan Kalidass, 2021. "Discussion on the transient behavior of single server Markovian multiple variant vacation queues," Operations Research and Decisions, Wroclaw University of Science Technology, Faculty of Management, vol. 31, pages 123-146.
    4. Abdoun Sylia & Taleb Samira, 2024. "Strategic Joining in an Unobservable Markovian Queue with Differentiated Vacations," SN Operations Research Forum, Springer, vol. 5(3), pages 1-27, September.
    5. Yang, Dong-Yuh & Tsao, Chih-Lung, 2019. "Reliability and availability analysis of standby systems with working vacations and retrial of failed components," Reliability Engineering and System Safety, Elsevier, vol. 182(C), pages 46-55.
    6. M. Vadivukarasi & K. Kalidass, 2022. "Discussion on the transient solution of single server Markovian multiple variant vacation queues with disasters," OPSEARCH, Springer;Operational Research Society of India, vol. 59(4), pages 1352-1376, December.
    7. Manickam Vadivukarasi & Kaliappan Kalidass, 2021. "Discussion on the transient behavior of single server Markovian multiple variant vacation queues," Operations Research and Decisions, Wroclaw University of Science and Technology, Faculty of Management, vol. 31(1), pages 123-146.
    8. 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.

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