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A Model for a Vacation Queuing Policy Considering Server’s Deterioration and Recovery

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  • Gabi Hanukov

    (Department of Industrial Engineering and Management, Ariel University, Kiriat Hamada, 3, Ariel 40700, Israel)

  • Shraga Shoval

    (Department of Industrial Engineering and Management, Ariel University, Kiriat Hamada, 3, Ariel 40700, Israel)

Abstract

In this paper, we present a vacation queue model in which the service rate of the server deteriorates during the service period (e.g., due to the fatigue of a human server or the wear and ageing of machinery) and recovers during the vacation period (e.g., following a recuperation period for a human sever or the servicing of a machine). During the recuperation period, the main server is replaced with a temporary server with inferior capabilities. Using the multi-dimensional Markov process, we analyze the effects of different vacation policies on the target function and focus on the scheduling of the vacation period as a function of the deterioration and recovery rates. It is shown that the use of vacations to allow the server to rest and regain efficiency has a strong and valuable effect on the mean customer waiting time, to the extent that switching servers may be beneficial for the system, even when implemented at a point in time when the main server’s service rate is still much higher than that of the temporary server.

Suggested Citation

  • Gabi Hanukov & Shraga Shoval, 2023. "A Model for a Vacation Queuing Policy Considering Server’s Deterioration and Recovery," Mathematics, MDPI, vol. 11(12), pages 1-21, June.
    • Handle: RePEc:gam:jmathe:v:11:y:2023:i:12:p:2640-:d:1167870
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    References listed on IDEAS

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    1. He, Gang & Wu, Wenqing & Zhang, Yuanyuan, 2018. "Analysis of a multi-component system with failure dependency, N-policy and vacations," Operations Research Perspectives, Elsevier, vol. 5(C), pages 191-198.
    2. Fitouhi, Mohamed-Chahir & Nourelfath, Mustapha, 2012. "Integrating noncyclical preventive maintenance scheduling and production planning for a single machine," International Journal of Production Economics, Elsevier, vol. 136(2), pages 344-351.
    3. Chakravarthy, Srinivas R. & Shruti, & Kulshrestha, Rakhee, 2020. "A queueing model with server breakdowns, repairs, vacations, and backup server," Operations Research Perspectives, Elsevier, vol. 7(C).
    4. Bouslah, Bassem & Gharbi, Ali & Pellerin, Robert, 2018. "Joint production, quality and maintenance control of a two-machine line subject to operation-dependent and quality-dependent failures," International Journal of Production Economics, Elsevier, vol. 195(C), pages 210-226.
    5. Kut C. So, 1992. "Optimality of control limit policies in replacement models," Naval Research Logistics (NRL), John Wiley & Sons, vol. 39(5), pages 685-697, August.
    6. Hanukov, Gabi, 2022. "Improving efficiency of service systems by performing a part of the service without the customer's presence," European Journal of Operational Research, Elsevier, vol. 302(2), pages 606-620.
    7. David L. Kaufman & Mark E. Lewis, 2007. "Machine maintenance with workload considerations," Naval Research Logistics (NRL), John Wiley & Sons, vol. 54(7), pages 750-766, October.
    8. Gabi Hanukov & Shoshana Anily & Uri Yechiali, 2020. "Ticket queues with regular and strategic customers," Queueing Systems: Theory and Applications, Springer, vol. 95(1), pages 145-171, June.
    9. 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.
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    Cited by:

    1. S. P. Niranjan & S. Devi Latha & Miroslav Mahdal & Krishnasamy Karthik, 2023. "Multiple Control Policy in Unreliable Two-Phase Bulk Queueing System with Active Bernoulli Feedback and Vacation," Mathematics, MDPI, vol. 12(1), pages 1-21, December.

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