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Optimal Maintenance Policies for Single-Server Queueing Systems Subject to Breakdowns

Author

Listed:
  • Awi Federgruen

    (Columbia University, New York, New York)

  • Kut C. So

    (University of California, Irvine, California)

Abstract

We consider a single-server queueing system with Poisson arrivals and general service times. While the server is up, it is subject to breakdowns according to a Poisson process. When the server breaks down, we need to repair the server immediately by initiating one of two available repair operations. The operating costs of the system include customer holding costs, repair costs and running costs. The objective is to find a corrective maintenance policy that minimizes the long-run average operating costs of the system. The problem is formulated as a semi-Markov decision process. Under some mild conditions on the repair time and service time distributions and the customer holding cost rate function, we prove that there exists an optimal stationary policy which is monotone, i.e., which is characterized by a single threshold parameter: The stochastically faster repair is initiated if and only if the number of customers in the system exceeds this threshold. We also present an efficient algorithm for the determination of an optimal monotone policy and its average cost. We then extend the problem to allow the system to postpone the repair until some future point in time. We provide a partial characterization of an optimal policy and show that monotone policies are, in general, not optimal. The latter problem also extends the authors' previous work.

Suggested Citation

  • Awi Federgruen & Kut C. So, 1990. "Optimal Maintenance Policies for Single-Server Queueing Systems Subject to Breakdowns," Operations Research, INFORMS, vol. 38(2), pages 330-343, April.
    • Handle: RePEc:inm:oropre:v:38:y:1990:i:2:p:330-343
    DOI: 10.1287/opre.38.2.330
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    Citations

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    Cited by:

    1. Liu, Gia-Shie, 2011. "Dynamic group instantaneous replacement policies for unreliable Markovian service systems," International Journal of Production Economics, Elsevier, vol. 130(2), pages 203-217, April.
    2. 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.
    3. Gao, Shan & Wang, Jinting, 2021. "Reliability and availability analysis of a retrial system with mixed standbys and an unreliable repair facility," Reliability Engineering and System Safety, Elsevier, vol. 205(C).
    4. Subba Rao, S. & Gunasekaran, A. & Goyal, S. K. & Martikainen, T., 1998. "Waiting line model applications in manufacturing," International Journal of Production Economics, Elsevier, vol. 54(1), pages 1-28, January.
    5. Xinshang Wang & Van-Anh Truong, 2018. "Multi-Priority Online Scheduling with Cancellations," Operations Research, INFORMS, vol. 66(1), pages 104-122, January.
    6. 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.
    7. Karamatsoukis, C.C. & Kyriakidis, E.G., 2009. "Optimal maintenance of a production-inventory system with idle periods," European Journal of Operational Research, Elsevier, vol. 196(2), pages 744-751, July.
    8. Wang, Kuo-Hsiung & Wu, Chia-Huang & Yen, Tseng-Chang, 2022. "Comparative cost-benefit analysis of four retrial systems with preventive maintenance and unreliable service station," Reliability Engineering and System Safety, Elsevier, vol. 221(C).
    9. Samira Taleb & Amar Aissani, 2016. "Preventive maintenance in an unreliable M/G/1 retrial queue with persistent and impatient customers," Annals of Operations Research, Springer, vol. 247(1), pages 291-317, December.
    10. Zhou, Wenhui & Zheng, Zhibin & Xie, Wei, 2017. "A control-chart-based queueing approach for service facility maintenance with energy-delay tradeoff," European Journal of Operational Research, Elsevier, vol. 261(2), pages 613-625.

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