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Modeling Load and Overwork Effects in Queueing Systems with Adaptive Service Rates

Author

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  • Mohammad Delasay

    (Tepper School of Business, Carnegie Mellon University, Pittsburgh, Pennsylvania 15213)

  • Armann Ingolfsson

    (Alberta School of Business, University of Alberta, Edmonton, Alberta T6G 2R6, Canada)

  • Bora Kolfal

    (Alberta School of Business, University of Alberta, Edmonton, Alberta T6G 2R6, Canada)

Abstract

Servers in many real queueing systems do not work at a constant speed. They adapt to the system state by speeding up when the system is highly loaded or slowing down when load has been high for an extended time period. Their speed can also be constrained by other factors, such as geography or a downstream blockage. We develop a state-dependent queueing model in which the service rate depends on the system “load” and “overwork.” Overwork refers to a situation where the system has been under a heavy load for an extended time period. We quantify load as the number of users in the system, and we operationalize overwork with a state variable that is incremented with each service completion in a high-load period and decremented at a rate that is proportional to the number of idle servers during low-load periods. Our model is a quasi-birth-and-death process with a special structure that we exploit to develop efficient and easy-to-implement algorithms to compute system performance measures. We use the analytical model and simulation to demonstrate how using models that ignore adaptive server behavior can result in inconsistencies between planned and realized performance and can lead to suboptimal, unstable, or oscillatory staffing decisions.

Suggested Citation

  • Mohammad Delasay & Armann Ingolfsson & Bora Kolfal, 2016. "Modeling Load and Overwork Effects in Queueing Systems with Adaptive Service Rates," Operations Research, INFORMS, vol. 64(4), pages 867-885, August.
    • Handle: RePEc:inm:oropre:v:64:y:2016:i:4:p:867-885
    DOI: 10.1287/opre.2016.1499
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    References listed on IDEAS

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    Cited by:

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    4. Yutaka Sakuma & Onno Boxma & Tuan Phung-Duc, 2021. "An M/PH/1 queue with workload-dependent processing speed and vacations," Queueing Systems: Theory and Applications, Springer, vol. 98(3), pages 373-405, August.
    5. Jingqi Wang & Yong-Pin Zhou, 2018. "Impact of Queue Configuration on Service Time: Evidence from a Supermarket," Management Science, INFORMS, vol. 64(7), pages 3055-3075, July.
    6. Xu, Shuling & Hall, Nicholas G., 2021. "Fatigue, personnel scheduling and operations: Review and research opportunities," European Journal of Operational Research, Elsevier, vol. 295(3), pages 807-822.
    7. Delasay, Mohammad & Ingolfsson, Armann & Kolfal, Bora & Schultz, Kenneth, 2019. "Load effect on service times," European Journal of Operational Research, Elsevier, vol. 279(3), pages 673-686.
    8. Matthias Thürer & Mark Stevenson & James Aitken & Cristovao Silva, 2020. "State-dependent service rates in make-to-order shops: an assessment by simulation," Operations Management Research, Springer, vol. 13(1), pages 70-84, June.
    9. David Azriel & Paul D. Feigin & Avishai Mandelbaum, 2019. "Erlang-S: A Data-Based Model of Servers in Queueing Networks," Management Science, INFORMS, vol. 65(10), pages 4607-4635, October.

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