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Stabilizing performance in a service system with time-varying arrivals and customer feedback

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  • Liu, Yunan
  • Whitt, Ward

Abstract

Analytical offered-load and modified-offered-load (MOL) approximations are developed to determine staffing levels that stabilize performance at designated targets in a non-Markovian many-server queueing model with time-varying arrival rates, customer abandonment from queue and random feedback with additional feedback delay in an infinite-server or finite-server queue. To provide a flexible model that can be readily fit to system data, the model has Bernoulli routing, where the feedback probabilities, service-time, patience-time and feedback-delay distributions all are general and may depend on the visit number. Simulation experiments confirm that the new MOL approximations are effective. A many-server heavy-traffic FWLLN shows that the performance targets are achieved asymptotically as the scale increases.

Suggested Citation

  • Liu, Yunan & Whitt, Ward, 2017. "Stabilizing performance in a service system with time-varying arrivals and customer feedback," European Journal of Operational Research, Elsevier, vol. 256(2), pages 473-486.
    • Handle: RePEc:eee:ejores:v:256:y:2017:i:2:p:473-486
    DOI: 10.1016/j.ejor.2016.07.018
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    References listed on IDEAS

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    1. Ward Whitt, 1982. "Approximating a Point Process by a Renewal Process, I: Two Basic Methods," Operations Research, INFORMS, vol. 30(1), pages 125-147, February.
    2. Ward Whitt, 2005. "Engineering Solution of a Basic Call-Center Model," Management Science, INFORMS, vol. 51(2), pages 221-235, February.
    3. Yunan Liu & Ward Whitt, 2012. "Stabilizing Customer Abandonment in Many-Server Queues with Time-Varying Arrivals," Operations Research, INFORMS, vol. 60(6), pages 1551-1564, December.
    4. Galit B. Yom-Tov & Avishai Mandelbaum, 2014. "Erlang-R: A Time-Varying Queue with Reentrant Customers, in Support of Healthcare Staffing," Manufacturing & Service Operations Management, INFORMS, vol. 16(2), pages 283-299, May.
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    8. Zohar Feldman & Avishai Mandelbaum & William A. Massey & Ward Whitt, 2008. "Staffing of Time-Varying Queues to Achieve Time-Stable Performance," Management Science, INFORMS, vol. 54(2), pages 324-338, February.
    9. Ward Whitt, 2013. "OM Forum —Offered Load Analysis for Staffing," Manufacturing & Service Operations Management, INFORMS, vol. 15(2), pages 166-169, May.
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    Cited by:

    1. Yongjiang Guo & Yunan Liu & Renhu Pei, 2018. "Functional law of the iterated logarithm for multi-server queues with batch arrivals and customer feedback," Annals of Operations Research, Springer, vol. 264(1), pages 157-191, May.
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    3. Yongkyu Cho & Young Myoung Ko, 2020. "Stabilizing the virtual response time in single-server processor sharing queues with slowly time-varying arrival rates," Annals of Operations Research, Springer, vol. 293(1), pages 27-55, October.
    4. Xu Sun & Yunan Liu, 2021. "Staffing many‐server queues with autoregressive inputs," Naval Research Logistics (NRL), John Wiley & Sons, vol. 68(3), pages 312-326, April.
    5. Eugene Furman & Adam Diamant & Murat Kristal, 2021. "Customer Acquisition and Retention: A Fluid Approach for Staffing," Production and Operations Management, Production and Operations Management Society, vol. 30(11), pages 4236-4257, November.
    6. Niyirora, Jerome & Zhuang, Jun, 2017. "Fluid approximations and control of queues in emergency departments," European Journal of Operational Research, Elsevier, vol. 261(3), pages 1110-1124.
    7. Ekin, Tahir & Aktekin, Tevfik, 2021. "Decision making under uncertain and dependent system rates in service systems," European Journal of Operational Research, Elsevier, vol. 291(1), pages 335-348.
    8. Ran Liu & Michael E. Kuhl & Yunan Liu & James R. Wilson, 2019. "Modeling and Simulation of Nonstationary Non-Poisson Arrival Processes," INFORMS Journal on Computing, INFORMS, vol. 31(2), pages 347-366, April.
    9. Alexander Zeifman & Yacov Satin & Ivan Kovalev & Rostislav Razumchik & Victor Korolev, 2020. "Facilitating Numerical Solutions of Inhomogeneous Continuous Time Markov Chains Using Ergodicity Bounds Obtained with Logarithmic Norm Method," Mathematics, MDPI, vol. 9(1), pages 1-20, December.
    10. Ward Whitt & Jingtong Zhao, 2017. "Many‐server loss models with non‐poisson time‐varying arrivals," Naval Research Logistics (NRL), John Wiley & Sons, vol. 64(3), pages 177-202, April.
    11. Jinting Wang & Zhongbin Wang & Yunan Liu, 2020. "Reducing Delay in Retrial Queues by Simultaneously Differentiating Service and Retrial Rates," Operations Research, INFORMS, vol. 68(6), pages 1648-1667, November.
    12. William A. Massey & Jamol Pender, 2018. "Dynamic rate Erlang-A queues," Queueing Systems: Theory and Applications, Springer, vol. 89(1), pages 127-164, June.

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