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Managing Queueing Systems Where Capacity is Random and Customers are Impatient

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  • Rouba Ibrahim

Abstract

One prevalent assumption in queueing theory is that the number of servers in a queueing model is deterministic. However, randomness in the number of available servers often arises in practice, e.g., in virtual call centers where agents are allowed to set their own schedules. In this paper, we study the problems of staffing and controlling queueing systems with an uncertain number of servers and impatient customers. Because randomness in the number of servers creates congestion in the system, the customer abandonment distribution plays an important role. We characterize how it affects both the optimal staffing policy and the cost incurred by the manager. Because of strong dependence on the abandonment distribution, it is natural to investigate ways of controlling customer abandonment behavior so as to mitigate that cost. Here, we propose doing so by making delay announcements in the system. We characterize how the manager may use three controls in her toolbox, staffing, compensation, and the announcements, to effectively control her system. We show that despite jointly optimizing the usage of those three controls, it may be cost effective for the manager to understaff, overstaff, or match supply and demand in any given shift.

Suggested Citation

  • Rouba Ibrahim, 2018. "Managing Queueing Systems Where Capacity is Random and Customers are Impatient," Production and Operations Management, Production and Operations Management Society, vol. 27(2), pages 234-250, February.
  • Handle: RePEc:bla:popmgt:v:27:y:2018:i:2:p:234-250
    DOI: 10.1111/poms.12796
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    Citations

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    Cited by:

    1. Liron Ravner & Yutaka Sakuma, 2021. "Strategic arrivals to a queue with service rate uncertainty," Queueing Systems: Theory and Applications, Springer, vol. 97(3), pages 303-341, April.
    2. Terry A. Taylor, 2018. "On-Demand Service Platforms," Manufacturing & Service Operations Management, INFORMS, vol. 20(4), pages 704-720, October.
    3. Zhong, Yuanguang & Zillmann, Stefan & Zhang, Ruijie & Zhou, Yong-Wu & Xie, Wei, 2023. "Vehicle repositioning for a ride-sourcing network system providing differentiated services," Transportation Research Part B: Methodological, Elsevier, vol. 170(C), pages 221-243.
    4. Barιş Ata & Deishin Lee & Erkut Sönmez, 2019. "Dynamic Volunteer Staffing in Multicrop Gleaning Operations," Operations Research, INFORMS, vol. 67(2), pages 295-314, March.
    5. Benjamin Legros, 2021. "Agents’ Self‐Routing for Blended Operations to Balance Inbound and Outbound Services," Production and Operations Management, Production and Operations Management Society, vol. 30(10), pages 3599-3614, October.
    6. Jiaqi Zhou & Ilya O. Ryzhov, 2021. "Equilibrium analysis of observable express service with customer choice," Queueing Systems: Theory and Applications, Springer, vol. 99(3), pages 243-281, December.
    7. Ming Hu, 2021. "From the Classics to New Tunes: A Neoclassical View on Sharing Economy and Innovative Marketplaces," Production and Operations Management, Production and Operations Management Society, vol. 30(6), pages 1668-1685, June.
    8. Dongyuan Zhan & Amy R. Ward, 2019. "Staffing, Routing, and Payment to Trade off Speed and Quality in Large Service Systems," Operations Research, INFORMS, vol. 67(6), pages 1738-1751, November.
    9. Li, Xiaonan & Li, Xiangyong & Wang, Hai & Shi, Junxin & Aneja, Y.P., 2022. "Supply regulation under the exclusion policy in a ride-sourcing market," Transportation Research Part B: Methodological, Elsevier, vol. 166(C), pages 69-94.
    10. Yiwei Chen & Ming Hu, 2020. "Pricing and Matching with Forward-Looking Buyers and Sellers," Manufacturing & Service Operations Management, INFORMS, vol. 22(4), pages 717-734, July.
    11. Saif Benjaafar & Ming Hu, 2020. "Operations Management in the Age of the Sharing Economy: What Is Old and What Is New?," Manufacturing & Service Operations Management, INFORMS, vol. 22(1), pages 93-101, January.

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