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Refined Models for Efficiency-Driven Queues with Applications to Delay Announcements and Staffing

Author

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  • Junfei Huang

    (Department of Decision Sciences and Managerial Economics, CUHK Business School, The Chinese University of Hong Kong, Shatin, Hong Kong)

  • Avishai Mandelbaum

    (Faculty of Industrial Engineering and Management, Technion - Israel Institute of Technology, 3200003 Haifa, Israel)

  • Hanqin Zhang

    (Department of Decision Sciences, NUS Business School, National University of Singapore, Singapore)

  • Jiheng Zhang

    (Department of Industrial Engineering and Logistics Management, The Hong Kong University of Science and Technology, Clear Water Bay, Hong Kong)

Abstract

Data has revealed a noticeable impact of delay-time-related information on phone-customers; for example and somewhat surprisingly, delay announcements can abruptly increase the likelihood to abandon (hang up). Our starting point is that the latter phenomena can be used to support the control of queue lengths and delays. We do so by timing the announcements appropriately and determining the staffing levels accordingly. To this end, we model a service system as an overloaded GI / M / s + GI queue, in which we seek to minimize the number of servers, s, subject to quality-of-service constraints (e.g., fraction abandoning), while accounting for the instantaneous (hence discontinuous) impact of an announcement on the distribution (hazard rate) of customer patience. For tractability, our analysis is asymptotic as s increases indefinitely, and it is naturally efficiency-driven (namely the servers are highly busy, and hence essentially all customers are delayed in queue prior to service). This requires one to go beyond existing theory, which turns out to be too crude for our needs (e.g., it requires a continuous hazard rate of impatience and hence cannot be applied). We thus develop a refined process and steady-state models, and use them to solve our minimization problem and more. The value and accuracy of our models are demonstrated via extensive numerical experiments.

Suggested Citation

  • Junfei Huang & Avishai Mandelbaum & Hanqin Zhang & Jiheng Zhang, 2017. "Refined Models for Efficiency-Driven Queues with Applications to Delay Announcements and Staffing," Operations Research, INFORMS, vol. 65(5), pages 1380-1397, October.
    • Handle: RePEc:inm:oropre:v:65:y:2017:i:5:p:1380-1397
    DOI: 10.1287/opre.2017.1619
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    References listed on IDEAS

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    Cited by:

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    2. Li Xiao & Susan H. Xu & David D. Yao & Hanqin Zhang, 2022. "Optimal staffing for ticket queues," Queueing Systems: Theory and Applications, Springer, vol. 102(1), pages 309-351, October.
    3. Liu, Zhongyi & Liu, Jingchen & Zhai, Xin & Wang, Guanying, 2019. "Police staffing and workload assignment in law enforcement using multi-server queueing models," European Journal of Operational Research, Elsevier, vol. 276(2), pages 614-625.
    4. Guodong Pang & Yuhang Zhou, 2018. "Two-parameter process limits for infinite-server queues with dependent service times via chaining bounds," Queueing Systems: Theory and Applications, Springer, vol. 88(1), pages 1-25, February.
    5. Noa Zychlinski, 2023. "Applications of fluid models in service operations management," Queueing Systems: Theory and Applications, Springer, vol. 103(1), pages 161-185, February.
    6. Shuangchi He, 2020. "Diffusion Approximation for Efficiency-Driven Queues When Customers Are Patient," Operations Research, INFORMS, vol. 68(4), pages 1265-1284, July.
    7. A. Korhan Aras & Xinyun Chen & Yunan Liu, 2018. "Many-server Gaussian limits for overloaded non-Markovian queues with customer abandonment," Queueing Systems: Theory and Applications, Springer, vol. 89(1), pages 81-125, June.

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