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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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    1. J. E. Reed & Amy R. Ward, 2008. "Approximating the GI/GI/1+GI Queue with a Nonlinear Drift Diffusion: Hazard Rate Scaling in Heavy Traffic," Mathematics of Operations Research, INFORMS, vol. 33(3), pages 606-644, August.
    2. Naor, P, 1969. "The Regulation of Queue Size by Levying Tolls," Econometrica, Econometric Society, vol. 37(1), pages 15-24, January.
    3. Avishai Mandelbaum & Petar Momčilović, 2012. "Queues with Many Servers and Impatient Customers," Mathematics of Operations Research, INFORMS, vol. 37(1), pages 41-65, February.
    4. Ward Whitt, 2004. "Efficiency-Driven Heavy-Traffic Approximations for Many-Server Queues with Abandonments," Management Science, INFORMS, vol. 50(10), pages 1449-1461, October.
    5. Gad Allon & Achal Bassamboo, 2011. "The Impact of Delaying the Delay Announcements," Operations Research, INFORMS, vol. 59(5), pages 1198-1210, October.
    6. Noah Gans & Ger Koole & Avishai Mandelbaum, 2003. "Telephone Call Centers: Tutorial, Review, and Research Prospects," Manufacturing & Service Operations Management, INFORMS, vol. 5(2), pages 79-141, September.
    7. Ohad Perry & Ward Whitt, 2009. "Responding to Unexpected Overloads in Large-Scale Service Systems," Management Science, INFORMS, vol. 55(8), pages 1353-1367, August.
    8. Lawrence Brown & Noah Gans & Avishai Mandelbaum & Anat Sakov & Haipeng Shen & Sergey Zeltyn & Linda Zhao, 2005. "Statistical Analysis of a Telephone Call Center: A Queueing-Science Perspective," Journal of the American Statistical Association, American Statistical Association, vol. 100, pages 36-50, March.
    9. Mor Armony & Nahum Shimkin & Ward Whitt, 2009. "The Impact of Delay Announcements in Many-Server Queues with Abandonment," Operations Research, INFORMS, vol. 57(1), pages 66-81, February.
    10. Achal Bassamboo & Ramandeep S. Randhawa, 2010. "On the Accuracy of Fluid Models for Capacity Sizing in Queueing Systems with Impatient Customers," Operations Research, INFORMS, vol. 58(5), pages 1398-1413, October.
    11. Oualid Jouini & Zeynep Akşin & Yves Dallery, 2011. "Call Centers with Delay Information: Models and Insights," Manufacturing & Service Operations Management, INFORMS, vol. 13(4), pages 534-548, October.
    12. Ward Whitt, 2006. "Fluid Models for Multiserver Queues with Abandonments," Operations Research, INFORMS, vol. 54(1), pages 37-54, February.
    13. Oualid Jouini & Zeynep Aksin & Yves Dallery, 2011. "Call Centers with Delay Information: Models and Insights," Post-Print hal-00680769, HAL.
    14. Avishai Mandelbaum & Sergey Zeltyn, 2009. "Staffing Many-Server Queues with Impatient Customers: Constraint Satisfaction in Call Centers," Operations Research, INFORMS, vol. 57(5), pages 1189-1205, October.
    15. Qiuping Yu & Gad Allon & Achal Bassamboo, 2017. "How Do Delay Announcements Shape Customer Behavior? An Empirical Study," Management Science, INFORMS, vol. 63(1), pages 1-20, January.
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    Cited by:

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    2. 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.
    3. Shuangchi He, 2020. "Diffusion Approximation for Efficiency-Driven Queues When Customers Are Patient," Operations Research, INFORMS, vol. 68(4), pages 1265-1284, July.
    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. 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.
    7. Rouba Ibrahim, 2018. "Sharing delay information in service systems: a literature survey," Queueing Systems: Theory and Applications, Springer, vol. 89(1), pages 49-79, June.

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