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Real-Time Delay Estimation in Overloaded Multiserver Queues with Abandonments

Author

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  • Rouba Ibrahim

    (Department of Industrial Engineering and Operations Research, Columbia University, New York, New York 10027)

  • Ward Whitt

    (Department of Industrial Engineering and Operations Research, Columbia University, New York, New York 10027)

Abstract

We use heavy-traffic limits and computer simulation to study the performance of alternative real-time delay estimators in the overloaded GI/GI/s+GI multiserver queueing model, allowing customer abandonment. These delay estimates may be used to make delay announcements in call centers and related service systems. We characterize performance by the expected mean squared error in steady state. We exploit established approximations for performance measures with a nonexponential abandonment-time distribution to obtain new delay estimators that effectively cope with nonexponential abandonment-time distributions.

Suggested Citation

  • Rouba Ibrahim & Ward Whitt, 2009. "Real-Time Delay Estimation in Overloaded Multiserver Queues with Abandonments," Management Science, INFORMS, vol. 55(10), pages 1729-1742, October.
    • Handle: RePEc:inm:ormnsc:v:55:y:2009:i:10:p:1729-1742
    DOI: 10.1287/mnsc.1090.1041
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    References listed on IDEAS

    as
    1. Ward Whitt, 2005. "Engineering Solution of a Basic Call-Center Model," Management Science, INFORMS, vol. 51(2), pages 221-235, February.
    2. 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.
    3. Rouba Ibrahim & Ward Whitt, 2009. "Real-Time Delay Estimation Based on Delay History," Manufacturing & Service Operations Management, INFORMS, vol. 11(3), pages 397-415, May.
    4. Pengfei Guo & Paul Zipkin, 2007. "Analysis and Comparison of Queues with Different Levels of Delay Information," Management Science, INFORMS, vol. 53(6), pages 962-970, June.
    5. Ward Whitt, 2006. "Fluid Models for Multiserver Queues with Abandonments," Operations Research, INFORMS, vol. 54(1), pages 37-54, February.
    6. Ward Whitt, 1999. "Predicting Queueing Delays," Management Science, INFORMS, vol. 45(6), pages 870-888, June.
    7. Ward Whitt, 2004. "Efficiency-Driven Heavy-Traffic Approximations for Many-Server Queues with Abandonments," Management Science, INFORMS, vol. 50(10), pages 1449-1461, October.
    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.
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    Citations

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    Cited by:

    1. Siddharth Prakash Singh & Mohammad Delasay & Alan Scheller‐Wolf, 2023. "Real‐time delay announcement under competition," Production and Operations Management, Production and Operations Management Society, vol. 32(3), pages 863-881, March.
    2. Miao Yu & Yu Zhao & Chunguang Chang & Liangliang Sun, 2023. "Fluid models for customer service web chat systems with interactive automated service," Flexible Services and Manufacturing Journal, Springer, vol. 35(2), pages 572-598, June.
    3. Rouba Ibrahim & Mor Armony & Achal Bassamboo, 2017. "Does the Past Predict the Future? The Case of Delay Announcements in Service Systems," Management Science, INFORMS, vol. 63(6), pages 1762-1780, June.
    4. Noa Zychlinski, 2023. "Applications of fluid models in service operations management," Queueing Systems: Theory and Applications, Springer, vol. 103(1), pages 161-185, February.
    5. Guo, Pengfei & Sun, Wei & Wang, Yulan, 2011. "Equilibrium and optimal strategies to join a queue with partial information on service times," European Journal of Operational Research, Elsevier, vol. 214(2), pages 284-297, October.
    6. Qiuping Yu & Gad Allon & Achal Bassamboo, 2021. "The Reference Effect of Delay Announcements: A Field Experiment," Management Science, INFORMS, vol. 67(12), pages 7417-7437, December.
    7. Rouba Ibrahim & Ward Whitt, 2011. "Wait-Time Predictors for Customer Service Systems with Time-Varying Demand and Capacity," Operations Research, INFORMS, vol. 59(5), pages 1106-1118, October.
    8. Guodong Pang & Ward Whitt, 2009. "Service Interruptions in Large-Scale Service Systems," Management Science, INFORMS, vol. 55(9), pages 1499-1512, September.
    9. Qiuping Yu & Gad Allon & Achal Bassamboo & Seyed Iravani, 2018. "Managing Customer Expectations and Priorities in Service Systems," Management Science, INFORMS, vol. 64(8), pages 3942-3970, August.
    10. Pengfei Guo & Zhe George Zhang, 2013. "Strategic Queueing Behavior and Its Impact on System Performance in Service Systems with the Congestion-Based Staffing Policy," Manufacturing & Service Operations Management, INFORMS, vol. 15(1), pages 118-131, September.
    11. Brett A. Hathaway & Seyed M. Emadi & Vinayak Deshpande, 2021. "Don’t Call Us, We’ll Call You: An Empirical Study of Caller Behavior Under a Callback Option," Management Science, INFORMS, vol. 67(3), pages 1508-1526, March.
    12. Lu, Yuwei & Xie, Xiaolan & Jiang, Zhibin, 2018. "Dynamic appointment scheduling with wait-dependent abandonment," European Journal of Operational Research, Elsevier, vol. 265(3), pages 975-984.
    13. 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.
    14. Najiya Fatma & Varun Ramamohan, 2023. "Patient diversion using real-time delay predictions across healthcare facility networks," OR Spectrum: Quantitative Approaches in Management, Springer;Gesellschaft für Operations Research e.V., vol. 45(2), pages 437-476, June.
    15. Tkachenko Andrey, 2013. "Multichannel queuing systems with balking and regenerative input fl ow," HSE Working papers WP BRP 14/STI/2013, National Research University Higher School of Economics.
    16. Hong Zhang & Saviour Worlanyo Akuamoah & Wilson Osafo Apeanti & Prince Harvim & David Yaro & Paul Georgescu, 2021. "The Stability Analysis of a Double-X Queuing Network Occurring in the Banking Sector," Mathematics, MDPI, vol. 9(16), pages 1-21, August.
    17. Zhang, Zhe George & Yin, Xiaoling, 2021. "Information and pricing effects in two-tier public service systems," International Journal of Production Economics, Elsevier, vol. 231(C).

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