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Predicting Queueing Delays

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  • Ward Whitt

    (Room A117, AT&T Labs, Shannon Laboratory, 180 Park Avenue, Florham Park, New Jersey 07932-0971)

Abstract

This paper investigates the possibility of predicting each customer's waiting time in queue before starting service in a multiserver service system with the first-come first-served service discipline, such as a telephone call center. A predicted waiting-time distribution or an appropriate summary statistic such as the mean or the 90th percentile may be communicated to the customer upon arrival and possibly thereafter in order to improve customer satisfaction. The predicted waiting-time distribution may also be used by the service provider to better manage the service system, e.g., to help decide when to add additional service agents. The possibility of making reliable predictions is enhanced by exploiting information about system state, including the number of customers in the system ahead of the current customer. Additional information beyond the number of customers in the system may be obtained by classifying customers and the service agents to which they are assigned. For nonexponential service times, the elapsed service times of customers in service can often be used to advantage to compute conditional-remaining-service-time distributions. Approximations are proposed to convert the distributions of remaining service times into the distribution of the desired customer waiting time. The analysis reveals the advantage from exploiting additional information.

Suggested Citation

  • Ward Whitt, 1999. "Predicting Queueing Delays," Management Science, INFORMS, vol. 45(6), pages 870-888, June.
    • Handle: RePEc:inm:ormnsc:v:45:y:1999:i:6:p:870-888
    DOI: 10.1287/mnsc.45.6.870
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    References listed on IDEAS

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    1. Joseph Abate & Ward Whitt, 1995. "Numerical Inversion of Laplace Transforms of Probability Distributions," INFORMS Journal on Computing, INFORMS, vol. 7(1), pages 36-43, February.
    2. Ward Whitt, 1999. "Improving Service by Informing Customers About Anticipated Delays," Management Science, INFORMS, vol. 45(2), pages 192-207, February.
    3. D. A. Stanford & B. Pagurek & C. M. Woodside, 1983. "Optimal Prediction of Times and Queue Lengths in the GI / M /1 Queue," Operations Research, INFORMS, vol. 31(2), pages 322-337, April.
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    Citations

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    Cited by:

    1. 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.
    2. 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.
    3. Stefan Helber & Raik Stolletz & Sophie Bothe, 2005. "Erfolgszielorientierte Agentenallokation in Inbound Call-Centern," Schmalenbach Journal of Business Research, Springer, vol. 57(1), pages 3-32, February.
    4. Zeynep Akşin & Baris Ata & Seyed Morteza Emadi & Che-Lin Su, 2017. "Impact of Delay Announcements in Call Centers: An Empirical Approach," Operations Research, INFORMS, vol. 65(1), pages 242-265, February.
    5. 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.
    6. Robert M. Saltzman & Vijay Mehrotra, 2001. "A Call Center Uses Simulation to Drive Strategic Change," Interfaces, INFORMS, vol. 31(3), pages 87-101, June.
    7. 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).
    8. Achal Bassamboo & Rouba Ibrahim, 2021. "A General Framework to Compare Announcement Accuracy: Static vs. LES-Based Announcement," Management Science, INFORMS, vol. 67(7), pages 4191-4208, July.
    9. Ward Whitt, 1999. "Improving Service by Informing Customers About Anticipated Delays," Management Science, INFORMS, vol. 45(2), pages 192-207, February.
    10. Jouini, Oualid & Dallery, Yves & Aksin, Zeynep, 2009. "Queueing models for full-flexible multi-class call centers with real-time anticipated delays," International Journal of Production Economics, Elsevier, vol. 120(2), pages 389-399, August.
    11. 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.
    12. Oualid Jouini & Yves Dallery, 2008. "Moments of first passage times in general birth–death processes," Mathematical Methods of Operations Research, Springer;Gesellschaft für Operations Research (GOR);Nederlands Genootschap voor Besliskunde (NGB), vol. 68(1), pages 49-76, August.
    13. 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.
    14. Chester Chambers & Panagiotis Kouvelis, 2006. "Modeling and Managing the Percentage of Satisfied Customers in Hidden and Revealed Waiting Line Systems," Production and Operations Management, Production and Operations Management Society, vol. 15(1), pages 103-116, March.
    15. Azam Asanjarani & Yoni Nazarathy & Peter Taylor, 2021. "A survey of parameter and state estimation in queues," Queueing Systems: Theory and Applications, Springer, vol. 97(1), pages 39-80, February.

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