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Hazard Rate Scaling of the Abandonment Distribution for the GI/M/n + GI Queue in Heavy Traffic

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  • Josh Reed

    (Stern School of Business, New York University, New York, New York 10012)

  • Tolga Tezcan

    (Simon Graduate School of Business, University of Rochester, Rochester, New York 14627)

Abstract

We obtain a heavy traffic limit for the GI/M/n + GI queue, which includes the entire patience time distribution. Our main approach is to scale the hazard rate function of the patience time distribution in such a way that our resulting diffusion approximation contains the entire hazard rate function. We then show through numerical studies that for various performance measures, our approximations tend to outperform those commonly used in practice. The robustness of our results is also demonstrated by applying them to solving constraint satisfaction problems arising in the context of telephone call centers.

Suggested Citation

  • Josh Reed & Tolga Tezcan, 2012. "Hazard Rate Scaling of the Abandonment Distribution for the GI/M/n + GI Queue in Heavy Traffic," Operations Research, INFORMS, vol. 60(4), pages 981-995, August.
    • Handle: RePEc:inm:oropre:v:60:y:2012:i:4:p:981-995
    DOI: 10.1287/opre.1120.1069
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    References listed on IDEAS

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    1. Avishai Mandelbaum & Petar Momčilović, 2012. "Queues with Many Servers and Impatient Customers," Mathematics of Operations Research, INFORMS, vol. 37(1), pages 41-65, February.
    2. Ward Whitt, 2005. "Engineering Solution of a Basic Call-Center Model," Management Science, INFORMS, vol. 51(2), pages 221-235, February.
    3. Shlomo Halfin & Ward Whitt, 1981. "Heavy-Traffic Limits for Queues with Many Exponential Servers," Operations Research, INFORMS, vol. 29(3), pages 567-588, June.
    4. J. G. Dai & Shuangchi He, 2010. "Customer Abandonment in Many-Server Queues," Mathematics of Operations Research, INFORMS, vol. 35(2), pages 347-362, May.
    5. 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.
    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. 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.
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    Cited by:

    1. Christos Zacharias & Mor Armony, 2017. "Joint Panel Sizing and Appointment Scheduling in Outpatient Care," Management Science, INFORMS, vol. 63(11), pages 3978-3997, November.
    2. Shuangchi He, 2020. "Diffusion Approximation for Efficiency-Driven Queues When Customers Are Patient," Operations Research, INFORMS, vol. 68(4), pages 1265-1284, July.
    3. Junfei Huang & Hanqin Zhang & Jiheng Zhang, 2016. "A Unified Approach to Diffusion Analysis of Queues with General Patience-Time Distributions," Mathematics of Operations Research, INFORMS, vol. 41(3), pages 1135-1160, August.
    4. Xin Liu, 2019. "Diffusion approximations for double-ended queues with reneging in heavy traffic," Queueing Systems: Theory and Applications, Springer, vol. 91(1), pages 49-87, February.
    5. Yunan Liu & Ward Whitt & Yao Yu, 2016. "Approximations for heavily loaded G/GI/n + GI queues," Naval Research Logistics (NRL), John Wiley & Sons, vol. 63(3), pages 187-217, April.
    6. Chihoon Lee & Amy R. Ward & Heng-Qing Ye, 2020. "Stationary distribution convergence of the offered waiting processes for $$GI/GI/1+GI$$GI/GI/1+GI queues in heavy traffic," Queueing Systems: Theory and Applications, Springer, vol. 94(1), pages 147-173, February.

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