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Optimal staffing for ticket queues

Author

Listed:
  • Li Xiao

    (Tsinghua University)

  • Susan H. Xu

    (The Pennsylvania State University)

  • David D. Yao

    (Columbia University)

  • Hanqin Zhang

    (National University of Singapore)

Abstract

Ticket queues are popular in many service systems. Upon arrival, each customer is issued a numbered ticket and receives service on a first-come-first-served basis according to the ticket number. There is no physical queue; customers may choose to walk away and return later (before their numbers are called) to receive service. We study the problem of optimal staffing in such a system with two capacity levels, where the staffing decision can only be based on ticket numbers, as opposed to the physical queue length in a traditional system. Using renewal reward theorem, we first derive the long-run average total cost (including customer delay and abandonment costs, operating cost and cost for changing staffing levels) and then obtain the optimal solution using fractional programming. In addition, we pursue a random-walk analysis, which leads to some highly accurate approximations.

Suggested Citation

  • 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.
    • Handle: RePEc:spr:queues:v:102:y:2022:i:1:d:10.1007_s11134-022-09854-8
    DOI: 10.1007/s11134-022-09854-8
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    References listed on IDEAS

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    1. Bo Zhang & Johan S. H. van Leeuwaarden & Bert Zwart, 2012. "Staffing Call Centers with Impatient Customers: Refinements to Many-Server Asymptotics," Operations Research, INFORMS, vol. 60(2), pages 461-474, April.
    2. Ety Zohar & Avishai Mandelbaum & Nahum Shimkin, 2002. "Adaptive Behavior of Impatient Customers in Tele-Queues: Theory and Empirical Support," Management Science, INFORMS, vol. 48(4), pages 566-583, April.
    3. Guodong Pang & Ohad Perry, 2015. "A Logarithmic Safety Staffing Rule for Contact Centers with Call Blending," Management Science, INFORMS, vol. 61(1), pages 73-91, January.
    4. Zhe George Zhang, 2009. "Performance Analysis of a Queue with Congestion-Based Staffing Policy," Management Science, INFORMS, vol. 55(2), pages 240-251, February.
    5. Susan H. Xu & Long Gao & Jihong Ou, 2007. "Service Performance Analysis and Improvement for a Ticket Queue with Balking Customers," Management Science, INFORMS, vol. 53(6), pages 971-990, June.
    6. Otis B. Jennings & Jamol Pender, 2016. "Comparisons of ticket and standard queues," Queueing Systems: Theory and Applications, Springer, vol. 84(1), pages 145-202, October.
    7. Mor Armony & Erica Plambeck & Sridhar Seshadri, 2009. "Sensitivity of Optimal Capacity to Customer Impatience in an Unobservable M/M/S Queue (Why You Shouldn't Shout at the DMV)," Manufacturing & Service Operations Management, INFORMS, vol. 11(1), pages 19-32, June.
    8. Shlomo Halfin & Ward Whitt, 1981. "Heavy-Traffic Limits for Queues with Many Exponential Servers," Operations Research, INFORMS, vol. 29(3), pages 567-588, June.
    9. Noah Gans & Yong-Pin Zhou, 2003. "A Call-Routing Problem with Service-Level Constraints," Operations Research, INFORMS, vol. 51(2), pages 255-271, April.
    10. C. J. Ancker & A. V. Gafarian, 1963. "Some Queuing Problems with Balking and Reneging---II," Operations Research, INFORMS, vol. 11(6), pages 928-937, December.
    11. M. Yadin & P. Naor, 1967. "On queueing systems with variable service capacities," Naval Research Logistics Quarterly, John Wiley & Sons, vol. 14(1), pages 43-53.
    12. Colin E. Bell, 1975. "Technical Note—Turning Off a Server with Customers Present: Is This Any Way to Run an M / M / c Queue with Removable Servers?," Operations Research, INFORMS, vol. 23(3), pages 571-574, June.
    13. 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.
    14. J. Michael Harrison & Assaf Zeevi, 2005. "A Method for Staffing Large Call Centers Based on Stochastic Fluid Models," Manufacturing & Service Operations Management, INFORMS, vol. 7(1), pages 20-36, September.
    15. Per Hokstad, 1979. "Note--A Single Server Queue with Constant Service Time and Restricted Accessibility," Management Science, INFORMS, vol. 25(2), pages 205-208, February.
    16. 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.
    17. Robert E. Stanford, 1979. "Reneging Phenomena in Single Channel Queues," Mathematics of Operations Research, INFORMS, vol. 4(2), pages 162-178, May.
    18. Michael C. Fu & Steven I. Marcus & I-Jeng Wang, 2000. "Monotone Optimal Policies for a Transient Queueing Staffing Problem," Operations Research, INFORMS, vol. 48(2), pages 327-331, April.
    19. Sem Borst & Avi Mandelbaum & Martin I. Reiman, 2004. "Dimensioning Large Call Centers," Operations Research, INFORMS, vol. 52(1), pages 17-34, February.
    20. 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.
    21. John F. Reynolds, 1968. "The Stationary Solution of a Multiserver Queuing Model with Discouragement," Operations Research, INFORMS, vol. 16(1), pages 64-71, February.
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