IDEAS home Printed from https://ideas.repec.org/a/spr/queues/v102y2022i1d10.1007_s11134-022-09854-8.html
   My bibliography  Save this article

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
    as

    Download full text from publisher

    File URL: http://link.springer.com/10.1007/s11134-022-09854-8
    File Function: Abstract
    Download Restriction: Access to the full text of the articles in this series is restricted.
    File URL: https://libkey.io/10.1007/s11134-022-09854-8?utm_source=ideas
    LibKey link: if access is restricted and if your library uses this service, LibKey will redirect you to where you can use your library subscription to access this item
    ---><---

    As the access to this document is restricted, you may want to search for a different version of it.

    References listed on IDEAS

    as
    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.
    Full references (including those not matched with items on IDEAS)

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Defraeye, Mieke & Van Nieuwenhuyse, Inneke, 2016. "Staffing and scheduling under nonstationary demand for service: A literature review," Omega, Elsevier, vol. 58(C), pages 4-25.
    2. 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.
    3. Achal Bassamboo & Ramandeep S. Randhawa & Assaf Zeevi, 2010. "Capacity Sizing Under Parameter Uncertainty: Safety Staffing Principles Revisited," Management Science, INFORMS, vol. 56(10), pages 1668-1686, October.
    4. Achal Bassamboo & J. Michael Harrison & Assaf Zeevi, 2006. "Design and Control of a Large Call Center: Asymptotic Analysis of an LP-Based Method," Operations Research, INFORMS, vol. 54(3), pages 419-435, June.
    5. Achal Bassamboo & Assaf Zeevi, 2009. "On a Data-Driven Method for Staffing Large Call Centers," Operations Research, INFORMS, vol. 57(3), pages 714-726, June.
    6. Merve Bodur & James R. Luedtke, 2017. "Mixed-Integer Rounding Enhanced Benders Decomposition for Multiclass Service-System Staffing and Scheduling with Arrival Rate Uncertainty," Management Science, INFORMS, vol. 63(7), pages 2073-2091, July.
    7. Kaan Kuzu & Refik Soyer, 2018. "Bayesian modeling of abandonments in ticket queues," Naval Research Logistics (NRL), John Wiley & Sons, vol. 65(6-7), pages 499-521, September.
    8. Shuangchi He, 2020. "Diffusion Approximation for Efficiency-Driven Queues When Customers Are Patient," Operations Research, INFORMS, vol. 68(4), pages 1265-1284, July.
    9. Josh Reed & Bo Zhang, 2017. "Managing capacity and inventory jointly for multi-server make-to-stock queues," Queueing Systems: Theory and Applications, Springer, vol. 86(1), pages 61-94, June.
    10. Noah Gans & Yong-Pin Zhou, 2007. "Call-Routing Schemes for Call-Center Outsourcing," Manufacturing & Service Operations Management, INFORMS, vol. 9(1), pages 33-50, May.
    11. Opher Baron & Joseph Milner, 2009. "Staffing to Maximize Profit for Call Centers with Alternate Service-Level Agreements," Operations Research, INFORMS, vol. 57(3), pages 685-700, June.
    12. Itai Gurvich & Junfei Huang & Avishai Mandelbaum, 2014. "Excursion-Based Universal Approximations for the Erlang-A Queue in Steady-State," Mathematics of Operations Research, INFORMS, vol. 39(2), pages 325-373, May.
    13. Jing Dong & Rouba Ibrahimb, 2020. "Managing Supply in the On-Demand Economy: Flexible Workers, Full-Time Employees, or Both?," Operations Research, INFORMS, vol. 68(4), pages 1238-1264, July.
    14. Eugene Furman & Adam Diamant & Murat Kristal, 2021. "Customer Acquisition and Retention: A Fluid Approach for Staffing," Production and Operations Management, Production and Operations Management Society, vol. 30(11), pages 4236-4257, November.
    15. Noa Zychlinski, 2023. "Applications of fluid models in service operations management," Queueing Systems: Theory and Applications, Springer, vol. 103(1), pages 161-185, February.
    16. Barış Ata & Xiaoshan Peng, 2020. "An Optimal Callback Policy for General Arrival Processes: A Pathwise Analysis," Operations Research, INFORMS, vol. 68(2), pages 327-347, March.
    17. Zhe George Zhang, 2009. "Performance Analysis of a Queue with Congestion-Based Staffing Policy," Management Science, INFORMS, vol. 55(2), pages 240-251, February.
    18. 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.
    19. Noah Gans & Haipeng Shen & Yong-Pin Zhou & Nikolay Korolev & Alan McCord & Herbert Ristock, 2015. "Parametric Forecasting and Stochastic Programming Models for Call-Center Workforce Scheduling," Manufacturing & Service Operations Management, INFORMS, vol. 17(4), pages 571-588, October.
    20. 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.

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:spr:queues:v:102:y:2022:i:1:d:10.1007_s11134-022-09854-8. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Sonal Shukla or Springer Nature Abstracting and Indexing (email available below). General contact details of provider: http://www.springer.com .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.