IDEAS home Printed from https://ideas.repec.org/a/inm/ormnsc/v50y2004i10p1449-1461.html
   My bibliography  Save this article

Efficiency-Driven Heavy-Traffic Approximations for Many-Server Queues with Abandonments

Author

Listed:
  • Ward Whitt

    (Department of Industrial Engineering and Operations Research, Columbia University, Mudd Building, 500 West 120th Street, New York, New York 10027-6699)

Abstract

To provide useful practical insight into the performance of service-oriented (non-revenue-generating) call centers, which often provide low-to-moderate quality of service, this paper investigates the efficiency-driven (ED), many-server heavy-traffic limiting regime for queues with abandonments. Attention is focused on the M/M/s/r + M model, having a Poisson arrival process, exponential service times, s servers, r extra waiting spaces, exponential abandon times (the final +M), and the first-come--first-served service discipline. Both the number of servers and the arrival rate are allowed to increase, while the individual service and abandonment rates are held fixed. The key is how the two limits are related: In the now common quality-and-efficiency-driven (QED) or Halfin-Whitt limiting regime, the probability of initially being delayed approaches a limit strictly between 0 and 1, while the probability of eventually being served (not abandoning) approaches 1. In contrast, in the ED limiting regime, the probability of eventually being served approaches a limit strictly between 0 and 1, while the probability of initially being delayed approaches 1. To obtain the ED regime, it suffices to let the arrival rate and the number of servers increase with the traffic intensity \rho held fixed with \rho > 1 (so that the arrival rate exceeds the maximum possible service rate). The ED regime can be realistic because with the abandonments, the delays need not be extraordinarily large. When the ED appropriations are appropriate, they are appealing because they are remarkably simple.

Suggested Citation

  • Ward Whitt, 2004. "Efficiency-Driven Heavy-Traffic Approximations for Many-Server Queues with Abandonments," Management Science, INFORMS, vol. 50(10), pages 1449-1461, October.
    • Handle: RePEc:inm:ormnsc:v:50:y:2004:i:10:p:1449-1461
    DOI: 10.1287/mnsc.1040.0279
    as

    Download full text from publisher

    File URL: http://dx.doi.org/10.1287/mnsc.1040.0279
    Download Restriction: no
    File URL: https://libkey.io/10.1287/mnsc.1040.0279?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
    ---><---

    References listed on IDEAS

    as
    1. 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.
    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. Shlomo Halfin & Ward Whitt, 1981. "Heavy-Traffic Limits for Queues with Many Exponential Servers," Operations Research, INFORMS, vol. 29(3), pages 567-588, June.
    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. 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.
    2. Ward Whitt, 2005. "Engineering Solution of a Basic Call-Center Model," Management Science, INFORMS, vol. 51(2), pages 221-235, February.
    3. Rami Atar & Adam Shwartz, 2008. "Efficient Routing in Heavy Traffic Under Partial Sampling of Service Times," Mathematics of Operations Research, INFORMS, vol. 33(4), pages 899-909, November.
    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. Niyirora, Jerome & Zhuang, Jun, 2017. "Fluid approximations and control of queues in emergency departments," European Journal of Operational Research, Elsevier, vol. 261(3), pages 1110-1124.
    6. 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.
    7. James W. Taylor, 2012. "Density Forecasting of Intraday Call Center Arrivals Using Models Based on Exponential Smoothing," Management Science, INFORMS, vol. 58(3), pages 534-549, March.
    8. Itai Gurvich & Ohad Perry, 2012. "Overflow Networks: Approximations and Implications to Call Center Outsourcing," Operations Research, INFORMS, vol. 60(4), pages 996-1009, August.
    9. 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.
    10. van Leeuwaarden, Johan S.H. & Knessl, Charles, 2011. "Transient behavior of the Halfin-Whitt diffusion," Stochastic Processes and their Applications, Elsevier, vol. 121(7), pages 1524-1545, July.
    11. Francis de Véricourt & Otis B. Jennings, 2008. "Dimensioning Large-Scale Membership Services," Operations Research, INFORMS, vol. 56(1), pages 173-187, February.
    12. Oualid Jouini & Zeynep Akşin & Yves Dallery, 2011. "Call Centers with Delay Information: Models and Insights," Manufacturing & Service Operations Management, INFORMS, vol. 13(4), pages 534-548, October.
    13. 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.
    14. Rami Atar & Avi Mandelbaum & Gennady Shaikhet, 2009. "Simplified Control Problems for Multiclass Many-Server Queueing Systems," Mathematics of Operations Research, INFORMS, vol. 34(4), pages 795-812, November.
    15. A. J. E. M. Janssen & J. S. H. van Leeuwaarden & Bert Zwart, 2011. "Refining Square-Root Safety Staffing by Expanding Erlang C," Operations Research, INFORMS, vol. 59(6), pages 1512-1522, December.
    16. J. G. Dai & Tolga Tezcan, 2011. "State Space Collapse in Many-Server Diffusion Limits of Parallel Server Systems," Mathematics of Operations Research, INFORMS, vol. 36(2), pages 271-320, May.
    17. Zeynep Akşin & Barış Ata & Seyed Morteza Emadi & Che-Lin Su, 2013. "Structural Estimation of Callers' Delay Sensitivity in Call Centers," Management Science, INFORMS, vol. 59(12), pages 2727-2746, December.
    18. Saif Benjaafar & Shining Wu & Hanlin Liu & Einar Bjarki Gunnarsson, 2022. "Dimensioning On-Demand Vehicle Sharing Systems," Management Science, INFORMS, vol. 68(2), pages 1218-1232, February.
    19. 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.
    20. 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.

    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:inm:ormnsc:v:50:y:2004:i:10:p:1449-1461. 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: Chris Asher (email available below). General contact details of provider: https://edirc.repec.org/data/inforea.html .

    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.