IDEAS home Printed from https://ideas.repec.org/a/eee/oprepe/v2y2015icp81-96.html
   My bibliography  Save this article

Fluid approximation analysis of a call center model with time-varying arrivals and after-call work

Author

Listed:
  • Kawai, Yosuke
  • Takagi, Hideaki

Abstract

Important features to be included in queueing-theoretic models of the call center operation are multiple servers, impatient customers, time-varying arrival process, and operator’s after-call work (ACW). We propose a fluid approximation technique for the queueing model with these features by extending the analysis of a similar model without ACW recently developed by Liu and Whitt (2012). Our model assumes that the service for each quantum of fluid consists of a sequence of two stages, the first stage for the conversation with a customer and the second stage for the ACW. When the duration of each stage has exponential, hyperexponential or hypo-exponential distribution, we derive the time-dependent behavior of the content of fluid in each stage of service as well as that in the waiting room. Numerical examples are shown to illustrate the system performance for the cases in which the input rate and/or the number of servers vary in sinusoidal fashion as well as in adaptive ways and in stationary cases.

Suggested Citation

  • Kawai, Yosuke & Takagi, Hideaki, 2015. "Fluid approximation analysis of a call center model with time-varying arrivals and after-call work," Operations Research Perspectives, Elsevier, vol. 2(C), pages 81-96.
  • Handle: RePEc:eee:oprepe:v:2:y:2015:i:c:p:81-96
    DOI: 10.1016/j.orp.2015.03.003
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S2214716015000093
    Download Restriction: Full text for ScienceDirect subscribers only

    File URL: https://libkey.io/10.1016/j.orp.2015.03.003?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. Yunan Liu & Ward Whitt, 2011. "A Network of Time-Varying Many-Server Fluid Queues with Customer Abandonment," Operations Research, INFORMS, vol. 59(4), pages 835-846, August.
    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. Ger Koole & Avishai Mandelbaum, 2002. "Queueing Models of Call Centers: An Introduction," Annals of Operations Research, Springer, vol. 113(1), pages 41-59, July.
    4. Yunan Liu & Ward Whitt, 2014. "Algorithms for Time-Varying Networks of Many-Server Fluid Queues," INFORMS Journal on Computing, INFORMS, vol. 26(1), pages 59-73, February.
    5. Zohar Feldman & Avishai Mandelbaum & William A. Massey & Ward Whitt, 2008. "Staffing of Time-Varying Queues to Achieve Time-Stable Performance," Management Science, INFORMS, vol. 54(2), pages 324-338, February.
    6. Carl M. Harris & Karla L. Hoffman & Patsy B. Saunders, 1987. "Modeling the IRS Telephone Taxpayer Information System," Operations Research, INFORMS, vol. 35(4), pages 504-523, August.
    7. 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.
    8. Ward Whitt, 2006. "Fluid Models for Multiserver Queues with Abandonments," Operations Research, INFORMS, vol. 54(1), pages 37-54, February.
    Full references (including those not matched with items on IDEAS)

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    Cited by:

    1. Yonit Barron, 2023. "Integrating Replenishment Policy and Maintenance Services in a Stochastic Inventory System with Bilateral Movements," Mathematics, MDPI, vol. 11(4), pages 1-35, February.
    2. Barron, Yonit, 2023. "A stochastic card balance management problem with continuous and batch-type bilateral transactions," Operations Research Perspectives, Elsevier, vol. 10(C).

    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. Max Tschaikowski & Mirco Tribastone, 2017. "A computational approach to steady-state convergence of fluid limits for Coxian queuing networks with abandonment," Annals of Operations Research, Springer, vol. 252(1), pages 101-120, May.
    2. 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.
    3. Noa Zychlinski, 2023. "Applications of fluid models in service operations management," Queueing Systems: Theory and Applications, Springer, vol. 103(1), pages 161-185, February.
    4. Dietz, Dennis C., 2011. "Practical scheduling for call center operations," Omega, Elsevier, vol. 39(5), pages 550-557, October.
    5. 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.
    6. Alexander L. Stolyar & Tolga Tezcan, 2011. "Shadow-Routing Based Control of Flexible Multiserver Pools in Overload," Operations Research, INFORMS, vol. 59(6), pages 1427-1444, December.
    7. Shuangchi He, 2020. "Diffusion Approximation for Efficiency-Driven Queues When Customers Are Patient," Operations Research, INFORMS, vol. 68(4), pages 1265-1284, July.
    8. Zhenghua Long & Nahum Shimkin & Hailun Zhang & Jiheng Zhang, 2020. "Dynamic Scheduling of Multiclass Many-Server Queues with Abandonment: The Generalized cμ / h Rule," Operations Research, INFORMS, vol. 68(4), pages 1128-1230, July.
    9. Ran Liu & Xiaolan Xie, 2018. "Physician Staffing for Emergency Departments with Time-Varying Demand," INFORMS Journal on Computing, INFORMS, vol. 30(3), pages 588-607, August.
    10. 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.
    11. Tolga Tezcan & Jiheng Zhang, 2014. "Routing and Staffing in Customer Service Chat Systems with Impatient Customers," Operations Research, INFORMS, vol. 62(4), pages 943-956, August.
    12. 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.
    13. Noa Zychlinski & Avishai Mandelbaum & Petar Momčilović, 2018. "Time-varying tandem queues with blocking: modeling, analysis, and operational insights via fluid models with reflection," Queueing Systems: Theory and Applications, Springer, vol. 89(1), pages 15-47, June.
    14. A. Korhan Aras & Xinyun Chen & Yunan Liu, 2018. "Many-server Gaussian limits for overloaded non-Markovian queues with customer abandonment," Queueing Systems: Theory and Applications, Springer, vol. 89(1), pages 81-125, June.
    15. J. G. Dai & Shuangchi He, 2010. "Customer Abandonment in Many-Server Queues," Mathematics of Operations Research, INFORMS, vol. 35(2), pages 347-362, May.
    16. Jun Luo & Jiheng Zhang, 2013. "Staffing and Control of Instant Messaging Contact Centers," Operations Research, INFORMS, vol. 61(2), pages 328-343, April.
    17. Achal Bassamboo & Ramandeep Singh Randhawa, 2016. "Scheduling Homogeneous Impatient Customers," Management Science, INFORMS, vol. 62(7), pages 2129-2147, July.
    18. Avishai Mandelbaum & Petar Momčilović, 2017. "Personalized queues: the customer view, via a fluid model of serving least-patient first," Queueing Systems: Theory and Applications, Springer, vol. 87(1), pages 23-53, October.
    19. 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.
    20. 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.

    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:eee:oprepe:v:2:y:2015:i:c:p:81-96. 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: Catherine Liu (email available below). General contact details of provider: http://www.journals.elsevier.com/operations-research-perspectives .

    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.