IDEAS home Printed from https://ideas.repec.org/a/bla/popmgt/v32y2023i10p3266-3285.html
   My bibliography  Save this article

A semiparametric Bayesian model for queueing arrival processes: An application to call centers

Author

Listed:
  • Kaan Kuzu
  • Refik Soyer
  • Murat T. Tarimcilar

Abstract

Nonhomogeneous Poisson process models have commonly been used to analyze and forecast arrivals. Such processes require specification of intensity (arrival rate) functions, which are typically defined in a parametric form. The accuracy of the parametric models is highly sensitive to the choice of the specific intensity function for the arrival process. We use a Bayesian framework by proposing a nonparametric form for the intensity function and introduce a robust semiparametric model. The model is suitable for analyzing both time of arrival data and interval censored count data and can capture both monotonic and non‐monotonic arrival intensity. The intensity function in the model can be modulated to incorporate auxiliary information as well as seasonal and random effect components. We develop the Bayesian analysis of the proposed model and implement it on two real call center datasets with different characteristics. We also consider several extensions to our model and develop their Bayesian analyses. Our random effects extension model with cumulative baseline intensity changing on the days of the week and interday correlation with the Markov evolution extension model both provide high predictive accuracy. We also show that our proposed semiparametric model has robust performance for out‐of‐sample predictions. Accurate predictions of arrivals will assist managers in determining appropriate staffing levels and effective workforce scheduling, resulting in more efficient operations.

Suggested Citation

  • Kaan Kuzu & Refik Soyer & Murat T. Tarimcilar, 2023. "A semiparametric Bayesian model for queueing arrival processes: An application to call centers," Production and Operations Management, Production and Operations Management Society, vol. 32(10), pages 3266-3285, October.
  • Handle: RePEc:bla:popmgt:v:32:y:2023:i:10:p:3266-3285
    DOI: 10.1111/poms.14034
    as

    Download full text from publisher

    File URL: https://doi.org/10.1111/poms.14034
    Download Restriction: no

    File URL: https://libkey.io/10.1111/poms.14034?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. Jason Merrick & Refik Soyer, 2017. "Rejoinder to ‘Semiparametric Bayesian Optimal Replacement Policies: Application to Railroad Tracks’," Applied Stochastic Models in Business and Industry, John Wiley & Sons, vol. 33(5), pages 463-464, September.
    2. Jason R. Merrick & Refik Soyer, 2017. "Semiparametric Bayesian optimal replacement policies: application to railroad tracks," Applied Stochastic Models in Business and Industry, John Wiley & Sons, vol. 33(5), pages 445-460, September.
    3. Athanassios N. Avramidis & Alexandre Deslauriers & Pierre L'Ecuyer, 2004. "Modeling Daily Arrivals to a Telephone Call Center," Management Science, INFORMS, vol. 50(7), pages 896-908, July.
    4. Aktekin, Tevfik, 2014. "Call center service process analysis: Bayesian parametric and semi-parametric mixture modeling," European Journal of Operational Research, Elsevier, vol. 234(3), pages 709-719.
    5. Song‐Hee Kim & Ward Whitt, 2014. "Choosing arrival process models for service systems: Tests of a nonhomogeneous Poisson process," Naval Research Logistics (NRL), John Wiley & Sons, vol. 61(1), pages 66-90, February.
    6. Tevfik Aktekin & Refik Soyer, 2012. "Bayesian analysis of queues with impatient customers: Applications to call centers," Naval Research Logistics (NRL), John Wiley & Sons, vol. 59(6), pages 441-456, September.
    7. Ibrahim, Rouba & Ye, Han & L’Ecuyer, Pierre & Shen, Haipeng, 2016. "Modeling and forecasting call center arrivals: A literature survey and a case study," International Journal of Forecasting, Elsevier, vol. 32(3), pages 865-874.
    8. Song-Hee Kim & Ward Whitt, 2014. "Are Call Center and Hospital Arrivals Well Modeled by Nonhomogeneous Poisson Processes?," Manufacturing & Service Operations Management, INFORMS, vol. 16(3), pages 464-480, July.
    9. Tevfik Aktekin & Tahir Ekin, 2016. "Stochastic call center staffing with uncertain arrival, service and abandonment rates: A Bayesian perspective," Naval Research Logistics (NRL), John Wiley & Sons, vol. 63(6), pages 460-478, September.
    10. Antonio Pievatolo & Fabrizio Ruggeri, 2004. "Bayesian reliability analysis of complex repairable systems," Applied Stochastic Models in Business and Industry, John Wiley & Sons, vol. 20(3), pages 253-264, July.
    11. 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.
    12. Song-Hee Kim & Ward Whitt, 2013. "Statistical Analysis with Little's Law," Operations Research, INFORMS, vol. 61(4), pages 1030-1045, August.
    13. Refik Soyer & M. Murat Tarimcilar, 2008. "Modeling and Analysis of Call Center Arrival Data: A Bayesian Approach," Management Science, INFORMS, vol. 54(2), pages 266-278, February.
    14. Weinberg, Jonathan & Brown, Lawrence D. & Stroud, Jonathan R., 2007. "Bayesian Forecasting of an Inhomogeneous Poisson Process With Applications to Call Center Data," Journal of the American Statistical Association, American Statistical Association, vol. 102, pages 1185-1198, December.
    15. Kaan Kuzu & Long Gao & Susan H. Xu, 2019. "To Wait or Not to Wait: The Theory and Practice of Ticket Queues," Manufacturing & Service Operations Management, INFORMS, vol. 21(4), pages 853-874, October.
    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. 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.
    2. Petropoulos, Fotios & Apiletti, Daniele & Assimakopoulos, Vassilios & Babai, Mohamed Zied & Barrow, Devon K. & Ben Taieb, Souhaib & Bergmeir, Christoph & Bessa, Ricardo J. & Bijak, Jakub & Boylan, Joh, 2022. "Forecasting: theory and practice," International Journal of Forecasting, Elsevier, vol. 38(3), pages 705-871.
      • Fotios Petropoulos & Daniele Apiletti & Vassilios Assimakopoulos & Mohamed Zied Babai & Devon K. Barrow & Souhaib Ben Taieb & Christoph Bergmeir & Ricardo J. Bessa & Jakub Bijak & John E. Boylan & Jet, 2020. "Forecasting: theory and practice," Papers 2012.03854, arXiv.org, revised Jan 2022.
    3. Ibrahim, Rouba & Ye, Han & L’Ecuyer, Pierre & Shen, Haipeng, 2016. "Modeling and forecasting call center arrivals: A literature survey and a case study," International Journal of Forecasting, Elsevier, vol. 32(3), pages 865-874.
    4. Ekin, Tahir & Aktekin, Tevfik, 2021. "Decision making under uncertain and dependent system rates in service systems," European Journal of Operational Research, Elsevier, vol. 291(1), pages 335-348.
    5. Kinshuk Jerath & Anuj Kumar & Serguei Netessine, 2015. "An Information Stock Model of Customer Behavior in Multichannel Customer Support Services," Manufacturing & Service Operations Management, INFORMS, vol. 17(3), pages 368-383, July.
    6. 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.
    7. Theresa Maria Rausch & Tobias Albrecht & Daniel Baier, 2022. "Beyond the beaten paths of forecasting call center arrivals: on the use of dynamic harmonic regression with predictor variables," Journal of Business Economics, Springer, vol. 92(4), pages 675-706, May.
    8. Ward Whitt & Jingtong Zhao, 2017. "Many‐server loss models with non‐poisson time‐varying arrivals," Naval Research Logistics (NRL), John Wiley & Sons, vol. 64(3), pages 177-202, April.
    9. Tevfik Aktekin & Refik Soyer, 2011. "Call center arrival modeling: A Bayesian state‐space approach," Naval Research Logistics (NRL), John Wiley & Sons, vol. 58(1), pages 28-42, February.
    10. Boris N. Oreshkin & Nazim Réegnard & Pierre L’Ecuyer, 2016. "Rate-Based Daily Arrival Process Models with Application to Call Centers," Operations Research, INFORMS, vol. 64(2), pages 510-527, April.
    11. Tevfik Aktekin & Refik Soyer, 2012. "Bayesian analysis of queues with impatient customers: Applications to call centers," Naval Research Logistics (NRL), John Wiley & Sons, vol. 59(6), pages 441-456, September.
    12. 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.
    13. Meade, Nigel & Islam, Towhidul, 2015. "Forecasting in telecommunications and ICT—A review," International Journal of Forecasting, Elsevier, vol. 31(4), pages 1105-1126.
    14. Heemskerk, M. & Mandjes, M. & Mathijsen, B., 2022. "Staffing for many-server systems facing non-standard arrival processes," European Journal of Operational Research, Elsevier, vol. 296(3), pages 900-913.
    15. Barrow, Devon & Kourentzes, Nikolaos, 2018. "The impact of special days in call arrivals forecasting: A neural network approach to modelling special days," European Journal of Operational Research, Elsevier, vol. 264(3), pages 967-977.
    16. Rouba Ibrahim & Pierre L'Ecuyer, 2013. "Forecasting Call Center Arrivals: Fixed-Effects, Mixed-Effects, and Bivariate Models," Manufacturing & Service Operations Management, INFORMS, vol. 15(1), pages 72-85, May.
    17. René Bekker & Dennis Moeke & Bas Schmidt, 2019. "Keeping pace with the ebbs and flows in daily nursing home operations," Health Care Management Science, Springer, vol. 22(2), pages 350-363, June.
    18. Albrecht, Tobias & Rausch, Theresa Maria & Derra, Nicholas Daniel, 2021. "Call me maybe: Methods and practical implementation of artificial intelligence in call center arrivals’ forecasting," Journal of Business Research, Elsevier, vol. 123(C), pages 267-278.
    19. Smirnov, Dmitry & Huchzermeier, Arnd, 2020. "Analytics for labor planning in systems with load-dependent service times," European Journal of Operational Research, Elsevier, vol. 287(2), pages 668-681.
    20. Ding, S. & Koole, G. & van der Mei, R.D., 2015. "On the estimation of the true demand in call centers with redials and reconnects," European Journal of Operational Research, Elsevier, vol. 246(1), pages 250-262.

    More about this item

    Statistics

    Access and download statistics

    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:bla:popmgt:v:32:y:2023:i:10:p:3266-3285. 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: Wiley Content Delivery (email available below). General contact details of provider: http://onlinelibrary.wiley.com/journal/10.1111/(ISSN)1937-5956 .

    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.