IDEAS home Printed from https://ideas.repec.org/a/inm/ormsom/v16y2014i3p464-480.html
   My bibliography  Save this article

Are Call Center and Hospital Arrivals Well Modeled by Nonhomogeneous Poisson Processes?

Author

Listed:
  • Song-Hee Kim

    (Department of Industrial Engineering and Operations Research, Columbia University, New York, New York 10027)

  • Ward Whitt

    (Department of Industrial Engineering and Operations Research, Columbia University, New York, New York 10027)

Abstract

Service systems such as call centers and hospitals typically have strongly time-varying arrivals. A natural model for such an arrival process is a nonhomogeneous Poisson process (NHPP), but that should be tested by applying appropriate statistical tests to arrival data. Assuming that the NHPP has a rate that can be regarded as approximately piecewise-constant, a Kolmogorov–Smirnov (KS) statistical test of a Poisson process (PP) can be applied to test for a NHPP by combining data from separate subintervals, exploiting the classical conditional-uniform property. In this paper, we apply KS tests to banking call center and hospital emergency department arrival data and show that they are consistent with the NHPP property, but only if that data is analyzed carefully. Initial testing rejected the NHPP null hypothesis because it failed to account for three common features of arrival data: (i) data rounding, e.g., to seconds; (ii) choosing subintervals over which the rate varies too much; and (iii) overdispersion caused by combining data from fixed hours on a fixed day of the week over multiple weeks that do not have the same arrival rate. In this paper, we investigate how to address each of these three problems.

Suggested Citation

  • 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.
    • Handle: RePEc:inm:ormsom:v:16:y:2014:i:3:p:464-480
    DOI: 10.1287/msom.2014.0490
    as

    Download full text from publisher

    File URL: http://dx.doi.org/10.1287/msom.2014.0490
    Download Restriction: no
    File URL: https://libkey.io/10.1287/msom.2014.0490?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. 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.
    2. Marsaglia, George & Tsang, Wai Wan & Wang, Jingbo, 2003. "Evaluating Kolmogorov's Distribution," Journal of Statistical Software, Foundation for Open Access Statistics, vol. 8(i18).
    3. 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.
    4. Guodong Pang & Ward Whitt, 2012. "The Impact of Dependent Service Times on Large-Scale Service Systems," Manufacturing & Service Operations Management, INFORMS, vol. 14(2), pages 262-278, April.
    5. Md Asaduzzaman & Thierry Chaussalet & Nicola Robertson, 2010. "A loss network model with overflow for capacity planning of a neonatal unit," Annals of Operations Research, Springer, vol. 178(1), pages 67-76, July.
    6. 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.
    7. 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.
    8. Geurt Jongbloed & Ger Koole, 2001. "Managing uncertainty in call centres using Poisson mixtures," Applied Stochastic Models in Business and Industry, John Wiley & Sons, vol. 17(4), pages 307-318, October.
    9. Litvak, Nelly & van Rijsbergen, Marleen & Boucherie, Richard J. & van Houdenhoven, Mark, 2008. "Managing the overflow of intensive care patients," European Journal of Operational Research, Elsevier, vol. 185(3), pages 998-1010, March.
    10. Simard, Richard & L'Ecuyer, Pierre, 2011. "Computing the Two-Sided Kolmogorov-Smirnov Distribution," Journal of Statistical Software, Foundation for Open Access Statistics, vol. 39(i11).
    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. 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.
    2. 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.
    3. 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.
    4. 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.
    5. 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.
    6. 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.
    7. Alex Roubos & Ger Koole & Raik Stolletz, 2012. "Service-Level Variability of Inbound Call Centers," Manufacturing & Service Operations Management, INFORMS, vol. 14(3), pages 402-413, July.
    8. 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.
    9. 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.
    10. 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.
    11. 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.
    12. Ward Whitt, 2006. "Staffing a Call Center with Uncertain Arrival Rate and Absenteeism," Production and Operations Management, Production and Operations Management Society, vol. 15(1), pages 88-102, March.
    13. 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.
    14. Ibrahim, Rouba & L’Ecuyer, Pierre & Shen, Haipeng & Thiongane, Mamadou, 2016. "Inter-dependent, heterogeneous, and time-varying service-time distributions in call centers," European Journal of Operational Research, Elsevier, vol. 250(2), pages 480-492.
    15. Haipeng Shen & Jianhua Z. Huang, 2008. "Interday Forecasting and Intraday Updating of Call Center Arrivals," Manufacturing & Service Operations Management, INFORMS, vol. 10(3), pages 391-410, July.
    16. James W. Taylor, 2008. "A Comparison of Univariate Time Series Methods for Forecasting Intraday Arrivals at a Call Center," Management Science, INFORMS, vol. 54(2), pages 253-265, February.
    17. 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.
    18. 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.
    19. 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.
    20. Yunan Liu & Ward Whitt & Yao Yu, 2016. "Approximations for heavily loaded G/GI/n + GI queues," Naval Research Logistics (NRL), John Wiley & Sons, vol. 63(3), pages 187-217, 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:inm:ormsom:v:16:y:2014:i:3:p:464-480. 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.