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Designing a Call Center with Impatient Customers


  • O. Garnet

    () (Davidson Faculty of Industrial Engineering and Management, Technion, Haifa 32000, Israel)

  • A. Mandelbaum

    () (Davidson Faculty of Industrial Engineering and Management, Technion, Haifa 32000, Israel)

  • M. Reiman

    () (Bell Laboratories, Murray Hill, New Jersey 07974)


The most common model to support workforce management of telephone call centers is the M/M/N/B model, in particular its special cases M/M/N (Erlang C, which models out busy signals) and M/M/N/N (Erlang B, disallowing waiting). All of these models lack a central prevalent feature, namely, that impatient customers might decide to leave (abandon) before their service begins. In this paper, we analyze the simplest abandonment model, in which customers' patience is exponentially distributed and the system's waiting capacity is unlimited (M/M/N + M). Such a model is both rich and analyzable enough to provide information that is practically important for call-center managers. We first outline a method for exact analysis of the M/M/N + M model, that while numerically tractable is not very insightful. We then proceed with an asymptotic analysis of the M/M/N + M model, in a regime that is appropriate for large call centers (many agents, high efficiency, high service level). Guided by the asymptotic behavior, we derive approximations for performance measures and propose "rules of thumb" for the design of large call centers. We thus add support to the growing acknowledgment that insights from diffusion approximations are directly applicable to management practice.

Suggested Citation

  • O. Garnet & A. Mandelbaum & M. Reiman, 2002. "Designing a Call Center with Impatient Customers," Manufacturing & Service Operations Management, INFORMS, vol. 4(3), pages 208-227, October.
  • Handle: RePEc:inm:ormsom:v:4:y:2002:i:3:p:208-227
    DOI: 10.1287/msom.

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    References listed on IDEAS

    1. Hoffman, Karla L. & Harris, Carl M., 1986. "Estimation of a caller retrial rate for a telephone information system," European Journal of Operational Research, Elsevier, vol. 27(2), pages 207-214, October.
    2. Ward Whitt, 1992. "Understanding the Efficiency of Multi-Server Service Systems," Management Science, INFORMS, vol. 38(5), pages 708-723, May.
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    Cited by:

    1. Aguir, M. Salah & Aksin, O. Zeynep & Karaesmen, Fikri & Dallery, Yves, 2008. "On the interaction between retrials and sizing of call centers," European Journal of Operational Research, Elsevier, vol. 191(2), pages 398-408, December.
    2. Kaplan, Edward H., 2013. "Staffing models for covert counterterrorism agencies," Socio-Economic Planning Sciences, Elsevier, vol. 47(1), pages 2-8.
    3. Walsh Zuñiga, Alexander, 2014. "Fluid limits of many-server queues with abandonments, general service and continuous patience time distributions," Stochastic Processes and their Applications, Elsevier, vol. 124(3), pages 1436-1468.
    4. repec:eee:ejores:v:261:y:2017:i:3:p:1110-1124 is not listed on IDEAS
    5. Dietz, Dennis C., 2011. "Practical scheduling for call center operations," Omega, Elsevier, vol. 39(5), pages 550-557, October.
    6. Jouini, Oualid & Pot, Auke & Koole, Ger & Dallery, Yves, 2010. "Online scheduling policies for multiclass call centers with impatient customers," European Journal of Operational Research, Elsevier, vol. 207(1), pages 258-268, November.
    7. Sobkowicz, Pawel, 2016. "Agent based model of effects of task allocation strategies in flat organizations," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 458(C), pages 17-30.
    8. repec:eee:ejores:v:265:y:2018:i:3:p:919-930 is not listed on IDEAS
    9. 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.
    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. Liu, Yunan & Whitt, Ward, 2017. "Stabilizing performance in a service system with time-varying arrivals and customer feedback," European Journal of Operational Research, Elsevier, vol. 256(2), pages 473-486.
    12. repec:eee:ejores:v:276:y:2019:i:2:p:614-625 is not listed on IDEAS
    13. Lee, Chihoon & Weerasinghe, Ananda, 2011. "Convergence of a queueing system in heavy traffic with general patience-time distributions," Stochastic Processes and their Applications, Elsevier, vol. 121(11), pages 2507-2552, November.
    14. 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.
    15. 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.
    16. 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.


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