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Designing a call center with an IVR (Interactive Voice Response)

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Abstract

A call center is a service operation that caters to customer needs via the telephone. Call centers typically consist of agents that serve customers, telephone lines, an Interactive Voice Response (IVR) unit, and a switch that routes calls to agents. In this paper we study a Markovian model for a call center with an IVR. We calculate operational performance measures, such as the probability for a busy signal and the average wait time for an agent. Exact calculations of these measures are cumbersome and they lack insight. We thus approximate the measures in an asymptotic regime known as QED (Quality and Efficiency Driven) or the Halfin–Whitt regime, which accommodates moderate to large call centers. The approximations are both insightful and easy to apply (for up to 1000’s of agents). They yield, as special cases, known and novel approximations for the M/M/N/N (Erlang-B), M/M/S (Erlang-C) and M/M/S/N queue.

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References

  1. Borst, S., Mandelbaum, A., Reiman, M.: Dimensioning large call centers. Oper. Res. 52(1), 17–34 (2004)

    Article  Google Scholar 

  2. Brandt, A., Brandt, M., Spahl, G., Weber, D.: Modelling and Optimization of Call Distribution Systems. Elsevier, Amsterdam (1997)

    Google Scholar 

  3. Brown, L., Gans, N., Mandelbaum, A., Sakov, A., Zeltyn, S., Zhao, L., Haipeng, S.: Statistical analysis of a telephone call center: a queueing-science perspective. J. Am. Stat. Assoc. 100, 36–50 (2005)

    Article  Google Scholar 

  4. Chen, H., Yao, D.D.: Fundamentals of Queueing Networks. Springer, Berlin (2001)

    Google Scholar 

  5. Donin, O., Feigin, P., Ishay, E., Khudyakov, P., Mandelbaum, A., Nadjarov, E., Trofimov, V., Zeltyn, S.: DATA-MOCCA: Data MOdel for Call Center Analysis. The Call Center of “US Bank”, vol. 4.1 (2006). Available at http://ie.technion.ac.il/Labs/Serveng/SEE_Documents_List.php

  6. Erlang, A.K.: On the rational determination of the number of circuits. In: Brochmeyer, E., Halstrom, H.L., Jensen, A. (eds.) The Life and Works of A.K. Erlang. The Copenhagen Telephone Company. 4.1.1, 4.2.1, Copenhagen (1948)

    Google Scholar 

  7. Gans, N., Koole, G., Mandelbaum, A.: Telephone call centers: tutorial, review, and research prospects. Manuf. Serv. Oper. Manag. 5(2), 79–141 (2003)

    Article  Google Scholar 

  8. Garnett, O., Mandelbaum, A., Reiman, M.: Designing a call center with impatient customers. Manuf. Serv. Oper. Manag. 4(3), 208–227 (2002)

    Article  Google Scholar 

  9. Gilson, K.A., Khandelwal, D.K.: Getting more from call centers. The McKinsey Quarterly, Web exclusive (2005). Available at http://www.mckinseyquarterly.com/article_page.aspx

  10. Halfin, S., Whitt, W.: Heavy-traffic limits for queues with many exponential servers. Oper. Res. 29, 567–587 (1981)

    Article  Google Scholar 

  11. Jagerman, D.L.: Some properties of the Erlang loss function. Bell Syst. Tech. J. 53(3), 525–551 (1974)

    Google Scholar 

  12. Jelenkovic, P., Mandelbaum, A., Momcilovic, P.: Heavy traffic limits for queues with many deterministic servers. Queueing Syst. 47, 53–69 (2004)

    Article  Google Scholar 

  13. Khudyakov, P.: Designing a call center with an IVR (Interactive Voice Response). M.Sc. Thesis, Technion (2006). Available at http://iew3.technion.ac.il/serveng/References/references.html

  14. Khudyakov, P., Feigin, P., Mandelbaum, A.: Internet Supplement to the paper: Designing a call center with an IVR (Interactive Voice Response) (2010). Available at http://iew3.technion.ac.il/serveng/References/references.html

  15. Liberman, P., Trofimov, V., Mandelbaum, A.: DATA-MOCCA: Data MOdel for Call Center Analysis. Skills-Based-Routing-USBank, vol. 5.1 (2008). Available at http://iew3.technion.ac.il/serveng/References/

  16. Maman, S.: Uncertainty in the demand for service: the case of call centers and emergency departments. M.Sc. Thesis, Technion (2009). Available at http://iew3.technion.ac.il/serveng/References/references.html

  17. Mandelbaum, A.: Lecture notes on QED queues. Available at http://iew3.technion.ac.il/serveng/Lectures

  18. Mandelbaum, A., Zeltyn, S.: Call centers with impatient customers: many-server asymptotics of the M/M/n + G queue. Queueing Syst. 51, 361–402 (2005). Available at http://iew3.technion.ac.il/serveng/References/references.html

    Article  Google Scholar 

  19. Massey, A.W., Wallace, B.R.: An optimal design of the M/M/C/K queue for call centers (to appear)

  20. Pang, R., Talreja, R., Whitt, W.: Martingale proofs of many-server heavy-traffic limits for Markovian queues. Probab. Surv. 4, 193–267 (2007). Available at http://www.columbia.edu/~ww2040/PangTalrejaWhitt2007pub.pdf

    Article  Google Scholar 

  21. Stolletz, R.: Performance Analysis and Optimization of Inbound Call Centers. Springer, Berlin (2003)

    Google Scholar 

  22. Srinivasan, R., Talim, J., Wang, J.: Performance analysis of a call center with interacting voice response units. TOP 12, 91–110 (2004)

    Article  Google Scholar 

  23. Trofimov, V., Feigin, P., Mandelbaum, A., Ishay, E., Nadjarov, E.: DATA-MOCCA: Data MOdel for Call Center Analysis. Model Description and Introduction to User Interface, vol. 1 (2006). Available at http://iew3.technion.ac.il/serveng/References/references.html

  24. Weerasinghe, A., Mandelbaum, A.: Abandonment vs. blocking in many-server queues: asymptotic optimality in the QED regime. Working paper (2008)

  25. Whitt, W.: Understanding the efficiency of multi-server service systems. Manag. Sci. 38, 708–723 (1992)

    Article  Google Scholar 

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Authors and Affiliations

  1. Faculty of Industrial Engineering and Management, Technion–Israel Institute of Technology, Haifa, Israel

    Polyna Khudyakov, Paul D. Feigin & Avishai Mandelbaum

Authors
  1. Polyna Khudyakov
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  2. Paul D. Feigin
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  3. Avishai Mandelbaum
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Corresponding author

Correspondence to Polyna Khudyakov.

Additional information

The research was supported by BSF (Binational Science Foundation) grant 2001685/2005175, ISF (Israeli Science Foundation) grants 388/99, 126/02 and 1046/04 and by the Technion funds for the promotion of research and sponsored research.

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Khudyakov, P., Feigin, P.D. & Mandelbaum, A. Designing a call center with an IVR (Interactive Voice Response). Queueing Syst 66, 215–237 (2010). https://doi.org/10.1007/s11134-010-9193-y

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  • DOI: https://doi.org/10.1007/s11134-010-9193-y

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