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Statistical Analysis of a Telephone Call Center: A Queueing-Science Perspective

Author

Listed:
  • Lawrence Brown
  • Noah Gans
  • Avishai Mandelbaum
  • Anat Sakov
  • Haipeng Shen
  • Sergey Zeltyn
  • Linda Zhao
  • Novemer

Abstract

A call center is a service network in which agents provide telephone-based services. Customers that seek these services are delayed in tele-queues. This paper summarizes an analysis of a unique record of call center operations. The data comprise a complete operational history of a small banking call center, call by call, over a full year. Taking the perspective of queueing theory, we decompose the service process into three fundamental components: arrivals, customer abandonment behavior and service durations. Each component involves different basic mathematical structures and requires a different style of statistical analysis. Some of the key empirical results are sketched, along with descriptions of the varied techniques required. Several statistical techniques are developed for analysis of the basic components. One of these is a test that a point process is a Poisson process. Another involves estimation of the mean function in a nonparametric regression with lognormal errors. A new graphical technique is introduced for nonparametric hazard rate estimation with censored data. Models are developed and implemented for forecasting of Poisson arrival rates. We then survey how the characteristics deduced from the statistical analyses form the building blocks for theoretically interesting and practically useful mathematical models for call center operations. Key Words: call centers, queueing theory, lognormal distribution, inhomogeneous Poisson process, censored data, human patience, prediction of Poisson rates, Khintchine-Pollaczek formula, service times, arrival rate, abandonment rate, multiserver queues.

Suggested Citation

  • Lawrence Brown & Noah Gans & Avishai Mandelbaum & Anat Sakov & Haipeng Shen & Sergey Zeltyn & Linda Zhao & Novemer, "undated". "Statistical Analysis of a Telephone Call Center: A Queueing-Science Perspective," Center for Financial Institutions Working Papers 03-12, Wharton School Center for Financial Institutions, University of Pennsylvania.
    • Handle: RePEc:wop:pennin:03-12
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    References listed on IDEAS

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    1. Ety Zohar & Avishai Mandelbaum & Nahum Shimkin, 2002. "Adaptive Behavior of Impatient Customers in Tele-Queues: Theory and Empirical Support," Management Science, INFORMS, vol. 48(4), pages 566-583, April.
    2. 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.
    3. David Y. Sze, 1984. "OR Practice—A Queueing Model for Telephone Operator Staffing," Operations Research, INFORMS, vol. 32(2), pages 229-249, April.
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