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

• Published in: Journal of the American Statistical Association 2005-03, Vol.100 (469), p.36-50
• Main Authors: Brown, Lawrence, Gans, Noah, Mandelbaum, Avishai, Sakov, Anat, Shen, Haipeng, Zeltyn, Sergey, Zhao, Linda
• Format: Article
• Language: English
• Subjects: Abandonment; Applications; Applications and Case Studies; Applied sciences; Approximation; Arrivals; Call center; Call centers; Censored data; Confidence interval; Erlang-A; Erlang-C; Estimation methods; Exact sciences and technology; Human patience; Inference from stochastic processes; time series analysis; Inhomogeneous poisson process; Insurance, economics, finance; Khintchine-Pollaczek formula; Lognormal distribution; Mathematical models; Mathematics; Modeling; Multiserver queue; Null hypothesis; Operational research and scientific management; Operational research. Management science; Poisson distribution; Poisson process; Prediction of poisson rates; Probability and statistics; Probability theory and stochastic processes; Queueing science; Queueing theory; Queuing theory; Queuing theory. Traffic theory; Sciences and techniques of general use; Service time; Special processes (renewal theory, markov renewal processes, semi-markov processes, statistical mechanics type models, applications); Statistical analysis; Statistical variance; Statistics; Telephone service; Telephones
• ISSN: 0162-1459; 1537-274X
• DOI: 10.1198/016214504000001808

A call center is a service network in which agents provide telephone-based services. Customers who seek these services are delayed in tele-queues. This article 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 patience, 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 techniques 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. Finally, the article surveys how the characteristics deduced from the statistical analyses form the building blocks for theoretically interesting and practically useful mathematical models for call center operations.