#04-17
Statistical Analysis of a Telephone Call Center:
A Queuing-Science Perspective
Lawrence Brown, Noah Gans, Avishai Mandelbaum,
Anat Sakov, Haipeng Shen, Sergey Zeltyn, and
Linda Zhao
Abstract: TA 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 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 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 educed from the statistical analyses form the building
blocks for theoretically interesting and practically useful mathematical models for call center operations.
Keywords: call centers, queueing theory, multiserver queues, Erlang-C, Erlang-A, queueing science, arrivals, abandonment, service times, lognormal distribution, inhomogeneous Poisson process, censored data, human patience, prediction of Poisson rates, Khintchine-Pollaczek formula.
JEL classification:
