Sergey Zeltyn

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

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.

Call Centers with Impatient Customers: Many-Server Asymptotics of the M/M/n + G Queue

AbstractThe subject of the present research is the M/M/n + G queue. This queue is characterized by Poisson arrivals at rate λ, exponential service times at rate μ, n service agents and generally distributed patience times of customers. The model is applied in the call center environment, as it captures the tradeoff between operational efficiency (staffing cost) and service quality (accessibility of agents).In our research, three asymptotic operational regimes for medium to large call centers are studied. These regimes correspond to the following three staffing rules, as λ and n increase indefinitely and μ held fixed: Efficiency-Driven (ED):

Service Engineering in Action: The Palm/Erlang-A Queue, with Applications to Call Centers

n\ \approx \ (\lambda / \mu)\cdot (1 - \gamma),\gamma > 0,

Simulation-based models of emergency departments:: Operational, tactical, and strategic staffing

Quality-Driven (QD):

Waiting and sojourn times in a multi-server queue with mixed priorities

n \ \approx \ ( \lambda / \mu)\cdot (1 + \gamma),\gamma > 0

Service Engineering of Call Centers: Research, Teaching, and Practice

, andQuality and Efficiency Driven (QED):