Avishai Mandelbaum

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.

Queueing models of call centers: An introduction

This is a survey of some academic research on telephone call centers. The surveyed research has its origin in, or is related to, queueing theory. Indeed, the “queueing-view” of call centers is both natural and useful. Accordingly, queueing models have served as prevalent standard support tools for call center management. However, the modern call center is a complex socio-technical system. It thus enjoys central features that challenge existing queueing theory to its limits, and beyond.The present document is an abridged version of a survey that can be downloaded from www.cs.vu.nl/obp/callcenters and ie.technion.ac.il/∼serveng.

Strong approximations for Markovian service networks

Inspired by service systems such as telephone call centers, we develop limit theorems for a large class of stochastic service network models. They are a special family of nonstationary Markov processes where parameters like arrival and service rates, routing topologies for the network, and the number of servers at a given node are all functions of time as well as the current state of the system. Included in our modeling framework are networks of Mt/Mt/nt queues with abandonment and retrials. The asymptotic limiting regime that we explore for these networks has a natural interpretation of scaling up the number of servers in response to a similar scaling up of the arrival rate for the customers. The individual service rates, however, are not scaled. We employ the theory of strong approximations to obtain functional strong laws of large numbers and functional central limit theorems for these networks. This gives us a tractable set of network fluid and diffusion approximations. A common theme for service network models with features like many servers, priorities, or abandonment is “non-smooth” state dependence that has not been covered systematically by previous work. We prove our central limit theorems in the presence of this non-smoothness by using a new notion of derivative.

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):

Adaptive Behavior of Impatient Customers in Tele-Queues: Theory and Empirical Support

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

Service-Level Differentiation in Call Centers with Fully Flexible Servers

Quality-Driven (QD):

On patient flow in hospitals: A data-based queueing-science perspective

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