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.

An algorithm for determination of the number of modes in a gray-level image histogram is presented in this paper. The hypothesis is that the image histogram's pdf is approached by a mixture of Gaussians. Then, the algorithm tries to estimate the number of components in the mixture, which is an important parameter when using the maximum likelihood technique to estimate the remaining of parameters of the mixture. The algorithm is divided into two parts. First, initial clustering using the k-means algorithm is performed. This allows to estimate the centers of each cluster. Second, a novel algorithm, denoted "Elimination of False Clusters" (EFC) based on the Gaussian characteristics tries to suppress clusters which have no corresponding modes in the histogram. The algorithm has been validated on both artificial and real histograms. Keywords: pdf estimation, mixture models, unsupervised learning, gray-level image histogram 1 INTRODUCTION Estimation of a histogram's probability density fu...

First of all, I wish to devote my sincere thanks and deep appreciation to my dissertation advisor, Professor Lawrence D. Brown, for his tremendous amount of encouragement, guidance and financial support during the development of my research. It is he who has brought me into the wonderful world of Statistics. It is him that I will keep learning from and living up to through the rest of my life. Special thanks are due to all those people who had advised and helped me at important steps of my life, among whom are Noah Gans, Jianhua Huang, Paul Shaman