ABSTRACT
Our professional and personal lives now depend on the internet. The
heterogeneous and largely unregulated structure of the Internet renders
tasks such as dynamic routing, optimized service provision, service level
verification, and detection of anomalous/malicious behavior extremely
challenging. The problem is compounded by the fact that one cannot rely on the cooperation of individual servers and routers to aid in the collection
of network traffic measurements vital for these tasks. In many ways,
network monitoring and inference problems bear a strong resemblance to other ``inverse problems'' in which key aspects of a system are not directly observable. This emerging new field is called {\em Internet Tomography}.

In this talk, I will first review the general problem of linear internet
tomography (cf. Coates, Hero, Nowak, and Yu, 2002, SP Magazine) and then conver in depth a special case: the estimation of Origin-Destination (OD) traffic matrix via link counts. The OD traffic information is very important for dynamic updating of routing tables for networks. Our approach to the OD estimation problem relies on a Gaussian model with a power relationship between the mean and variance of OD traffic over a fixed small time interval (e.g. 5 or 10 min) (cf. Cao, Davis, Vander Wiel and Yu, 2000, J. Amer. Statist. Assoc.). Recognizing Maximum Likelihood Estimation (MLE) for solving inverse problems in internet tomography is usually computationally intractable for large networks, we use (Liang and Yu, IEEE-SP, 2003) a maximum pseudo-likelihood estimation (MPLE) approach to solve a group of internet tomography problems including the OD problem.
MPLE keeps a good balance between the computational complexity and the statistical efficiency of the parameter estimation. A
pseudo-expectation-maximization (EM) algorithm is developed to maximize the pseudo-log-likelihood function. Finally, we will present some recent work (Liang, Yu and Taft, 2003) using a Sprint network data set with validation to compare our approach with that of the ATT group.

Refreshments will be served at 3:45 p.m. in Room 008 of the Statistics
Building