A Failure Analysis of the Tomogravity and EM Methods

Abstract — A traffic matrix provides a major input to the design, planning and management of a telecommunications network. Unfortunately, computation of the traffic matrix from measurements of individual flows is extremely difficult due to the fact that the problem formulation generally leads to the need to solve an under-determined system of equations. Thus, there has been a major effort from among researchers to obtain the traffic matrix using various inference techniques. In this paper, we have studied the impact of the underlying assumptions for two methods that have shown promise in the estimation of Internet traffic demand matrices known as the Tomogravity and EM (Expectation and Maximization) methods respectively. As the Tomogravity model is a combination of the well-known gravity model and the method of least squares we have also considered the problem of obtaining a good prior traffic matrix for the least squares component of this model. We have demonstrated that the accuracy of these methods is highly dependent upon the underlying assumptions of these models, as well as the selection of an appropriate prior traffic matrix. Index Terms — Traffic Matrix, Tomogravity, EM method I