Generalized Kruithof approach for traffic matrix estimation

[Abstract]: In this paper, the traffic matrix estimation problem is formulated as an nonlinear optimization problem based on the generalized Kruithof approach which uses the Kullback distance to measure the probabilistic distance between two traffic matrices. In addition, an algorithm using the affine scaling method is provided to solve the constraint optimization problem

A Unique "Nonnegative" Solution to an Underdetermined System: from Vectors to Matrices

This paper investigates the uniqueness of a nonnegative vector solution and the uniqueness of a positive semidefinite matrix solution to underdetermined linear systems. A vector solution is the unique solution to an underdetermined linear system only if the measurement matrix has a row-span intersecting the positive orthant. Focusing on two types of binary measurement matrices, Bernoulli 0-1 matrices and adjacency matrices of general expander graphs, we show that, in both cases, the support size of a unique nonnegative solution can grow linearly, namely O(n), with the problem dimension n. We also provide closed-form characterizations of the ratio of this support size to the signal dimension. For the matrix case, we show that under a necessary and sufficient condition for the linear compressed observations operator, there will be a unique positive semidefinite matrix solution to the compressed linear observations. We further show that a randomly generated Gaussian linear compressed observations operator will satisfy this condition with overwhelmingly high probability

Robust routing

In a network, traffic demands are known with a degree of uncertainty, traffic engineering should take into account the traffic variability. In this research work we focus on the robust routing under changing network conditions. Daily Internet traffic pattern shows that network is vulnerable to malicious attacks, denial of service attacks, worms and viruses. Oblivious routing has a substantially better performance than open shortest path first [OSPF] routing for different level of uncertainty. We propose a theoretical framework for Robust Routing aiming to improve online and offline traffic engineering approaches

Traffic matrix estimation on a large IP backbone: a comparison on real data

This paper considers the problem of estimating the point-to-point traffic matrix in an operational IP backbone. Contrary to previous studies, that have used a partial traffic matrix or demands estimated from aggregated Netflow traces, we use a unique data set of complete traffic matrices from a global IP network measured over five-minute intervals. This allows us to do an accurate data analysis on the time-scale of typical link-load measurements and enables us to make a balanced evaluation of different traffic matrix estimation techniques. We describe the data collection infrastructure, present spatial and temporal demand distributions, investigate the stability of fan-out factors, and analyze the mean-variance relationships between demands. We perform a critical evaluation of existing and novel methods for traffic matrix estimation, including recursive fanout estimation, worst-case bounds, regularized estimation techniques, and methods that rely on mean-variance relationships. We discuss the weaknesses and strengths of the various methods, and highlight differences in the results for the European and American subnetworks