Identifying lossy links in wired/wireless networks by exploiting sparse characteristics

In this paper, we consider the problem of estimating link loss rates based on end-to-end path loss rates in order to identify lossy links on the network. We first derive a maximum likelihood estimate for the problem and show that the problem boils down to the matrix inversion problem for an under-determined system of linear equations. Without any prior knowledge of the statistics of packet loss rates, most of the existing work uses the minimum norm solution for the under-determined linear system. We devise, under the assumption that link failures are abnormal events in real networks and lossy links are sparse among all the internal links, an iterative algorithm to identify non-lossy links and to remove the corresponding terms from the under-determined linear system. To identify non-lossy links, we propose to use three different criteria (and a combination thereof): the criterion determined by a basis selection technique, that obtained by sorting path loss rates, and that determined by the minimum norm least square solution. We show via simulation and empirical studies on the MIT Roofnet traces that the computational complexity of the iterative algorithm is comparable to that of the minimum norm least square approach, and that the solution obtained under the iterative algorithm achieves high coverage of lossy links, while incurring only a small number of false positives in various network scenarios. (c) 2007 Elsevier B.V. All rights reserved.