Network link tomography and compressive sensing

Abstract

Accurate and timely performance data are of vital importance for network administration. However, modern networks are so large and transmit such enormous quantities of data that a single backbone link could fill a terabyte drive in about 3 minutes. Taking and processing all the desirable performance measurements can be wildly impractical. Aside from matters of scale there may be other difficulties, such as unreliable measurement that mean network administrators cannot make all the performance measurements they desire. Consequently, it is necessary to make the most of the measurements that are available. Network Tomography does just that, by inferring underlying performance statistics from the available measurements. This paper considers the problem of link loss tomography: inference of link parameters from a series of end-to-end probes through a network. We specifically estimate average link loss rates. Typical problems in this setting are highly underconstrained, and so the measurements often admit infinitely many solutions. Some method is needed to select the correct solution from this possible set, and in this paper we shall use sparsity. Network tomography is a well developed field [1, 4, 7]. However, the vast majority of performance tomography has concentrated on trees. In that setting, it is possible to develop fast, recursive algorithms [2, 4], and to employ side information such as sparsity relatively easily [3]. However, many networks are not trees. Some work has looked at combining measurements from multiple tree-like views of the network [6], however, the approach meets immediate difficulties. Intuitively we can see that it would be hard to use sparsity in the same way because there is no longer a “top” of the tree towards which we can push “bad” links. In this paper we attack the problem on a general network. We exploit sparsity, but without reducing the problem to a binary problem. We test the idea of applying the field of Compressive Sensing to this link tomography problem. Compressive Sensing exploits the fact that many large data-sets are comprised of only a few significant elements. In practice, this means that either the data itself, or some simple transform of the data, is sparse in the sense that only a few of the values are non-zero. Compressive Sensing is a rapidly growing area of research, and there are many pow-