Generalized network tomography

For successful estimation, the usual network tomography algorithms crucially require i) end-to-end data generated using multicast probe packets, real or emulated, and ii) the network to be a tree rooted at a single sender with destinations at leaves. These requirements, consequently, limit their scope of application. In this paper, we address successfully a general problem, henceforth called generalized network tomography, wherein the objective is to estimate the link performance parameters for networks with arbitrary topologies using only end-to-end measurements of pure unicast probe packets. Mathematically, given a binary matrix A, we propose a novel algorithm to uniquely estimate the distribution of X, a vector of independent non-negative random variables, using only IID samples of the components of the random vector Y = AX. This algorithm, in fact, does not even require any prior knowledge of the unknown distributions. The idea is to approximate the distribution of each component of X using linear combinations of known exponential bases and estimate the unknown weights. These weights are obtained by solving a set of polynomial systems based on the moment generating function of the components of Y. For unique identifiability, it is only required that every pair of columns of the matrix A be linearly independent, a property that holds true for the routing matrices of all multicast tree networks. Matlab based simulations have been included to illustrate the potential of the proposed scheme.