Network Tomography: Identifiability and Fourier Domain Estimation

The statistical problem for network tomography is to infer the distribution of X, with mutually independent components, from a measurement model Y = AX, where A is a given binary matrix representing the routing topology of a network under consideration. The challenge is that the dimension of X is much larger than that of Y and thus the problem is often ill-posed. This paper studies some statistical aspects of network tomography. We first develop a unifying theory on the identifiability of the distribution of X. We then focus on an important instance of network tomography-network delay tomography, where the problem is to infer internal link delay distributions using end-to-end delay measurements. We propose a novel mixture model for link delays and develop a fast algorithm for estimation based on the General Method of Moments. Through extensive model simulations and real Internet trace driven simulation, the proposed approach is shown to be favorable to previous methods using simple discretization for inferring link delays in a heterogeneous network.