Network Tomography: Identifiability and Fourier Domain Estimation

Network tomography has been regarded as one of the most promising methodologies for performance evaluation and diagnosis of the massive and decentralized Internet. It can be used to infer unobservable network behaviors from directly measurable metrics and it does not require cooperation between the network internal elements and the end users. For instance, the Internet users may estimate the link level characteristics such as loss and delay from end-to-end measurements, whereas the network operators can evaluate the Internet path-level traffic intensity based on link-level traffic measurements. In this paper, we present a novel estimation approach for the network tomography problem. Unlike previous likelihood based methods, our approach is based on characteristic functions, i.e. the Fourier transform, of the distributions of observed measurements. We focus on network delay tomography and develop a Fourier domain inference algorithm based on flexible mixture models of link delays. Through extensive model simulation and simulation using real Internet trace, we are able to demonstrate that the new algorithm is computationally more efficient and yields more accurate estimates than previous methods, especially for a network with heterogeneous link delays. In addition, we obtain some identifiability results that can be applied to general distribution models for link delays.