Method of One Dimensional Projections for Network Tomography

Network tomography has been regarded as one of the most promising methodologies for performance evaluation and diagnosis of the massive and decentralized Internet. This paper proposes a new estimation approach for solving a class of inverse problems in network tomography. Rather than using the multivariate distribution of observed data, the statistical inference is based on the marginal distributions of a sequence of its one-dimensional linear projections. We give a general identifiability result for the proposed method and study the design issue of these one dimensional projections in terms of statistical efficiency. We show that for a simple Gaussian tomography model, there is an optimal set of one-dimensional projections such that the estimator obtained from these projections is asymptotically as efficient as the usual maximum likelihood estimator. For practical applications, we carry out simulation studies of the proposed method for two instances of network tomography, one for traffic demand tomography using a Gaussian Origin-Destination traffic model with a power relation between its mean and variance, and the other for network delay tomography where the link delays are to be estimated from the end-to-end path delays. In both cases, the proposed method yields satisfactory results.