Person:

Liu, Jun

As an active branch of network tomography, delay tomography has received considerable attentions in recent years. However, most methods in the literature assume that the delays of different links are independent of each other, and pursuit sub-optimal estimate instead of the maximum likelihood estimate (MLE) due to computational challenges. In this paper, we propose a novel method to implement the EM algorithm widely used in delay tomography analysis for multicast networks. The proposed method makes use of a “delay pattern database” to avoid all redundant computations in the E-step, and is much faster than the traditional implementation. With the help of this new implementation, finding MLE for large networks, which was considered impractical previously, becomes an easy task. Taking advantage of this computational breakthrough, we further consider models for potential spatial dependence of links, and propose a novel adaptive spatially dependent model (ASDM) for delay tomography. In ASDM, Markov dependence among nearby links is allowed, and spatially dependent links (SDLs) can be automatically recognized via model selection. The superiority of the new methods is confirmed by simulation studies.

As a technique to investigate link-level loss rates of a computer network with low operational cost, loss tomography has received considerable attentions in recent years. A number of parameter estimation methods have been proposed for loss tomography of networks with a tree structure as well as a general topological structure. However, these methods suffer from either high computational cost or insufficient use of information in the data. In this paper, we provide both theoretical results and practical algorithms for parameter estimation in loss tomography. By introducing a group of novel statistics and alternative parameter systems, we find that the likelihood function of the observed data from loss tomography keeps exactly the same mathematical formulation for tree and general topologies, revealing that networks with different topologies share the same mathematical nature for loss tomography. More importantly, we discover that a reparametrization of the likelihood function belongs to the standard exponential family, which is convex and has a unique mode under regularity conditions. Based on these theoretical results, novel algorithms to find the MLE are developed. Compared to existing methods in the literature, the proposed methods enjoy great computational advantages.