Multicast-based loss inference with missing data

Network tomography using multicast probes enables inference of loss characteristics of internal network links from reports of end-to-end loss seen at multicast receivers. In this paper, we develop estimators for internal loss rates when reports are not available on all probes or from all receivers. This problem is motivated by the use of unreliable transport protocols, such as reliable transport protocol, to transmit loss reports to a collector for inference. We use a maximum-likelihood (NIL) approach in which we apply the expectation maximization (EM) algorithm to provide an approximating solution to the the NIL estimator for the incomplete data problem. We present a concrete realization of the algorithm that can be applied to measured data. For classes of models. we establish identifiability of the probe and report loss parameters, and convergence of the EM sequence to the maximum-likelihood estimator (MLE). Numerical results suggest that these properties hold more generally. We derive convergence rates for the EM iterates, and the estimation error of the MLE. Finally, we evaluate the accuracy and convergence rate through extensive simulations.