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 some probes or from some receivers. This problem is motivated by the use of unreliable transport control protocols, such as RTCP, to transmit loss reports to a collector for inference. We use a maximum likelihood (ML) approach in which we apply the Expectation Maximization (EM) algorithm to provide an approximate value for the ML estimator for the incomplete data problem. We present a concrete implementation of the algorithm that can be applied to measured data. For certain classes of models we establish identifiability of the probe and report loss parameters, and convergence of the EM sequence to the 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. Last, we evaluate the accuracy and convergence rate through extensive simulations.