Network Loss Inference with Second Order Statistics of End-to-End Flows

We address the problem of calculating link loss rates from end-to-end measurements. Contrary to existing works that use only the average end-to-end loss rates or strict temporal correlations between probes, we exploit second-order moments of end-to-end flows. We first prove that the variances of link loss rates can be uniquely calculated from the covariances of the measured end-to-end loss rates in any realistic topology. After calculating the link variances, we remove the un-congested links with small variances from the first-order moment equations to obtain a full rank linear system of equations, from which we can calculate precisely the loss rates of the remaining congested links. This operation is possible because losses due to congestion occur in bursts and hence the loss rates of congested links have high variances. On the contrary, most links on the Internet are un-congested, and hence the averages and variances of their loss rates are virtually zero. Our proposed solution uses only regular unicast probes and thus is applicable in today's Internet. It is accurate and scalable, as shown in our simulations and experiments on PlanetLab.