Maximum likelihood estimation of the flow size distribution tail index from sampled packet data

In the context of network traffic analysis, we address the problem of estimating the tail index of flow (or more gener-ally of any group) size distribution from the observation of a sampled population of packets (individuals). We give an exhaustive bibliography of the existing methods and show the relations between them. The main contribution of this work is then to propose a new method to estimate the tail index from sampled data, based on the resolution of the maximum likelihood problem. To assess the performance of our method, we present a full performance evaluation based on numerical simulations, and also on a real traffic trace corresponding to internet traffic recently acquired