Scalable algorithms for estimating flow length distributions from sampled data

With the rapid growth of link speed, obtaining detailed traffic statistics becomes much more difficult. In order to reduce the resource consumption of measurement systems, more and more passive traffic measurement employs sampling at the packet level. Packet sampling has become an attractive and scalable method to measure flow data on high-speed links. However, knowing the length distributions of traffic flows passing through a network link is very useful for network operation and management. In this paper, we consider the problem of estimating flow length distributions based on sampled flow data. This paper introduces two algorithms for estimating flow length distributions, fitting estimation and factoring estimation. The fitting estimation uses piecewise Pareto distribution to fit the original traffic for a small sampling period. The factoring estimation is used for a large sampling period. It first factorizes the large sampling period into a product of some smaller integer factors, then iteratively invokes fitting estimation or other algorithms such as ${textit{EM}}$ in the arranged order of the factors. Evaluations of the proposed algorithms on large Internet traces obtained from several sources demonstrate that they have high measurement accuracy with low computation overhead. The algorithms allow us to recover the complete flow length distributions.