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This paper proposes a new measurement architecture and associated traffic estimation algorithm called FastFlow that uses the heavy-tailed nature of Internet traffic in order to distinguish packets belonging to short lived flows (SLFs) and long lived flows (LLFs). While complete information is stored for SLFs, only partial information related to LLFs is collected using systematic sampling. The absence of data points in LLFs is approximated using a likelihood function defined over the coupon collector problem and the distribution of underlying traffic estimated using the non-parametric Parzen window technique. We validate the performance of our approach using traffic traces collected from our lab and observe that the estimated statistics match the observed traces with high accuracy.