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This paper presents an analytic framework to evaluate the performance of peer to peer (P2P) networks. Using the time to download or replicate an arbitrary file as the metric, we present a model which accurately captures the impact of various network and peer level characteristics on the performance of a P2P network. We propose a queueing model which evaluates the delays in the routers using a single class open queueing network and the peers as M/G/1/K processor sharing queues. The framework takes into account the underlying physical network topology and arbitrary file sizes, the search time, load distribution at peers and number of concurrent downloads allowed by a peer. The model has been validated using extensive simulations with campus level, power law AS level and ISP level topologies. The paper also describes the impact of various parameters associated with the network and peers including external traffic rates, service variability, file popularity etc. on the download times. We also show that in scenarios with multi-part downloads from different peers, a rate proportional allocation strategy minimizes the download times.