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P2P applications are among the most popular Internet applications and constitute a majority of Internet traffic today. From the perspective of network management, a thorough understanding of the stochastic properties of P2P traffic is thus crucial to designing better traffic/resource control algorithms. However, previous work on measuring and analyzing P2P traffic focuses either on a specific type of P2P applications or report only qualitative or quantitative findings in the measured traffic, without systematically analyzing and modeling P2P traffic. In this paper, we aim to bridge the gap and perform a detailed analysis and modeling of P2P traffic of different types. We first gather and identify P2P traffic on a trans-pacific link between Japan and US. Then based on the flow level (transport layer) information, we analyze and model the marginal distributions of the traffic volume, connection duration, and connection interarrival times for P2P connections of Napster, BitTorrent (BT), eDonkey, Gnutella, and Fasttrack, respectively. We also study the burstiness property of P2P traffic generated by these five different applications and the implication/impact of connections with zero traffic volumes. A major finding of our study is that due to the different parameters/strategies used in the file sharing mechanism, P2P traffic of different applications exhibits different traffic characteristics. As a result, the traffic metrics of interest (i.e., the per-connection traffic volume, the connection duration, and the connection interarrival times) cannot be characterized uniformly with a single model among the different types of applications, but instead have to be modeled with different probability distributions.