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Peer-to-peer (P2P) networks are emerging as an interesting alternative to media streaming delivery with respect to content delivery networks (CDN). Although several P2P protocols have been proposed to support video streaming with an adequate degree of quality of service (QoS), a critical point today is how to evaluate them and optimize their parameters. The difficulty lies in the fact that the behavior of the P2P overlay network and the one of the underlying packet network are closely related and need to be analyzed simultaneously. Ad-hoc simulators for each P2P architecture have been proposed but they neglect the interactions between peers and the underlying network. This paper proposes a new approach to P2P video streaming performance analysis and system design which provides a very accurate cross-layer simulation of the real behavior of P2P clients over TCP/IP networks. A fluid-flow approach has been adopted to simulate the behavior of the network elements supporting an emulated overlay network consisting of real implementations of P2P clients. The P2P SplitStream video streaming protocol is considered as a case study to demonstrate that the tool is able to capture performance parameters at both the overlay (e.g. inter description synchronization) and packet network levels (e.g. traffic source round-trip time and router queue behavior).