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The success of file swarming mechanisms such as BitTorrent has motivated a new approach for scalable streaming of live content that we call mesh-based Peer-to-Peer (P2P) streaming. In this approach, participating end-systems (or peers) form a randomly connected mesh and incorporate swarming content delivery to stream live content. Despite the growing popularity of this approach, neither the fundamental design tradeoffs nor the basic performance bottlenecks in mesh-based P2P streaming are well understood. In this paper, we follow a performance-driven approach to design PRIME, a scalable mesh-based P2P streaming mechanism for live content. The main design goal of PRIME is to minimize two performance bottlenecks, namely bandwidth bottleneck and content bottleneck. We show that the global pattern of delivery for each segment of live content should consist of a diffusion phase which is followed by a swarming phase. This leads to effective utilization of available resources to accommodate scalability and also minimizes content bottleneck. Using packet level simulations, we carefully examine the impact of overlay connectivity, packet scheduling scheme at individual peers and source behavior on the overall performance of the system. Our results reveal fundamental design tradeoffs of mesh-based P2P streaming for live content.