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This paper develops analytical models that characterize the behavior of on-demand stored media content delivery using BitTorrent-like protocols. The models capture the effects of different piece selection policies, including Rarest-First, two variants of In-Order, and two probabilistic policies (Portion and Zipf). Our models provide insight into system behavior and help explain the sluggishness of the system with In-Order streaming. We use the models to compare different retrieval policies across a wide range of system parameters, including peer arrival rate, upload/download bandwidth, and seed residence time. We also provide quantitative results on the startup delays and retrieval times for streaming media delivery. Our results provide insights into the design tradeoffs for on-demand media streaming in peer-to-peer networks. Finally, the models are validated using simulations.