P2P streaming tries to achieve scalability (like P2P file distribution) and at the same time meet real-time playback requirements. It is a challenging problem still not well understood. In this paper, we describe a simple stochastic model that can be used to compare different data-driven downloading strategies based on two performance metrics: continuity (probability of continuous playback), and startup latency (expected time to start playback). We first study two simple strategies: Rarest

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... and Greedy. The former is a well-known strategy for P2P file sharing that gives good scalability, whereas the latter an intuitively reasonable strategy to optimize continuity and startup latency from a single peer's viewpoint. Greedy, while achieving low startup latency, fares poorly in continuity by failing to maximize P2P sharing; whereas Rarest First is the opposite. This highlights the trade-off between startup latency and continuity, and how system scalability improves continuity. Based on this insight, we propose a mixed strategy that can be used to achieve the best of both worlds. Our algorithm dynamically adapts to the peer population size to ensure scalability; at the same time, it reserves part of a peer's effort to the immediate playback requirements to ensure low startup latency.