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Given the growing popularity of peer-to-peer file distribution in commercial applications, it is important to understand the challenges of using p2p file-sharing protocols for file distribution, and how extreme conditions such as flash crowds affect the efficiency of file distribution. In this light, there is a need to understand the impact of the utilization of available bandwidth on the performance of peer-assisted file distribution systems. With a simple measurement study on PlanetLab, we identified distinct phases in peer bandwidth utilization over the download duration. Based on the evolution of the utilization of available peer bandwidth over time, we formulated an analytical model for flash crowds in homogeneous and heterogeneous bandwidth swarms. The model estimates the instantaneous download rate and the average file download time with 10% error for swarms up to 160 peers. Our model can be used to predict the scalability of the system when the number of peers increases, and to provision for flash crowds by estimating the server bandwidth to achieve a minimum quality of service. Lastly, we demonstrate how our model is applied to new p2p protocols to understand their design and performance problems.