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The bandwidth-intensive and long-lived nature of high quality digital video makes it a challenging problem to transmit such video over the Internet. In this paper, we propose a scalable and flexible framework integrating proxy-based prefix caching with periodic broadcast of the suffix of a video from the server, for efficiently streaming a set of popular videos to a large number of asynchronous clients. We develop a methodology for (i) determining appropriate prefix and suffix transmission schemes based on a principle of decoupling the two transmissions from each other, and (ii) optimally allocating the proxy buffer space among the set of videos. A buffer allocation algorithm is presented that minimizes the aggregate bandwidth usage on the server-proxy path. Our studies show that our approach yields a buffer allocation close to the optimal solution minimizing both server-proxy and proxy-client path bandwidth usage for practical settings where the proxy-client path bandwidth is much cheaper than the long-haul server-proxy path bandwidth. When the proxy buffer is allocated to a set of videos using our scheme, a total buffer space of just 5-20% of the video repository is adequate to realize substantial reductions in the aggregate bandwidth usage on the server-proxy path.