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In this paper we propose a novel segmentation-based approach for delivering multimedia files in content distribution networks. Each media file is divided into segments and the number of copies distributed to replica servers for each segment is designed in such a way that we can reduce the storage requirement at the replica servers, accommodate the bursty arrival of client requests, and at the same time achieve a small latency for the clients. We analyze the effect of the size of segments on the total storage requirement and give a lower bound. We design a scheduling algorithm that can take advantage of the increased capacity of access links of clients. Our simulations show that the segmentation-based approach can reduce the latency and the rejection rate significantly over those approaches that deliver the whole or the prefix part of media files to replica servers.