Multimedia streaming is a technique that allows users to play media content as it is beingrnreceived without waiting for the entire file to download. It can be live-streaming or OnDemand.rnrnIn On-Demand multimedia streaming systems, streaming techniques arernusually combined with proxy caching to obtain better performance. A number of cachingrnschemes are proposed and some are optimized for a conventional multicast or batchrnstreaming system. These caching schemes reduce the startup latency of this technique. rnHowever, patch streaming, which has no startup latency inherent to it, requires extrarnbandwidth to deliver the media data in patch streams. rnThis thesis work proposes a caching technique which aims at reducing the bandwidthrncost of patch streaming technique. It uses the neural networksâ€™ reservoir computing (RC)rnapproach for the popularity prediction in the optimization of media prefix design andrnselection. The system is implemented and the performance of the proposed cachingrnscheme is compared with the popularity and prefix aware interval caching (2PIC)rnscheme [prefix part] and patch streaming with no caching using an extensive simulationrnon a synthetically generated media server workload. The bandwidth saving, hit ratio andrnconcurrent number of clients are used to compare the performance in which the proposedrnscheme is found to perform better for different caching capacities of the proxy server.rnThe bandwidth saving of as high as 36% can be obtained from the proposed schemernwhile 32% from 2PIC compared to the no caching scheme for proxy caching capacity ofrnabout 16.7% of the total media size on the server. Higher hit ratio is obtained usingrnproposed scheme than the 2PIC scheme. The number of concurrent clients that can be rnserved is large when using proposed scheme followed by 2PIC and no caching schemes.