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Video prefetching is a technique that has been proposed for the transmission of variable-bit-rate (VBR) videos over packet-switched networks. The objective of these protocols is to prefetch future frames at the customers' set-top box (STB) during light load periods. Experimental results have shown that video prefetching is very effective and it achieves much higher network utilization (and potentially larger number of simultaneous connections) than the traditional video smoothing schemes. The previously proposed prefetching algorithms, however, can only be efficiently implemented when there is one centralized server. In a distributed environment there is a large degradation in their performance. In this paper we introduce a new scheme that utilizes smoothing along with prefetching, to overcome the problem of distributed prefetching. We show that our scheme performs almost as well as the centralized prefetching protocol even though it is implemented in a distributed environment. In addition, we introduce a call admission control algorithm for a fully interactive video-on-demand (VoD) system that utilizes this concept of distributed video prefetching. Using the theory of effective bandwidths, we develop an admission control algorithm for new requests, based on the user's viewing behavior and the required quality of service (QoS).