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Transmission of continuous media streams has been a challenging problem of multimedia service. Lots of works have been done trying to figure out the best solution for this problem, and some works presented the optimal solution for transmitting the stored video using smoothing schemes applied to each individual stream. But those smoothing schemes considered only one stream, not the whole streams being serviced, to apply themselves, which could only achieve local optimum not the global optimum. Most of all, they did not exploit statistical multiplexing gain that can be obtained before smoothing. In this paper, we propose a new smoothing scheme that deals with not an individual stream but the whole streams being serviced simultaneously to achieve the optimal network bandwidth utilization and maximize the number of streams that can be serviced simultaneously. We formally proved that the proposed scheme not only provides deterministic QoS for each client but also maximizes number of clients that can be serviced simultaneously and hence achieves maximum utilization of transmission bandwidth.