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Most of the existing video streaming systems employ the worst case analysis in application layer buffer size dimensioning. Even though the worst case buffer size dimensioning provides deterministic quality of service (QoS) guarantees that are desirable in multimedia transmission, however, this also over-provisions the scarce memory resources. In this paper, we propose a dynamic technique for buffer and rate allocation under two scenarios: (1) when the channel conditions are known a-priori, and (2) when the channel conditions are unknown. Simulation results show up to an order of magnitude savings in the application layer buffer requirements for the two scenarios considered. Furthermore, a-priori knowledge of the channel conditions at the application layer yields an improved video quality.