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We consider the transmission of multiple video streams from one server to multiple clients over a shared channel. Transcoders are used to dynamically adapt encoded source rates as link capacities vary. We present a closed-form solution for determining optimal values for the transcoded source rates in this case where multiple video streams with independently varying link capacities share time on a channel. We also present a real-time algorithm for optimized packet transmission scheduling and source pruning. Experimental results show gains of 2.5 dB in PSNR when our optimized pruning and scheduling technique is added to a system that uses transcoding, in the case when there is time lag in the control of transcoders. We also show results in which our pruning scheme performs within 1 dB of off-line, R-D optimal pruning.