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Statistical multiplexing aims at transmitting several variable bit rate (VBR) encoded video streams over a bandlimited channel. Rate-distortion (RD) models for the encoded streams are often used to control the video encoders. As discrepancies frequently occur between the actual RD characteristics and their models, buffers are placed at the output of each coder to facilitate regulation. In this paper, a statistical multiplexer is proposed where video coders and buffers are controlled in a closed loop. First, a predictive joint rate controller accounting for maximum distortion, fairness, and smoothness constraints is considered. Second, all buffers are controlled simultaneously to limit deviations from a reference buffer occupancy to prevent buffer under and overflow. The main idea is to update the encoding rate for each encoding unit according to the average level of the buffers, to maximize the quality of each program. Simulation results show that the proposed scheme yields a smooth and fair video quality among programs thanks to the predictive control and allows an efficient use of the available bandwidth.