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Digital TV transmission systems allow a transmission channel to be shared by a number of sources. In order to improve the bandwidth utilization, variable bit rate encoding and statistical multiplexing techniques are usually used. However, the channel sharing requires a careful scheduling method for multiplexing. This is because the video and audio materials have to be presented at the receivers at specific points in time. In this paper, we present a novel scheduling scheme for statistical multiplexing of VBR sources. Our method is sensitive to the timing requirements of the sources and sends the packets as close to their transmission deadlines as possible. The advantages of our method are: (1) it decreases the broadcast deadline violation probability (or improves the bandwidth utilization), (2) it minimizes the delay and delay jitter of packets and (3) it generates a transport stream compliant with all the standard TV receivers. Simulations were conducted to compare our algorithm with the first-come-first-serve scheduling method. The results show that our algorithm significantly reduces both the percentage of dropped packets (by 35%-50%) and the average packet delay.