Techniques for determining an output rate for a bit stream, the output rate being determined by applying information read from the bit stream to available bandwidths. The techniques are employed to construct a statistical multiplexer 80 that multiplexes varying bit-rate bit streams. Minimum and maximum output rates for each bit stream are determined such that neither a queue for the bit stream in the multiplexer nor the bit stream's decoder will underflow or overflow. The multiplexer first allocates each bit stream its minimum bandwidth and then allocates any remaining bandwidth to the bit streams in proportion to the difference between the minimum and maximum output rates for the bit streams, with no bit stream receiving more than its maximum output rate. If there is not enough bandwidth to give every bit stream its minimum rate, glue frames may be inserted, or low priority channels dropped.
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