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Systems in which many data sources are multiplexed over a single communication channel are considered. Data from all the sources are generated in fixed-length packets and are stored in a common buffer with finite capacity. Packets that overflowed or were removed from the buffer prior to transmission are lost. The system performance measure is the set of packet loss probabilities associated with the sources. Queueing disciplines vary depending on the stringency of prioritization and the utilization of the system resources. The set of all possible performances is characterized as we span the set of all queueing disciplines. Whether a given performance is possible can be deduced. Strategies that achieve the minimum overall loss probability are identified. The extreme disciplines are specified, and their performances are calculable by means of a given algorithm.