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A bursty multiple-access communication channel with constrained total system bandwidth, total average power, and message error rates is considered. A stochastic model for the number of active transmitters is developed. Four schemes for the dynamic assignment of power and coding rate to active transmitters are considered and compared under the expected burst system time criterion. Necessary and sufficient conditions for system operation are given, and all schemes are shown to have the same saturation behavior. Adaptive coding rates are shown to enjoy substantial advantages over fixed coding; adaptive power assignment does not offer advantages over fixed power assignment.