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We present MPARC (multi-priority admission and rate control), a novel joint admission control and rate policing protocol for multi-priority ad hoc networks. MPARC is based on our novel bandwidth allocation model and guarantees that the throughput of admitted realtime flows will not decrease due to later arriving realtime flows with equal or lower priorities or due to best effort flows. MPARC achieves this goal by performing accurate admission control on every newly arriving realtime flow and appropriate rate policing on all best effort traffic. Through simulation, we demonstrate that MPARC has better performance than existing approaches.