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In this paper, a random access protocol for quality of service (QoS) support targeted for medical wireless body area sensor networks (WBASNs) is proposed. In this proposal, the sensor nodes are classified into nodes of life-critical health information, and nodes of non-critical health information. The proposed QoS-based MAC protocol prioritizes the critical packets access to the transmission medium by cutting of the number of retransmissions of the collided non critical packets. Therefore, the critical traffic throughput is increased and its rejection rate is decreased while maintaining the non critical traffic QoS parameters above a minimum provisioned level. The proposed protocol is evaluated analytically and through simulation. The obtained results demonstrate a dramatic increase in the critical traffic throughput.