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A wireless body area sensor network (WBASN) is a wireless networking technology that interconnects tiny nodes with sensing capabilities in, on or around a human body. The vital-sign information collected by these sensors can then be used by care-givers to assess the health of a patient. Therefore, it is necessary to provide reliable communication services to prioritized WBASN data streams with quality of service (QoS) guarantees. However, existing research has not devoted enough attention to this issue. This paper proposes a QoS provisioning framework for WBASN traffic employing the IEEE 802.15.4 super-frame structure in the beacon-enabled mode. A method of prioritizing WBASN traffic is proposed, along with algorithms for admission control and scheduling. Computer simulations reveal that our scheme is able to guarantee a 100% time constraint compliance ratio for traffic in contention access periods, and a 99.2% to 99.9% constraint compliance ratio for traffic in contention-free periods, while still admitting and accommodating tens of WBASN traffic streams.