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IEEE 802.15.4 networks are a feasible platform candidate for connecting all health-care-related equipment dispersed across a hospital room to collect critical time-sensitive data about patient health state, such as the heart rate and blood pressure. To meet the quality of service requirements of health-care systems, this paper proposes a multi-priority queue system that differentiates between various types of frames. The effect of the proposed system on the average delay and throughput is explored herein. By employing different contention window parameters, as in IEEE 802.11e, this multi-queue system prioritizes frames on the basis of priority classes. Performance under both saturated and unsaturated traffic conditions was evaluated using a novel analytical model that comprehensively integrates two legacy models for 802.15.4 and 802.11e. To improve the accuracy, our model also accommodates the transmission retries and deferment algorithms that significantly affect the performance of IEEE 802.15.4. The multi-queue scheme is predicted to separate the average delay and throughput of two different classes by up to 48.4 % and 46 %, respectively, without wasting bandwidth. These outcomes imply that the multi-queue system should be employed in health-care systems for prompt allocation of synchronous channels and faster delivery of urgent information. The simulation results validate these model's predictions with a maximum deviation of 7.6%.