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The IEEE 802.15.4 standard defines physical layer and medium access control (MAC) layer protocols for the low rate wireless personal areas network (LR-WPAN). The analytical models of 802.15.4 MAC have been primarily developed under the assumptions of the ideal channels or uniform error channels which fail to capture the characteristics of bursty and correlated channel errors in the practical wireless network environment. In this paper, we propose an analytical model for 802.15.4 MAC in LR-WPAN in the presence of bursty error channels. This model can be adopted to obtain the quality-of-service (QoS) performance metrics in terms of throughput, service time, and total delay. Utilizing the analytical model, we investigate the QoS performance of 802.15.4 MAC under various traffic loads, backoff parameters, numbers of stations, and channel conditions.