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In this paper, we propose a simple yet accurate analytical model for the slotted non-persistent carrier sense multiple access protocol with binary exponential backoff, as specified in the medium access control (MAC) protocol of the IEEE 802.15.4 standard for the contention access period. The model is based on a three-level renewal process, which leads to a general analytical framework applicable to the protocol variants of either single or double sensing, in a saturated or unsaturated case, under a general traffic arrival distribution and with various backoff policies. The analytical model can be used to obtain some important performance metrics, such as MAC throughput and average frame service time. The accuracy of the analytical model is demonstrated by extensive simulation results. The applicability of this model to the performance analysis of other slotted MAC protocols is also briefly discussed.