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The IEEE 802.15.4 standard is uniquely designed to meet the requirements of the low data-rate, low power-consumption applications in the low rate wireless personal areas network (LR-WPAN) with a focus on enabling wireless sensor network applications. Recently, analytical modelling of IEEE 802.15.4 contention-based Medium Access Control (MAC) protocol has received significant research efforts. However, the development of existing models has been mainly based on the use of the bi-dimensional Markov chain. Different from the previous work, this paper presents a new model which adopts the analysis of the average backoff period length rather than the bi-dimensional Markov chain to derive the sensing probability. Using the proposed model, we investigate the impact of the backoff exponent, frame size and number of stations on the performance metrics including sensing failure probability and saturation throughput.