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In this paper a mathematical model for the non-beacon enabled mode of the IEEE 802.15.4 Multiple access control (MAC) protocol, is provided. A wireless sensor network (WSN) composed of nodes which transmit data to a sink through direct links, is considered. Upon reception of a query from the sink, the nodes transmit their packets by using the carrier sensing multiple access with collision avoidance algorithm defined by IEEE 802.15.4. The model allows the evaluation of the statistical distribution of the traffic generated by the nodes, the success probability for the transmission of a packet, and the mean energy spent by a node for a transmission. The results are validated through simulations. The model differs from those previously published by other authors in the literature as it precisely follows the MAC procedure defined by the standard, in the context of the WSN scenario described above. Performance obtained by varying the parameters of the backoff algorithm, are evaluated and compared. Results show that a tradeoff between energy efficiency and reliability is needed.