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In this paper, an analytical model for the non beacon-enabled mode of the IEEE 802.15.4 medium 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-sense multiple access with collision-avoidance algorithm defined by IEEE 802.15.4. Our mathematical model allows the evaluation of the statistical distribution of the traffic generated by the nodes. In particular, the probability that a node succeeds when accessing the channel, and that the final sink receives a packet coming from whatever node, is derived. The results show how the distribution of traffic changes when different loads are offered to the network. Moreover, the model allows the evaluation of the optimum size a packet should have so that the success …