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Abstract-This paper introduces a new 4D Markov chain model for IEEE 802.15.4 wireless transmission, which corrects errors in an existing 3D model and provides more accurate results. It also introduces an analytical technique for calculating the pdf and mean of the number of time slots required to complete all transmissions, when a set of nodes contend for the channel at the beginning of a superframe. It is assumed that transmission takes place in beacon mode but without acknowledgement (NACK mode). The model can determine the optimum value of the MAC attribute SO required to save energy, and the shortest delay required to receive all transmitted packets with an acceptable probability. This model also suggests an upper threshold for the number of nodes, and the packet length required, to achieve acceptable end-to-end delay. A traffic model for the aggregated data generated by the coordinating node may also be derived based upon this analysis.Keywords-802.15.4 beacon enabled mode, Markov chain, analytical modeling, traffic model analysis I. BACKGROUND AND MOTIVATION

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