Four-dimensional Markov chain model of single-hop data aggregation with IEEE 802.15.4 in wireless sensor networks

This paper introduces a new 4D Markov chain model for IEEE 802.15.4 wireless transmission, which corrects and extends an existing 3D model, providing more accurate and comprehensive results. It also introduces an analytical technique for calculating both the pdf and mean of the number of timeslots 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 be used to determine the optimum value of the MAC attribute macSuperframeOrder (SO) required for saving energy, and the shortest delay required to receive all transmitted packets with a specified probability. It can also specify an upper threshold on the number of nodes and the packet length required, in order to achieve acceptable end-to-end delay. The potential creation of a traffic model for the aggregated data generated by the coordinating node is also discussed.