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Here we propose an analytical model of energy usage hierarchical wireless sensor network protocols such as LEACH . LEACH has been used as a foundation for much of the wireless sensor network research, so results addressing the underlying nature of these systems build understanding of a wide range of existing protocols. First, we derive the probability density functions of the distance to the nearest cluster head, the distance to the nearest cluster head squared, and the expected number of nodes per cluster. These results are then applied to produce a model of the amount of average energy used per node for each data report. Using this model we give an analytic expression for the optimal cluster-head selection rate. The model is further improved to give an approximate adjustment for distortions in energy usage near the edges of the field. This final model is then compared to the simulation results presented in the original LEACH paper  and shown to be accurate. Sensor network protocol researchers can apply results presented here to improve performance of existing systems by making the cluster head selection rate adaptive to external factors.
Date of Conference: 19-21 Dec. 2010