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A method to determine the optimal clusterhead number in a clustered wireless sensor network is proposed to improve the energy efficiency of clustering schemes. The wireless sensor network is modeled as points locating randomly on the plane according to a homogeneous spatial Poisson process. This leads to derive the means of some typical cluster parameters accordingly. After that, the total energy cost consumed in the system is calculated based on a practical radio model. As a result, the optimal probability of becoming a clusterhead for each node is deduced via minimizing the system energy cost.
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