Determination method of optimal number of clusters for clustered wireless sensor networks

In this paper, we present an analytical model for determining the optimal number of clusters, with the objective of minimizing the communication costs in a clustered wireless sensor network (WSN). Sensor nodes are located randomly and distributed according to a homogeneous two-dimensional Poisson point process. Overall communication costs in the network are calculated analytically based on a practical energy consumption model at node level. The optimal probability of being a cluster head (CH) for each node is deduced by minimizing a cost function taking into account the energy dissipation of nodes. The scenarios with single-hop and multi-hop clustered networks are investigated. Simulation results show the existence of the optimum number of clusters which improves the energy efficiency of clustering schemes. We also verify by simulations that the analytical optimal probability of being a CH can provide a good approximation of the actual optimum probability, regardless of the different densities of nodes in the network.