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Clustering sensor nodes into groups is an effective way of reducing the transmission of duplicated information in energy-constraint wireless sensor networks (WSNs). The performance of clustering is greatly influenced by the selection of cluster-heads, which are in charge of creating clusters and controlling member nodes. In selecting cluster-heads, a probabilistic method where each sensor node selects itself as a cluster-head with a given probability is often used in large-scale and dense WSNs because it enables all nodes to independently decide their roles while keeping the signaling overhead low. In this method, the probability of being a cluster-head should be optimally chosen to maximize the energy efficiency of the nodes. In this article, we propose a novel energy model to estimate the energy consumed in a multi-hop WSN clustered with probabilistic cluster-head selection. Then, based on our model, we determine optimal probability that maximizes the lifetime of a network. Simulation results achieved by the Monte Carlo method show that our model estimates well in energy consumption from a network and also predicts the optimal clustering probability accurately.

Energy consumption and lifetime analysis in clustered multi-hop wireless sensor networks using the probabilistic cluster-head selection method