
Clustering schemes have been adopted as an efficient solution to prolong network lifetime and improve network scalability. In such clustering schemes cluster ratio is represented by the rate of the number of cluster heads and the number of total nodes, and affects the performance of clustering schemes. In this paper, we mathematically analyze an optimal clustering ratio in wireless sensor networks. We consider a multi-hop to one-hop transmission case and aim to provide the optimal cluster ratio to minimize the system hop-count and maximize packet reception ratio between nodes. We examine its performance through a set of simulations. The simulation results show that the proposed optimal cluster ratio effectively reduce transmission count and enhance energy efficiency in wireless sensor networks.
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