Network lifetime is one of the important metrics that indicate the performance of a sensor network. Different techniques are used to elongate network lifetime. Among them, clustering is one of the popular techniques. LEACH (Low-Energy Adaptive Clustering Hierarchy) is one of the most widely cited clustering solutions due to its simplicity and effectiveness. LEACH has several parameters that can be tuned to get better performance. Percentage of cluster heads is one such important parameter which affects the network lifetime significantly. At present it is hard to find the optimum value for the percentage of cluster head parameter due to the absence of a complete mathematical model on LEACH. A complete mathematical model on LEACH can be used to tune other LEACH parameters in order to get better performance. In this paper, we formulate a new and complete mathematical model on LEACH. From this new mathematical model, we compute the value for the optimal percentage of cluster heads in order to increase the network lifetime. Simulation results verify both the correctness of our mathematical model and the effectiveness of computing the optimal percentage of cluster heads to increase the network lifetime.
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