A novel approach for finding optimal number of cluster head in wireless sensor network

Prolonging life time is the most important designing objectives in wireless sensor networks (WSN). In WSN the total amount of energy is limited, how to make best use of the limited resource energy is a very important aspect in research of WSN. In this paper we provide a method for determining the optimal number of cluster head for homogeneous sensor networks deployed in different scenario using a reasonable energy consumption model. In the first scenario nodes are thrown randomly, which can be modeled using two-dimensional homogeneous spatial Poisson point process. In the second scenario, nodes are deterministically placed along the grid. For these two scenario we calculate the average energy spend in the network in each round according to LEACH protocol for both single and multi-hop between cluster head and sink (base station) as a function of the probability of the node to become a cluster head. Then we find optimal probability of becoming a cluster head hence the optimal number of cluster head that would lead to minimize the average energy spends in the network for each round. Simulation results shows that optimal probability of becoming a cluster heads that leads to minimize energy dissipation in the network is not only depend on the total number of nodes, but also depends on area of the network A, packet length L and processing energy of nodes.