Energy efficiency and network lifetime are the most critical issues for Wireless Sensor Networks (WSNs). Clustering is one of the well-known techniques to reduce the energy consumption of the network and improving its lifetime as well. However, clustering itself is time and energy-consuming. Besides, some other ultimate factors such as radio propagation models; network traffic probability are also influencing factors of energy consumption. To ensure the energy efficient network operation, it is essential to taken into account the mentioned factors. Since the number of events occurred inside the network are directly related to the node's energy consumption. For this reason based on the random event arrival; it is crucial to determine an appropriate clustering frequency so that the network lifetime is maximized. We rely on the Poisson distribution, where we can assume random event arrival inside the network. Again formulate clustering problem and sketch a guideline on acquiring an optimal number of clustering in favor of height network lifetime.