Modeling wireless sensor networks using random graph theory

A critical issue in wireless sensor networks (WSNs) is represented by limited availability of energy within network nodes. Therefore, making good use of energy is necessary in modeling sensor networks. In this paper we proposed a new model of WSNs on a two-dimensional plane using site percolation model, a kind of random graph in which edges are formed only between neighbouring nodes. Then we investigated WSNs connectivity and energy consumption at percolation threshold when a so-called phase transition phenomena happen. Furthermore, we proposed an algorithm to improve the model; as a result the lifetime of networks is prolonged. We analyzed the energy consumption with Markov process and applied these results to simulation.