Analysis of Connectivity for Sensor Networks Using Geometrical Probability

Sensors typically have limited power of transmission. Thus desired connectivity probability (CP) between the sensors is critical in the given deployment area. The paper presents a novel approach for analysing the lower bound of CP for sensor networks under uniformly distribution of the sensors in a given area. Initially, the area is divided into a grid (mesh) of blocks. The CP for each small block is then calculated and the small blocks are aggregated into a large one and the desired CP for the entire network is derived progressively. More specifically, given n sensors in each block, the CP is derived by (1) computing the CP of two adjacent blocks using a geometrical probabilistic approach when n1⁄4 1, which is the precise result; (2) based on (1), the CP for n>1 is derived, which is very close to the simulation results within an error of 1%; (3) progressively deriving the CP of an entire network through aggregations of the small blocks. Simulation results demonstrate the feasibility of the algorithm.