Critical sensor density for partial connectivity in large area wireless sensor networks

In this article, we study the critical sensor density for partial connectivity of a large area sensor network. We assume that sensor deployment follows the Poisson distribution. For a given partial connectivity requirement ρ, 0.5 < ρ < 1, we prove that there exists a critical sensor density λ 0 , around which the probability that at least a fraction ρ of sensors are connected in the network increases sharply from ε to 1-ε within a short interval of sensor density λ. The length of this interval is in the order of O (-log ε/log A ) as A → ∞, where A is the area of the sensor field, and the location of λ 0 is at the sensor density where the aforesaid probability is about 1/2. We prove the preceding theoretical results in the hexagonal model. We also extend our results to the disk model that models transmission range of sensors as disks. Simulations are performed to confirm the analytical results.