Critical Sensor Density for Partial Connectivity in Large Area Wireless Sensor Networks

Assume sensor deployment follows the Poisson distribution. For a given partial connectivity requirement ¿, 0.5 < ¿ < 1, we prove, for a hexagon model, that there exists a critical sensor density ¿₀, around which the probability that at least 100¿% of sensors are connected in the network increases sharply from ¿ to 1-¿ within a short interval of sensor density ¿. The location of ¿₀ is at the sensor density where the above probability is about 1/2. We also extend the results to the disk model. Simulations are conducted to confirm the theoretical results.