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 &#961;, 0.5 < &#961; < 1, we prove, for a hexagon model, that there exists a critical sensor density &#955;0, around which the probability that at least 100&#961;% of sensors are connected in the network increases sharply from &#949; to 1-&#949; within a short interval of sensor density &#961;. The location of &#961;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.

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