On the Network Connectivity of Wireless Sensor Networks following a Random and Non-uniform Distribution

Network connectivity is a critical property that provides communication foundation for most wireless sensor network (WSN) applications to operate successfully. Existing results on the WSN connectivity analysis are primarily based on a uniform distribution of sensors in a bounded field of interest. However, the sensor distribution can be non-uniform in practice due to diverse deployment strategies, deployment deviations and geographical limitations. We thus investigate the network connectivity of a random WSN following a Gaussian distribution in that it can simulate various non-uniform sensor distributions. Specifically, we examine the impact of sensor distribution on the network connectivity in term of full connectivity, partial theta(theta < 1)-connectivity, and sensor connection rate. It was found that 1) different sensor distribution leads to significantly different network connectivity when other network parameters remain the same; 2) full connectivity contrasts sharply with the partial theta-connectivity in terms of the required number of sensors; and 3) there exists critical network parameters around which there is a sharp change in the resulting network theta(theta <= 1) connectivity. The results help in selecting critical network parameters and deriving appropriate requirements for practical WSN application design and deployments.