Analysis of Stochastic $k$-Coverage and Connectivity in Sensor Networks With Boundary Deployment

Coverage and connectivity are important metrics used to evaluate the quality of service of wireless sensor networks (WSNs) monitoring a field of interest (FoI). Most of the literature assumes that the sensors are deployed directly in the FoI. In this paper we assume that the sensors are stochastically deployed outside the FoI. For such WSNs, we derive probabilistic expressions for k-coverage and connectivity using exact geometry. We validate our analysis and demonstrate its utility to estimate the minimum number of sensors required for a desired level of coverage and connectivity. We also demonstrate an on-campus traffic monitoring system to count the number of vehicles, detect the direction of vehicle, and to identify the vehicle (two-wheeler or four-wheeler) using sensors along both sides of the road.