Analysis of Coverage Under Border Effects in Three-Dimensional Mobile Sensor Networks

Recent advances in robotics and low-power embedded systems made three-dimensional (3D) mobile wireless sensor networks (MSNs) an effective solution for monitoring a field of interest (FoI). From a cost perspective, it is often important to ensure the desired coverage ratio for the FoI within a maximum allowable response (MAR) time, by using a minimum number of sensors in MSNs. The literature on determining the minimum number of sensors for the desired coverage ratio assumes that the FoI is unbounded to overcome the border effects. Since the entire sensing sphere of the sensors near the boundary may not be useful for the coverage, the number of sensors estimated without the border effects is lower than the actual value. In this paper, we estimate the minimum number of sensors required to achieve a desired coverage ratio in a given MAR time for a 3D FoI. We term this problem (α; V; T)-coverage problem, where a, V , and T are the desired coverage ratio, average speed of sensors, and MAR time, respectively. We assume straight line mobility model for the sensors and consider the border effects while deriving the expected sensing volume of a sensor useful in coverage. We also consider the restriction of sampling rate of the sensors in this analysis. We discuss the application of our analysis for a non-hyper-rectangle shaped FoI, random walk, and waypoint mobility models, and also the impact of neglecting the border effects. Our numerical and simulation results demonstrate the significance of border effects on the number of sensors and also the relationship between the coverage ratio, MAR time, sampling period, and the sensing range.