Coverage by randomly deployed wireless sensor networks

One of the main applications of wireless sensor networks is to provide proper coverage of their deployment regions. A wireless sensor network k-covers its deployment region if every point in its deployment region is within the coverage ranges of at least k sensors. In this paper, we assume that the sensors are deployed as either a Poisson point process or a uniform point process in a square or disk region, and study how the probability of the k-coverage changes with the sensing radius or the number of sensors. Our results take the complicated boundary effect into account, rather than avoiding it by assuming the toroidal metric as done in the literature.