On Path Coverage of Wireless Sensor Networks

Path coverage is one of the applications of wireless sensor networks where the network is responsible for monitoring a path and detecting any object that crosses it. Here, we study the path coverage of a randomly deployed wireless sensor network when the path length and number of sensors are finite (thus the widely used Boolean model is not applicable). More specifically, we find the probability of complete path coverage, the distribution of the number of uncovered gaps, and the probability of having all the gaps smaller than a given size. Furthermore, we investigate the distribution of the covered length of the path. The accuracy of our analysis is also verified through computer simulations, where it is observed that for non-asymptotic cases the Boolean model can be inaccurate.