Path coverage properties of randomly deployed sensors with finite data-transmission ranges

We analyze the path coverage properties of a sensor network, where numerous sensors are randomly deployed. We characterize the path coverage in terms of three metrics: fraction of coverage, probability of complete coverage, and probability of partial coverage. We derive the expressions for the three coverage metrics as functions of the sensor density, the sensing range of a sensor, and the data-transmission range of a sensor. Based on the derived expressions, we study the impact of the data-transmission range on the path coverage and show, for example, that a sensor should have a long data-transmission range in order to achieve high detectability of intruding objects (partial coverage probability of the trajectories of objects) with a modest sensor density.