Path Coverage Property of Randomly Deployed Sensor Networks with Finite Communication Ranges

We analyze the path coverage property of a sensor network, where a large number of 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 communication range of a sensor. Based on the derived expressions, we study the impact of the communication range on the path coverage and, for example, show that a sensor should have a long wireless-communication range to obtain large detectability of intruding objects (partial coverage probability of the trajectories of objects) with modest density of sensors.