A Tractable Framework for Exact Probability of Node Isolation in Finite Wireless Sensor Networks

We present a tractable analytical framework for the exact calculation of probability of node isolation when N sensor nodes are independently and uniformly distributed inside a finite square region. The proposed framework can accurately account for the boundary effects by partitioning the square into subregions, based on the transmission range and the node location. We show that for each subregion, the probability that a random node falls inside a disk centered at an arbitrary node located in that subregion can be expressed analytically in closed-form. Using the results for the different subregions, we obtain the exact probability of node isolation. The proposed framework is validated by comparison with simulation results.