Rate-of-decay of probability of isolation in dense sensor networks with bounding constraints

The work establishes the asymptotic rate of decay for the probability of node isolation in bounded wireless sensor networks, in the high density regime. In this regime, the exposition reveals the role of the most isolated neighborhoods of the bounding region in exponentially increasing the average probability of isolation. The problem is treated for a large family of random spatial distributions of nodes, random shapes of node coverage areas, and random topography of the network's bounding region. Different examples are presented to insightfully describe the detrimental effect of boundedness in network isolation. Finally we address different aspects relating to extremely isolating bounding regions, and densities that vary exponentially in time.