Critical node lifetimes in random networks via the Chen-Stein method

This correspondence considers networks where nodes are connected randomly and can fail at random times. It provides scaling laws that allow to find the critical time at which isolated nodes begin to appear in the system as its size tends to infinity. Applications are in the areas of sensor and ad-hoc networks where nodes are subject to battery drainage and ´blind spots´ formation becomes a primary concern. The techniques adopted are based on the Chen-Stein method of Poisson approximation, which allows to obtain elegant derivations that are shown to improve upon and simplify previous related results that appeared in the literature. Since blind spots are strongly related to full connectivity, we also obtain some scaling results about the latter.