Distance distributions in random networks

To account for stochastic properties when modeling connectivity in wireless mobile systems such as cellular, ad-hoc and sensor networks, spatial points processes are used. Since connectivity can be expressed as a function of distance between nodes distance distributions between points in spatial processes are of special importance. In this paper we survey those results available for distance distributions between points in two mostly used spatial point models, namely, homogeneous Poisson process in <2 and independently uniformly distributed points in a certain region of <2. These two models are known for decades and various distance-related results have been obtained. Unfortunately, due to wide application area of spatial point processes they are scattered among multiple field-specific journals and researchers are still wasting their time rediscovering them time after time. We attempt to unify these results providing an ultimate reference. We will also briefly discuss some of their applications.