Invariance Property of Isotropic Random Walk Mobility Patterns in Mobile Ad-Hoc Networks

The class of isotropic random walk mobility models, including random direction mobility model, random walk mobility model and Brownian motion mobility model, has been widely used in the study of Mobile Ad-Hoc Networks for mobility modeling and control. In this paper, we show an important property for contact time of isotropic random walk mobility models. Specifically, we find that the mean contact time of two mobile nodes following isotropic random walk mobility models is invariant with respect to the step-length distribution under both the simplest distance-based (Boolean) interference model and the more realistic SINR-based interference model. We also study the effect of system parameters on the contact and inter-meeting time of mobile nodes and discuss their higher-order statistics.