Two-Dimensional Modeling and Analysis of Generalized Random Mobility Models for Wireless Ad Hoc Networks

Most important characteristics of wireless ad hoc networks, such as link distance distribution, connectivity, and network capacity are dependent on the long-run properties of the mobility profiles of communicating terminals. Therefore, the analysis of the mobility models proposed for these networks becomes crucial. The contribution of this paper is to provide an analytical framework that is generalized enough to perform the analysis of realistic random movement models over two-dimensional regions. The synthetic scenarios that can be captured include hotspots where mobiles accumulate with higher probability and spend more time, and take into consideration location and displacement dependent speed distributions. By the utilization of the framework to the random waypoint mobility model, we derive an approximation to the spatial distribution of terminals over rectangular regions. We validate the accuracy of this approximation via simulation, and by comparing the marginals with proven results for one-dimensional regions, we find out that the quality of the approximation is insensitive to the proportion between dimensions of the terrain.