Node distribution of the random direction model in a square region

Because it is hard to depict real world traces, researchers proposed some mobility models in the study of mobile ad-hoc networks. It is aware recently that some mobility models will lead to non-uniform node distribution, which decreases the credibility and validity of simulations. Many researchers reconsider the node distribution characteristic for random waypoint model and have gotten some valuable and quantitative results. But similar investigations on the random direction model (RD) in square region are still missing. We presented a detailed analysis to the probability behavior of RD model in square region. Numerical solutions of node distribution are obtained. It shows that node distribution probability is higher and higher as its location varies by the sequence of center, border, and corner. It is to say that the stationary node distribution of random direction model is non-uniform.