Asymptotic node distribution of random direction model for Ad hoc networks

Asymptotic node distribution of random direction model for Ad hoc networks is analyzed by the method of geometric probability. The analysis is done on two types of simulation regions. In circular regions, rigorous closed-form solutions of cumulative distribution function and probability density function are obtained. In square regions, we get numerical integral ones. Theoretical analysis and simulation experiments prove that when a network with random direction model achieves its steady state, the nodes appearing probability near the region border is higher than at the region center.