Utilizing distance distribution in determining topological characteristics of multi-hop wireless networks

Understanding the topological characteristics of communications networks is essential to the design and operation of such networks. Accordingly, the researchers have been analyzing the topological characteristics of various networks. In this paper, we focus on multi-hop wireless networks with uniformly distributed nodes in 2D and 3D environments. Using the geometrical relations in 2D, researchers have provided analytical formulas for some topological characteristics. However, generalizing this approach to 3D is difficult as it requires to carefully analyze several geometrical relations that overlap. Instead, we consider the distance distribution between two random points, which has been extensively studied in both 2D and 3D. Using these important results, we derive analytical formulas for various topological characteristics in both 2D and 3D. Using simulations, we verify the correctness of our analytical formulas.