Using Beta Distributions for Modeling Distances in Random Finite Networks

Distance distributions in random networks affect various performance metrics and operating protocols. For scenarios with the uniform node distribution, the statistical models of distances have been derived for common shapes of operating areas such as disks, rectangles, and regular polygons. Fewer results have been reported for scenarios where node distributions are nonuniform. Often, the closed-form statistical models are described by complicated expressions making their further usage challenging. In this work, we study the application of beta distributions as substitutes to statistical models of distances. We show that this approximation results in accurate and analytically tractable estimates for different operating scenarios. The proposed approach provides uniform solutions to design and analysis tasks for different node distributions and shapes of operating areas.