Distance Distributions in Finite Uniformly Random Networks: Theory and Applications

TL;DR

This paper analyzes the distribution of distances in finite, uniformly random networks, providing a more realistic model than the traditional infinite Poisson process, with applications to network performance metrics.

Contribution

It introduces a finite uniform random network model and derives the distance distribution as a generalized beta distribution, improving realism over traditional models.

Findings

Distance from center to nth neighbor follows a generalized beta distribution

Results applicable to energy, interference, outage, and connectivity analysis

Provides a more practical network modeling framework

Abstract

In wireless networks, the knowledge of nodal distances is essential for several areas such as system configuration, performance analysis and protocol design. In order to evaluate distance distributions in random networks, the underlying nodal arrangement is almost universally taken to be an infinite Poisson point process. While this assumption is valid in some cases, there are also certain impracticalities to this model. For example, practical networks are non-stationary, and the number of nodes in disjoint areas are not independent. This paper considers a more realistic network model where a finite number of nodes are uniformly randomly distributed in a general d-dimensional ball of radius R and characterizes the distribution of Euclidean distances in the system. The key result is that the probability density function of the distance from the center of the network to its nth nearest neighbor follows a generalized beta distribution. This finding is applied to study network characteristics such as energy consumption, interference, outage and connectivity.