Nearest-Neighbor and Contact Distance Distributions for Matern Cluster Process

TL;DR

This paper derives the distributions of nearest neighbor and contact distances in the Matern cluster process, providing tools for analyzing wireless networks with clustered node distributions.

Contribution

It presents the first derivation of the cumulative density functions for these distances in MCP, aiding performance analysis of clustered wireless networks.

Findings

Contact distance stochastically dominates nearest-neighbor distance in MCP.

Contact distance of MCP also stochastically dominates that of homogeneous PPP.

Results are useful for analyzing real-world wireless networks with clustering.

Abstract

In this letter, we derive the cumulative density function (CDF) of the nearest neighbor and contact distance distributions of the Matern cluster process (MCP) in R2. These results will be useful in the performance analysis of many real-world wireless networks that exhibit inter-node attraction. Using these results, we concretely demonstrate that the contact distance of the MCP stochastically dominates its nearest-neighbor distance as well as the contact distance of the homogeneous Poisson point process (PPP) with the same density.