Percolation for D2D Networks on Street Systems

TL;DR

This paper analyzes the connectivity of device-to-device networks on street systems using stochastic geometry models, deriving critical thresholds and comparing models for urban and rural scenarios.

Contribution

It introduces a percolation-based framework for D2D network connectivity on street systems modeled by Poisson tessellations, providing new approximations for critical device density.

Findings

Poisson Boolean Model approximates urban connectivity well.

Percolation probability remains low in rural areas even above threshold.

Derived critical device-intensity thresholds for network percolation.

Abstract

We study fundamental characteristics for the connectivity of multi-hop D2D networks. Devices are randomly distributed on street systems and are able to communicate with each other whenever their separation is smaller than some connectivity threshold. We model the street systems as Poisson-Voronoi or Poisson-Delaunay tessellations with varying street lengths. We interpret the existence of adequate D2D connectivity as percolation of the underlying random graph. We derive and compare approximations for the critical device-intensity for percolation, the percolation probability and the graph distance. Our results show that for urban areas, the Poisson Boolean Model gives a very good approximation, while for rural areas, the percolation probability stays far from 1 even far above the percolation threshold.