Connectivity in mobile device-to-device networks in urban environments

TL;DR

This paper models and analyzes the connectivity and percolation properties of mobile device-to-device networks in urban street environments, revealing conditions for network percolation and the impact of device velocity.

Contribution

It introduces a dynamic model combining random mobility, street layouts, and connectivity, providing new insights into percolation regimes and phase transitions in urban D2D networks.

Findings

Percolation occurs at high device densities and favorable parameters.

Percolation is absent at low device densities or long connectivity times.

Velocity changes can cause in-and-out percolation phenomena.

Abstract

In this article we setup a dynamic device-to-device communication system where devices, given as a Poisson point process, move in an environment, given by a street system of random planar-tessellation type, via a random-waypoint model. Every device independently picks a target location on the street system using a general waypoint kernel, and travels to the target along the shortest path on the streets with an individual velocity. Then, any pair of devices becomes connected whenever they are on the same street in sufficiently close proximity, for a sufficiently long time. After presenting some general properties of the multi-parameter system, we focus on an analysis of the clustering behavior of the random connectivity graph. In our main results we isolate regimes for the almost-sure absence of percolation if, for example, the device intensity is too small, or the connectivity time is too large. On the other hand, we exhibit parameter regimes of sufficiently large intensities of devices, under favorable choices of the other parameters, such that percolation is possible with positive probability. Most interestingly, we also show an in-and-out of percolation as the velocity increases. The rigorous analysis of the system mainly rests on comparison arguments with simplified models via spatial coarse graining and thinning approaches. Here we also make contact to geostatistical percolation models with infinite-range dependencies.