Poisson Cox Point Processes for Vehicular Networks

TL;DR

This paper models vehicular networks using a Poisson line Cox point process, deriving key statistical properties relevant for understanding vehicle distributions and network behavior.

Contribution

It introduces a novel two-stage Poisson line Cox process model for vehicular networks and derives its fundamental statistical properties.

Findings

Derived the distribution of nearest distances between vehicles.

Analyzed the asymptotic behavior of Voronoi cells under densification.

Provided formulas for the Laplace functional and facet densities.

Abstract

This paper analyzes statistical properties of the Poisson line Cox point process useful in the modeling of vehicular networks. The point process is created by a two-stage construction: a Poisson line process to model road infrastructure and independent Poisson point processes, conditionally on the Poisson lines, to model vehicles on the roads. We derive basic properties of the point process, including the general quadratic position of the points, the nearest distance distribution, the Laplace functional, the densities of facets of the Cox-Voronoi tessellation, and the asymptotic behavior of the typical Voronoi cell under vehicular densification. These properties are closely linked to features that are important in vehicular networks.