Cox Models for Vehicular Networks: SIR Performance and Equivalence

TL;DR

This paper develops a comprehensive framework for modeling vehicular networks using random street systems and analyzes communication reliability, establishing model equivalences that simplify analysis and comparison.

Contribution

It introduces a novel Cox process framework for vehicular networks and proves equivalence between different street-based models in terms of communication reliability.

Findings

Poisson stick process is equivalent to Poisson line process models.

Reliability analysis varies with street configurations and intersections.

Model equivalences facilitate simplified analysis of complex vehicular networks.

Abstract

We introduce a general framework for the modeling and analysis of vehicular networks by defining street systems as random 1D subsets of $\mathbb{R}^{2}$. The street system, in turn, specifies the random intensity measure of a Cox process of vehicles, i.e., vehicles form independent 1D Poisson point processes on each street. Models in this Coxian framework can characterize streets of different lengths and orientations forming intersections or T-junctions. The lengths of the streets can be infinite or finite and mutually independent or dependent. We analyze the reliability of communication for different models, where reliability is the probability that a vehicle at an intersection, a T-junction, or a general location can receive a message successfully from a transmitter at a certain distance. Further, we introduce a notion of equivalence between vehicular models, which means that a representative model can be used as a proxy for other models in terms of reliability. Specifically, we prove that the Poisson stick process-based vehicular network is equivalent to the Poisson line process-based and Poisson lilypond model-based vehicular networks, and their rotational variants.