Cox Models for Vehicular Networks: SIR Performance and Equivalence
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 Tjunctions. 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 Tjunction, 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 processbased vehicular network is equivalent to the Poisson line processbased and Poisson lilypond modelbased vehicular networks, and their rotational variants.
 Publication:

arXiv eprints
 Pub Date:
 June 2021
 arXiv:
 arXiv:2106.06836
 Bibcode:
 2021arXiv210606836P
 Keywords:

 Computer Science  Networking and Internet Architecture;
 Computer Science  Information Theory
 EPrint:
 15 pages, 11 figures