  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.
