  This paper analyzes the performance of a vehicular ad hoc network (VANET)
modeled as a Cox process, where the spatial layout of the roads is modeled by a
Poisson line process (PLP) and the locations of nodes on each line are modeled
as a 1D Poisson point process (PPP). For this setup, we characterize the
success probability of a typical link and the area spectral efficiency (ASE) of
the network assuming slotted ALOHA as the channel access scheme. We then
concretely establish that the success probability of a typical link in a VANET
modeled using a Cox process converges to that of a 1D and 2D PPP for some
extreme values of the line and node densities. We also study the trends in
success probability as a function of the system parameters and show that the
optimum transmission probability that maximizes the ASE for this Cox process
model differs significantly from those of the relatively-simpler 1D and 2D PPP
models used commonly in the literature to model vehicular networks.
