  Vehicular platooning is a promising way to facilitate efficient movement of
vehicles with a shared route. Despite its relevance, the interplay of
platooning and the communication performance in the resulting vehicular network
(VN) is largely unexplored. Inspired by this, we develop a comprehensive
approach to statistical modeling and system-level analysis of VNs with
platooned traffic. Modeling the network of roads using the by-now well-accepted
Poisson line process (PLP), we place vehicles on each road according to an
independent Matern cluster process (MCP) that jointly captures randomness in
the locations of platoons on the roads and vehicles within each platoon. The
resulting triply-stochastic point process is a PLP-driven-Cox process, which we
term the PLP-MCP. We first present this new point process's distribution and
derive several fundamental properties essential for the resulting VN's
analysis. Assuming that the cellular base-stations (BSs) are distributed as a
Poisson point process (PPP), we derive the distribution of the loads served by
the typical BS and the BS associated with the typical user. In deriving the
latter, we also present a new approach to deriving the length distribution of a
tagged chord in a Poisson Voronoi tessellation. Using the derived results, we
present the rate coverage of the typical user while considering partial loading
of the BSs. We also provide a comparative analysis of VNs with and without
platooning of traffic.
