On the Load Distribution of Vehicular Users Modeled by a Poisson Line Cox Process

In this letter, we characterize the load on the cellular macro base stations (MBSs) due to vehicular users modeled by a Poisson line Cox process (PLCP). Modeling the locations of MBSs by a homogeneous 2D Poisson point process (PPP), we first characterize the total chord length distribution of the lines of the Poisson line process (PLP) intersecting the typical Poisson Voronoi (PV) cell. Using this result, we derive the exact probability mass function (PMF) of the load on the typical MBS. Considering the computational complexity of this expression, we propose an easy-to-use approximation for the PMF that is also remarkably accurate. Building on this result, we also compute the PMF of the load on the tagged MBS that serves the typical vehicular user. This result enables the characterization of the rate coverage of the typical receiver in the network, which is also included as a useful case study.