A Transdimensional Poisson Model for Vehicular Networks

Poisson line processes (PLPs) describe a street system as a random collection of lines. Poisson point processes (PPPs) model vehicle locations on each line or street as random points. The characterization of vehicular networks as their combination, i.e., the PLP-PPP model, is relevant and widely used in the literature. However, the analytical expression for even a simple performance metric such as the probability of successful message reception in the PLP-PPP is quite complex and provides little insights into the network behavior. Here, we propose a transdimensional Poisson model-superposition of the 1D and 2D PPPs- as an alternative. It considers the vehicles on the same line as the receiving vehicle as a 1D PPP and the vehicles on the other streets as random points on the 2D plane neglecting their street geometry. We show that the success probability in the proposed transdimensional model is tractable and provides a tight approximation to that of the PLP- PPP. Also, it is asymptotically exact on both the upper and lower tails of the success probability.