Mean and Variance of Interference in Vehicular Networks with Hardcore Headway Distance

Interference statistics in vehicular networks have long been studied using the Poisson Point Process (PPP) for the locations of vehicles. Under congested traffic, this model becomes unrealistic because it assumes that the vehicles can come arbitrarily close to each other. In this paper, we model the headway distance (the distance between the head of a vehicle and the head of its follower) equal to the sum of a constant hardcore distance and an exponentially distributed random variable. We investigate the impact of this model on the mean and the variance of interference at the origin in comparison with a PPP model of equal intensity. Even though the pair correlation function becomes much more complex as compared to the PPP, we develop simple models to capture the impact of hardcore distance on the variance of interference. In addition, we study the extreme scenario where the interference originates from a lattice. We show how to relate the variance of interference due to a lattice to that of a PPP of half intensity under Rayleigh fading.