The Meta Distribution of the SIR in Linear Motorway VANETs

Abstract: The meta distribution of the signal-to-interference-ratio (SIR) is an important performance indicator for wireless networks because, for ergodic point processes, it describes the fraction of scheduled links that achieve certain reliability, conditionally on the point process. The calculation of the moments of the meta distribution requires the probability generating functional (PGFL) of the point process. In vehicular ad hoc networks (VANETs) along high-speed motorways, the Poisson point process (PPP) is a poor deployment model, because the drivers, due to the high speeds, maintain large safety distances. In this paper, we model the distribution of inter-vehicle distance equal to the sum of a constant hardcore distance and an exponentially distributed random variable. We design a novel \emph{discretization model} for the locations of vehicles which can be used to approximate well the PGFL due to the hardcore point process and the meta distribution of the SIR generated from synthetic motorway traces. On the other hand, the PPP overestimates significantly the coefficient-of-variation of the meta distribution due to the hardcore process, and its predictions fail. In addition, we show that the calculation of the meta distribution becomes especially meaningful in the upper tail of the SIR distribution.