The Meta Distribution of the SIR in Linear Motorway VANETs

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. In this paper, we calculate the moments of the meta distribution in vehicular ad hoc networks (VANETs) along high-speed motorways. Due to the high speeds, the drivers maintain large safety distances, and the Poisson point process (PPP) becomes a poor deployment model. Because of that, 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 meta distribution of the SIR due to the hardcore process. We validate the model against 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.