Two-Hop Connectivity to the Roadside in a VANET Under the Random Connection Model

We compute the expected number of cars that have at least one two-hop path to a fixed roadside unit in a one-dimensional vehicular ad hoc network in which other cars can be used as relays to reach a roadside unit when they do not have a reliable direct link. The pairwise channels between cars experience Rayleigh fading in the random connection model, and so exist, with probability function of the mutual distance between the cars, or between the cars and the roadside unit. We derive exact equivalents for this expected number of cars when the car density $\rho$ tends to zero and to infinity, and determine its behaviour using an infinite oscillating power series in $\rho$, which is accurate for all regimes. We also corroborate those findings to a realistic situation, using snapshots of actual traffic data. Finally, a normal approximation is discussed for the probability mass function of the number of cars with a two-hop connection to the origin. The probability mass function appears to be well fitted by a Gaussian approximation with mean equal to the expected number of cars with two hops to the origin.Comment: 21 pages, 7 figure

Fine-Grained vs. Average Reliability for V2V Communications around Intersections

Intersections are critical areas of the transportation infrastructure associated with 47% of all road accidents. Vehicle-to-vehicle (V2V) communication has the potential of preventing up to 35% of such serious road collisions. In fact, under the 5G/LTE Rel.15+ standardization, V2V is a critical use-case not only for the purpose of enhancing road safety, but also for enabling traffic efficiency in modern smart cities. Under this anticipated 5G definition, high reliability of 0.99999 is expected for semi-autonomous vehicles (i.e., driver-in-the-loop). As a consequence, there is a need to assess the reliability, especially for accident-prone areas, such as intersections. We unpack traditional average V2V reliability in order to quantify its related fine-grained V2V reliability. Contrary to existing work on infinitely large roads, when we consider finite road segments of significance to practical real-world deployment, fine-grained reliability exhibits bimodal behavior. Performance for a certain vehicular traffic scenario is either very reliable or extremely unreliable, but nowhere in relative proximity to the average performance.Comment: 5 pages, 4 figures. arXiv admin note: substantial text overlap with arXiv:1706.1001

Simple Approximations of the SIR Meta Distribution in General Cellular Networks

Compared to the standard success (coverage) probability, the meta distribution of the signal-to-interference ratio (SIR) provides much more fine-grained information about the network performance. We consider general heterogeneous cellular networks (HCNs) with base station tiers modeled by arbitrary stationary and ergodic non-Poisson point processes. The exact analysis of non-Poisson network models is notoriously difficult, even in terms of the standard success probability, let alone the meta distribution. Hence we propose a simple approach to approximate the SIR meta distribution for non-Poisson networks based on the ASAPPP ("approximate SIR analysis based on the Poisson point process") method. We prove that the asymptotic horizontal gap $G_0$ between its standard success probability and that for the Poisson point process exactly characterizes the gap between the $b$th moment of the conditional success probability, as the SIR threshold goes to $0$. The gap $G_0$ allows two simple approximations of the meta distribution for general HCNs: 1) the per-tier approximation by applying the shift $G_0$ to each tier and 2) the effective gain approximation by directly shifting the meta distribution for the homogeneous independent Poisson network. Given the generality of the model considered and the fine-grained nature of the meta distribution, these approximations work surprisingly well.Comment: This paper has been accepted in the IEEE Transactions on Communications. 14 pages, 13 figure