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

On the asymptotic connectivity of random networks under the random connection model

Consider a network where all nodes are distributed on a unit square following a Poisson distribution with known density ρand a pair of nodes separated by an Euclidean distance x are directly connected with probability g(x/rρ ), where g : [0,∞ρ+b/cp) [0,1] satisfies three conditions: rotational invariance, qnon-increasing monotonicity and integral boundedness, √ρ+b/Cp = ∫R2g(∥x∥)dx and bis a constant, independent of the event that another pair of nodes are directly connected. In this paper, we analyze the asymptotic distribution of the number of isolated nodes in the above network using the Chen-Stein technique and the impact of the boundary effect on the number of isolated nodes as ρ. On that basis we derive a necessary condition for the above network to be asymptotically almost surely connected. These results form an important link in expanding recent results on the connectivity of the random geometric graphs from the commonly used unit disk model to the more generic and more practical random connection model. © 2011 IEEE

On the Asymptotic Connectivity of Random Networks under the Random Connection Model

Consider a network where all nodes are distributed on a unit square following a Poisson distribution with known density ρand a pair of nodes separated by an Euclidean distance x are directly connected with probability g(x/rρ ), where g : [0,∞ρ+b/cp