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

TL;DR

This paper analyzes the expected number of vehicles with two-hop connectivity to a roadside unit in a VANET, deriving exact formulas under the random connection model and validating with real traffic data.

Contribution

It provides exact expressions for two-hop connectivity in VANETs under Rayleigh fading, covering all traffic densities and including real-world validation.

Findings

Expected number of connected vehicles derived for low and high densities

Exact formulas using oscillating power series applicable across densities

Validation with real traffic data confirms theoretical results

Abstract

In this paper, we compute the expected number of vehicles with at least one two-hop path to a fixed roadside unit (RSU) in a multi-hop, one-dimensional vehicular ad hoc network (VANET) where other cars can act as relays. The pairwise channels experience Rayleigh fading in the random connection model, and so exist, with a probability given by a function of the mutual distance between the cars, or between the cars and the RSU. We derive exact expressions for the expected number of cars with a two-hop connection to the RSU when the car density $\rho$ tends to zero and infinity, and determine its behaviour using an infinite oscillating power series in $\rho$, which is accurate for all regimes of traffic density. We also corroborate those findings with a realistic scenario, 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 RSU.