2 research outputs found
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 tends to zero and to infinity, and determine its behaviour using
an infinite oscillating power series in , 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
Two-Hop connectivity to the roadside in a VANET under the Random Connection Model
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 probability function of the mutual distance between the cars, or between the cars and the RSU. We derive exact equivalents for the expected number of cars with a two-hop connection to the RSU when the car density ρ tends to zero and infinity, and determine its behaviour using an infinite oscillating power series in ρ, 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 RSU