1. Two-Hop Connectivity to the Roadside in a VANET Under the Random Connection Model
- Author
-
Alexander P. Kartun-Giles, Konstantinos Koufos, Xiao Lu, and Dusit Niyato
- Subjects
Networking and Internet Architecture (cs.NI) ,FOS: Computer and information sciences ,Statistical Mechanics (cond-mat.stat-mech) ,Computer Networks and Communications ,Information Theory (cs.IT) ,Computer Science - Information Theory ,Probability (math.PR) ,ComputerSystemsOrganization_COMPUTER-COMMUNICATIONNETWORKS ,FOS: Physical sciences ,Aerospace Engineering ,Data_CODINGANDINFORMATIONTHEORY ,Computer Science - Networking and Internet Architecture ,ComputerSystemsOrganization_MISCELLANEOUS ,Automotive Engineering ,FOS: Mathematics ,Computer Science::Networking and Internet Architecture ,Mathematics - Combinatorics ,Combinatorics (math.CO) ,Electrical and Electronic Engineering ,Condensed Matter - Statistical Mechanics ,Mathematics - Probability - 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., Comment: 5 pages, 5 figures
- Published
- 2023