2020/05/29 by Alexander P. Kartun-Giles, Konstantinos Koufos, Kartun-Giles, Alexander P. +5
Computer Science · Engineering · Social Sciences · #Combinatorics (math.CO) #FOS: Computer and information sciences #FOS: Mathematics #FOS: Physical sciences #Human Mobility and Location-Based Analysis #Information Theory (cs.IT) #Networking and Internet Architecture (cs.NI) #Opportunistic and Delay-Tolerant Networks #Probability (math.PR) #Statistical Mechanics (cond-mat.stat-mech) #Vehicular Ad Hoc Networks (VANETs)
paper · pdf · doi:10.48550/arxiv.2005.14407
openalex publication_date 2020/05/29 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
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 ρ tends to zero and infinity, and determine its behaviour using an infinite oscillating power series in ρ, 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.