Mathematics and Computer Science: Research Updates Vol. 11

Vehicular Ad Hoc Networks (VANETs) are critical for inter-vehicle communication, enabling timely information exchange for ‘safety ‘and emergency applications. However, dynamic network topology and environmental obstructions pose persistent challenges, causing intermittent connectivity. This study proposes a generalized statistical channel model to characterize vehicle transmission ranges under realistic urban conditions, incorporating wireless fading (Weibull, Nakagamim, Rayleigh, and lognormal) and large-vehicle obstructions. Connectivity probability is evaluated for two traffic models—free-flow and synchronized Gaussian Unitary Ensemble (GUE)—capturing multi-lane vehicle dynamics. Results show that for persistent connectivity between vehicle nodes, an inter-vehicle distance less 50m is required for vehicular network design in the fading channels considered. Big vehicle obstructions is shown to be the principle cause of path-loss in all the environments. Furthermore, Nakagami-m fading yields the largest mean transmission range (≈ 220 m), outperforming Rayleigh (≈ 180 m) and Weibull (≈ 195 m) scenarios, while lognormal shadowing due to large vehicles can reduce effective range by up to 30%, lowering connectivity probability under dense traffic. Incorporating inter-vehicle safety gaps in synchronized traffic further decreases link reliability by 10%. These findings quantify the combined effects of fading, vehicle density, and obstructions on VANET performance, providing guidance for robust network design under diverse traffic scenarios.