The insights of message delivery delay in VANETs with a bidirectional traffic model

Message delivery delay is mainly caused by mobility and sparse distribution of vehicles in Vehicular Ad hoc NETworks (VANETs). It directly impacts the application design and deployments for VANETs. In this paper, we conduct an in-depth study on the insights of message delivery delay in VANETs towards the identified two major factors: (1) message delivery distance, (2) density of vehicles, based on a bidirectional vehicle traffic model. The bidirectional vehicle traffic was modeled as a combination of multiple Poisson point processes. Based on the sub-additive ergodic theory, theoretically, we found that the message delivery delay has a linear relationship with the message delivery distance. Furthermore, the upper bound of the coefficient of the linear relationship has an exponential polynomial relationship with the density of vehicles on the road and decreases with the increase of the velocity of the traffic.