Multi-lane Vehicle-to-Vehicle Networks with Time-Varying Radio Ranges: Information Propagation Speed Properties

In this paper, we study the information propagation speed in multi-lane vehicle-to-vehicle networks such as multi-lane roads or highways. We focus on the impact of time-varying radio ranges and of multiple lanes of vehicles, varying in speed and in density. We assess the existence of a density threshold under which information propagates on average at the fastest vehicle speed and above which information propagates dramatically faster. We first prove that no such phase transition occurs if there is only one lane, regardless of the density of vehicles, when one takes into account real-time radio communication range variations at the MAC layer. We then prove that, on the other hand, a phase transition exists as soon as there is a second lane with different vehicle speed and appropriate density. We derive a lower bound on information propagation speed with respect to the vehicle densities in this context. We finally focus on information propagation speed when there are three lanes or more. We show that under certain conditions a phase transition exists and we derive bounds on the threshold as a simple relationship between the vehicle density on the fastest lane and the sum of the vehicle densities on the other lanes. Our results intrinsically encompass a wide range of vehicular network scenarios, including one-way and two-way cases, as well as special cases such as road side units and/or parked cars being used as relays. We confirm our analytical results using simulations carried out in several environments (The One and Maple).