Connectivity of Vehicular Ad Hoc Networks in Downtown Scenarios

We study the connectivity in vehicular ad-hoc networks in a downtown scenario, where the mobility of vehicles is constrained on a lattice-shaped road network. We theoretically investigate the connectivity under the Poisson-positioning assumption, where vehicles are positioned according to a Poisson process on each road at any arbitrary instants. We find that the Poisson-positioning assumption allows the existence of the finite critical-vehicle density; that is, if (and only if) the density of vehicles is greater than the finite critical density, then there exists a large (theoretically infinite) cluster of vehicles and an arbitrary pair of vehicles in the cluster is connected in single or multiple hops. Under the Poisson-positioning assumption, we derive two approximation formulas for the critical density, which are given as a function of the transmission range of each vehicle and the distance between intersections. We also consider the connectivity under more realistic movement patterns of vehicles where the Poisson-positioning assumption does not hold. We numerically find that, even in non-Poisson-positioning cases, there exists the critical vehicle density, which is larger than the one under the Poisson-positioning assumption. The effectiveness of deploying roadside-relay stations to provide better connectivity between vehicles is also investigated.