Analytical Model for Connectivity in Vehicular Ad Hoc Networks

We investigate connectivity in the ad hoc network formed between vehicles that move on a typical highway. We use a common model in vehicular traffic theory in which a fixed point on the highway sees cars passing it that are separated by times with an exponentially distributed duration. We obtain the distribution of the distances between the cars, which allows us to use techniques from queuing theory to study connectivity. We obtain the Laplace transform of the probability distribution of the connectivity distance, explicit expressions for the expected connectivity distance, and the probability distribution and expectation of the number of cars in a platoon. Then, we conduct extensive simulation studies to evaluate the obtained results. The analytical model that we present is able to describe the effects of various system parameters, including road traffic parameters (i.e., speed distribution and traffic flow) and the transmission range of vehicles, on the connectivity. To more precisely study the effect of speed on connectivity, we provide bounds obtained using stochastic ordering techniques. Our approach is based on the work of Miorandi and Altman, which transformed the problem of connectivity distance distribution into that of the distribution of the busy period of an equivalent infinite server queue. We use our analytical results, along with common road traffic statistical data, to understand connectivity in vehicular ad hoc networks.