Study of connectivity in vehicular ad hoc networks

We investigate connectivity in ad hoc network formed between vehicles that move in the same direction on a typical highway. We use the common model in vehicular traffic theory in which a fixed point on the highway sees cars passing it separated by times with exponentially distributed duration. We obtain the distribution of the distances between cars, which allows us to use techniques from queuing theory for studying connectivity. We obtain explicit expressions for the expected connectivity distance as well as the probability distribution and expectation of the number of cars in a platoon. The analytical model we present is able to describe the effects of various system´s parameters, including road traffic parameters (i.e. speed distribution and traffic flow) and transmission range of vehicles, on the connectivity. We further provide bounds obtained using stochastic ordering techniques. Our approach is based on the work of Miorandi and Altman [13] that 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 publicly available road traffic statistical data to understand connectivity in VANETs.