Geometric connectivity of vehicular ad hoc networks: analytical characterization

In this paper, based on approved traffic flow distributions, we develop analytical expressions for Vehicular Ad Hoc Network (VANET) connectivity with respect to the number of reachable neighbors. Node mobility is accounted for by assuming probabilistic disturbance events that instantaneously disrupt the connection between nodes. Next, the lower bound of reachable neighbors for each vehicle to keep VANET connectivity is proposed. Furthermore, we derive the relationship between the number of vehicles in VANETs and the reachable neighbors under which the network is asymptotically connected. Our results facilitate building VANETs with high connectivity on a single road under conditions that the traffic is homogenously distributed as well as the traffic density and the road length are known.

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