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In this paper we analyze connectivity of one-dimensional Vehicular Ad Hoc Networks where vehicle gap distribution can be approximated by an exponential distribution. The probabilities of Vehicular Ad Hoc Network connectivity for difference cases are derived. Furthermore we proof that the nodes in a sub-interval [z1,z1 +Δz] of interval [0, z], z>0 where all the nodes are independently uniform distributed is a Poisson process and the relationship of Vehicle Ad hoc Networks and one-dimensional Ad Hoc networks where nodes independently uniform distributed in [z1,z1 +Δz] is explained. The analysis is validated by computing the probability of network connectivity and comparing it with the Mont Carlo simulation results.
In this paper we analyze connectivity of one-dimensional Vehicular Ad Hoc Networks where vehicle gap distribution can be approximated by an exponential distribution. The probabilities of Vehicular Ad Hoc Network connectivity for difference cases are derived. Furthermore we proof that the nodes in a sub- interval [z1, z1 + Δz] of interval [0, z], z> 0 where all the nodes are independently uniform distributed is a Poisson process and the relationship of Vehicle Ad hoc Networks and one-dimensional Ad Hoc networks where nodes optionally uniform distributed in [z1, z1 + Δz] is explained. The analysis is validated by computing the probability of network connectivity and practices it with the Mont Carlo simulation results.