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In this paper, we study the statistical properties of continuous communication path availability in vehicular ad hoc networks at the steady state. We assume a network of highways with arbitrary topology. The nodes arrive at the network through one of the traffic entry points following a Poisson process and move along a path according to a mobility model. We model the number of clusters in the node population along a path as a Markovian birth-death process. This model enables us to determine the distribution of the number of clusters and continuous communication path availability and unavailability times as functions of mobility and traffic arrival parameters in the path. The numerical results show that the mean path availability duration varies logarithmically with the transmission range. In practice, an adaptive transmission range may be needed to have very high path availability.