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In this paper, we study the steady-state statistical properties of continuous communication path availability in vehicular ad hoc networks. We assume a network of highways with arbitrary topology. The mobile 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 with a state-dependent mean speed. First, the joint distribution of the number of nodes in the highway segments of the network is determined. Then, the number of clusters in the node population of a network path is modeled as a Markovian birth-death process where a cluster is defined as a group of nodes that may communicate with each other directly or indirectly. Thus, the probability distributions of the number of clusters in a path and duration of continuous communication path availability time are derived as functions of mobility and traffic arrival parameters. We present mean durations of continuous availability and unavailability times and mean packet delay for end-to-end communications in a path. The given numerical results illustrate the effects of mobility and traffic arrival process on continuous communication path availability and packet delay. The results show that the mean durations of path availability and mean packet delay increase with the increasing transmission range. Clearly, while high path availability duration is desired but not high packet delay. Thus, the transmission range should not be chosen higher than needed for acceptable communication path availability, so as to maintain an acceptable mean packet delay. In practice, an adaptive transmission range may be required to achieve the right balance between the communication path availability and delay. The analytical results have also been compared with some available experimental studies and verified by two different simulation approaches.