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IEEE 802.11p and 1609 standards are currently under development to support Vehicle-to-Vehicle and Vehicle-to-Infrastructure communications in vehicular networks. For infrastructure-based vehicular relay networks, access probability is an important measure which indicates how well an arbitrary vehicle can access the infrastructure, i.e. a base station (BS). On the other hand, connectivity probability, i.e. the probability that all the vehicles are connected to the infrastructure, indicates the service coverage performance of a vehicular relay network. In this paper, we develop an analytical model with a generic radio channel model to fully characterize the access probability and connectivity probability performance in a vehicular relay network considering both one-hop (direct access) and two-hop (via a relay) communications between a vehicle and the infrastructure. Specifically, we derive close-form equations for calculating these two probabilities. Our analytical results, validated by simulations, reveal the tradeoffs between key system parameters, such as inter-BS distance, vehicle density, transmission ranges of a BS and a vehicle, and their collective impact on access probability and connectivity probability under different communication channel models. These results and new knowledge about vehicular relay networks will enable network designers and operators to effectively improve network planning, deployment and resource management.