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Wireless access in vehicular environment (WAVE) architecture of intelligent transportation system has been standardized in the IEEE 802.11p specification. The WAVE network supports the features of multi-rate and multi-channel and it is going to be widely deployed in realistic roadway environments in order to provide traffic information and convenient services. However, the adopted contention-based medium access control protocol, which confronts the performance anomaly problem, would severely downgrade transmission efficiency between road-side-unit (RSU) and on-board-unit (OBU) because they may use diverse data transmission rates to access channel. As a solution, this paper proposes the vehicular channel access scheme (VCAS) to group a number of OBUs with similar transmission rates into one channel to optimize the channel throughput, while the group sizes of channels are controlled in order to fulfill the fairness requirement. To flexibly compromise the tradeoff between throughput and fairness, a marginal utility model is proposed in this paper. Simulation results demonstrate that the proposed VCAS with marginal utility provides a flexible way to handle versatile vehicular scenarios.