The emergence of computationally rich vehicles and recent advances in wireless communication technologies are fuelling vehicular network research in industry and academia. A key challenge to the successful deployment of vehicular communication is the implementation and efficiency of the medium access control (MAC) layer. There are mainly two types of MAC approaches, namely contention based and contention free. The current standard, IEEE 802.11p, is a contention-based approach, which has the severe limitation of unbounded transmission delays. An alternative contention-free approach called dedicated multi-channel MAC (DMMAC) has been proposed in the literature. In this work the authors analyse these two approaches, discuss their limitations and introduce an improved approach called medium access with memory bifurcation and administration (MAMBA). The authors evaluate the performance of the three approaches in highway and urban scenarios, for both low- and high-density traffic. The authors' performance evaluation results show that MAMBA improves throughput and message delivery ratio by up to 150 and 205' over IEEE 802.11p and DMMAC approaches, respectively. MAMBA also improves on the latency achieved by the other methods by up to 72 and 99' respectively, compared to IEEE 802.11p and DMMAC.