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IEEE 802.11p is the proposed wireless technology for communication between vehicles in a vehicular ad hoc network (VANET) aiming to increase road traffic safety. In a VANET, the network topology is constantly changing, which requires distributed self-organizing medium access control (MAC) algorithms, but more importantly the number of participating nodes cannot be restricted. This means that MAC algorithms with good scalability are needed, which can fulfill the concurrent requirements on delay and reliability from road traffic safety applications. The MAC method of IEEE 802.11p is a carrier sense multiple access (CSMA) scheme, which scales badly in terms of providing timely channel access for a high number of participating nodes. We therefore propose using another MAC method: selforganizing time division multiple access (STDMA) with which all nodes achieve timely channel access regardless of the number of participating nodes. We evaluate the performance of the two MAC methods in terms of the MAC-to-MAC delay, a measure which captures both the reliability and the delay of the delivered data traffic for a varying number of vehicles. The numerical results reveal that STDMA can support almost error-free transmission with a 100 ms deadline to all receivers within 100 m, while CSMA suffers from packet errors. Moreover, for all considered cases, STDMA offers better reliability than CSMA.