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Vehicular ad hoc networks (VANETs) provide the communication framework for the dissemination of safety-critical messages such as beacons and emergency messages. The communication channel witnesses significant network load generated by frequently exchanged beacons. Under high-density situations, it leads to a serious scalability problem in VANETs. Moreover, contention-based medium access control (MAC) protocols suffer from a great number of packet collisions, and as a result, the reliability and latency of safety messages are severely affected. Because of the periodic nature of beacons, time-division multiple access (TDMA) can be a good choice over contention-based MAC. In this paper, we propose congestion-controlled-coordinator-based MAC (CCC-MAC), which is a time-slot-based medium access protocol that addresses beacons and emergency messages. Basically, the network is virtually partitioned into a number of segments. Within a segment, medium access is accomplished by using a time-slot-scheduling mechanism supervised by a local coordinator vehicle. A significant number of vehicles can be supported under the proposed configuration. In fact, the proposed scheduling mitigates channel congestion by reducing the transmission time of beacons through the use of multiple data rates. Bandwidth utilization is also improved by reusing the unoccupied time slots. Finally, CCC-MAC ensures fast and reliable propagation of emergency messages by employing a pulse-based reservation mechanism. In the simulations, we demonstrate the ability of CCC-MAC to scale well in different vehicular density scenarios. Moreover, it outperforms existing MAC-layer protocols with respect to packet reception probability and latency of safety messages.