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Ad-hoc multi-hop broadcast protocols are usually used in vehicular networks to provide safety services. However, these protocols face several issues, namely broadcast storms, hidden nodes, and message delivery failures, that prevent safety applications from guaranteeing their required high message delivery ratio and low delays. In this paper, we tackle these issues using a novel cluster-based contention-free broadcast protocol. Particularly, we propose an efficient time slot reservation protocol, centralized in stable cluster heads that continuously adapts to vehicles dynamics. Thus, using a centralized protocol, we ensure an efficient utilization of the time slots for the exact number of active vehicles including hidden nodes; our protocol also ensures a bounded delay for safety applications to access communication channel. We reduce the overhead of our reservation protocol using a directed broadcast propagation and a single reservation request for a periodic medium access during a vehicle's cluster session. During the recurrent service interval, a contention-based period follows the efficiently-used contention free period; it is dynamically adjusted to improve throughput-sensitive non-safety applications. Extensive simulation results show that the proposed scheme can significantly improve the periodic safety application performance in terms of safety message delivery ratio and delay.