In this paper, we consider relay-based broadcasting in wireless ad hoc networks, which can enable various emerging services in the Internet of Things (IoT). In this kind of traffic dissemination scheme, also known as flooding, all the nodes not only receive frames but also rebroadcast them. However, without an appropriate relay suppression, a broadcast storm problem arises, i.e., the transmission may fail due to severe collisions and/or interference, many duplicate frames are unnecessarily transmitted, and the traffic dissemination time increases. To mitigate the broadcast storm problem, we propose a reasonable criterion to restrict the rebroadcasting named the duplication ratio. Based on this, we propose an efficient mechanism consisting of duplication suppression and re-queuing schemes. The former discards duplicate frames proactively in a probabilistic manner to decrease the redundancy whereas the latter provides a secondary transmission opportunity reactively to compensate for the delivery failure. Moreover, to apply the duplication ratio practically, we propose a simple method to approximate it based on the number of adjacent nodes. The simulation study confirms that the proposed mechanism tightly ensured the reliability and decreased the traffic dissemination time by up to 6-fold compared to conventional mechanisms.