There are a lot of studies about automatic driving cooperative platooning in order to realize energy-efficient ITS systems. The platoon consists of multiple vehicles and drive close to each other. It inevitably means the platoon occupies a long part of the lane, more than 50 meters. It causes some kinds of difficult situations. One of them is the overtaking conflict, we named. When a vehicle in low speed is coming close to the platoon from forward and another vehicle in high speed is coming up from behind, the conflict between those vehicles would occur. In this paper, in order to avoid this situation, a priority management method is proposed and it is based on the distributed mutual exclusion, especially token-based algorithm. The proposed method consists of four phases and, in each phase, it rules platoons' and other vehicles action. Our proposal also consider about starving problem and dead lock, we solve those problems. We evaluate the proposed method by computer simulation in terms of the amount of carbon dioxide emission and we show the effectiveness of our proposal.