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Traffic control at intersections is a key issue and hot research topic in intelligent transportation systems. Existing approaches, including traffic light scheduling and trajectory maneuver, are either inaccurate and inflexible or complicated and costly. More importantly, due to the dynamics of traffic, it is really difficult to obtain the optimal solution in a real-time way. Inspired by the emergence of vehicular ad hoc network, we propose a novel approach to traffic control at intersections. Via vehicle to vehicle or vehicle to infrastructure communications, vehicles can compete for the privilege of passing the intersection, i.e., traffic is controlled via coordination among vehicles. Such an approach is flexible and efficient. To realize the coordination among vehicles, we first model the problem as a new variant of the classic mutual exclusion problem, and then design algorithms to solve new problem. Both centralized and distributed algorithms are. We conduct extensive simulations to evaluate the performance of our proposed algorithms. The results show that, our approach is efficient and outperforms a reference algorithm based on optimal traffic light scheduling. Moreover, our approach does not rely on traffic light or intersection controller facilities, which makes it flexible and applicable to various kinds of intersections. [ABSTRACT FROM PUBLISHER]