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Valuation-aware traffic-control mechanisms for road intersections take the valuations of reduced waiting time of the individual drivers into account. They use agents to avoid any disturbance of the driver, and they feature mechanisms specifically designed for negotiating valuations. While such mechanisms do indeed increase overall driver satisfaction, they only allow one vehicle at a time to use the intersection so far. But the concurrent utilization of an intersection is an important feature needed in reality. This paper proposes new auction-based intersection control mechanisms allowing for concurrency. Their design has been challenging due to complex traffic-specific requirements like the high number of agents involved or varying space and time consumption of vehicles crossing the intersection. Experiments show that they yield a significantly higher degree of overall driver satisfaction than state-of-the-art mechanisms.