Today, automated vehicles mostly rely on ego vehicle sensors such as cameras, radar or LiDAR sensors that are limited in their sensing capability and range. Vehicle-to-everything (V2X) communication has the potential to appropriately complement these sensors and even allow for a cooperative, proactive interaction of vehicles. As such, V2X communication might play a vital role on the way to smart and efficient traffic solutions. In the public funded research project UK Autodrive, we are currently investigating and experimentally evaluating V2X-based applications based on dedicated short range communication (DSRC). Moreover, the novel application intersection priority management (IPM) is part of the research project. IPM aims at automating intersections in such a way that vehicles can pass safely and even more efficiently without the use of traffic lights or signs. After a brief outline of our research project and its experimental setup, we will discuss the challenges that arise with IPM. Assuming fully automated vehicles as a first step, we propose a control concept based on distributed model predictive control to solve the intersection automation problem. Compared to previous concepts, our control scheme is less restrictive such that more vehicles can pass the intersection simultaneously and allows for an implementation in an actual vehicle due to a fully parallelized optimization approach. Finally, first simulation results highlight the efficacy of the proposed control concept.