In the context of Intelligent Transportation Systems based on driverless vehicles, one important issue is the passing of a crossroads. This paper presents a supervised reservation system. Extending previous works in this direction, the proposed algorithm determines trajectories and speeds for all the vehicles willing to pass the intersection. The work is separated into tasks shared between the vehicles and an infrastructure in charge of the crossroads. This paper describes the characteristics of the algorithm, as well as considerations which led to it. Simulation results are given and support the argument that this algorithm is probably suboptimal but still performs well. Finally, this work shows there is place for ameliorations and hints to further improve the algorithm are given.