Describing 4-D space for air traffic scheduling

In order to allow a better exploitation of available airspace, it has been proposed to assign a volume of space for a certain amount of time to aircraft operators instead of a trajectory. Although some approaches to do this have been studied, it is not yet clear what the best way is to do this so that it is both efficient and acceptable for air traffic controllers. This paper studies several formats for describing 4-D trajectories and 4-D space-time. For distributing airspace over several operators the use of a Voronoi decomposition was studied, but it was found to result in significantly complex solutions that may not be very desirable from the perspective of a human operator. The use of 4-D spheres on the other hand was found to be a suitable way for describing navigational freedom in a relatively simple format