The conflict resolution problem is quite simple as long as the number of aircraft involved is small. Many automation projects disregarded the problem of clusters and failed on real traffic tests because they were unable to deal with complex conflicts. The first definition of cluster appeared in the middle of the nineties when theoretical research started on conflict resolution. The n-aircraft conflict resolution problem is highly combinational and cannot be optimally solved using classical mathematical optimisation techniques. The set of admissible solutions is made of many unconnected subsets enclosing different local optima, but the subset enclosing the optimum cannot be found a priori. Using a priority order to solve a n-aircraft conflict is much easier but the solution is not optimal. However it is difficult to determine the best order or even a good order that ensures that a solution exists. In this paper, a theoretical study of the possible structures of clusters is presented. A simulation using French real traffic data compares the structure of clusters with direct and standard routes. The sensitivity of cluster sizes to uncertainties on trajectories forecast is studied.
