Aircraft Flows Merging: Velocity Control and Interactions between Air Traffic Controller and Pilot

A problem of safe aircraft flows merging in an airport approach zone is studied. In the situation under consideration, the air routes of aircraft flows have a branched structure, that is, there can be multiple paths leading an aircraft from the entry point of the flow to the final point of the scheme. Also, there may be several merge points, at which an aircraft flow joins other ones, original and/or merged earlier. At each point of the air route scheme, a safe passage of vessels must be provided, that is, the presence of a safe time interval between the instants of aircraft passage must be guaranteed. Regulation of the arrival instants to points of a scheme is carried out by changing aircraft velocities, routes, or usage of special scheme elements: holding areas, point-merge schemes, path alignments, etc. In the problem, some model is considered taking into account directions from an air traffic controller to a pilot connected with changing the aircraft’s velocity and/or route. The resultant schedule of the aircraft arrivals to the scheme points is optimized from the point of view of a criterion minimizing the deviations of aircraft arrivals to the final point of the scheme from the nominal ones and the number of directions from air traffic controllers to pilots. The methodology for constructing the model for such a problem is proposed within the mixed integer linear programming framework. The case of several runways is not included, but the model can be easily extended to cover this case. Results of numerical modeling are given.