Effects of aircraft separation on air traffic flow management models

The Air Traffic Flow Management (ATFM) problem aims at optimizing flight trajectories taking into account the capacity of the air traffic network resources. To this end, mathematical models for ATFM (e.g. Bertsimas and Stock-Patterson 1998) include capacity constraints at airports and en-route sectors, to limit the number of aircraft that simultaneously use the same resource: for example, in Europe, a feasible plan ensures that the overall number of aircraft entering a sector in one hour is below a given threshold. Capacities are determined at a strategic phase such that many requirements, including available control facilities and aircraft separation, can be matched. However, the trajectories corresponding to actually filed flight plans in the European Airspace (Eurocontrol, 2017) show that declared capacities are often conservative and a larger number or aircraft is allowed. Starting from Djeumou Fomeni et al. (2017), we propose a new Integer Programming model for ATFM aiming at better exploiting the available observed capacity. The model considers further flow management actions related to changes in the flight level and includes constraints to guarantee horizontal and vertical aircraft separation. It has been tested on European ATFM instances, and an analysis of the possible improvements that can be obtained in terms of airport throughput, flight delays and costs is presented.