Macroscopic Fundamental Diagram for Airplane Traffic: Empirical Findings

For car traffic it was found that a more crowded area leads to a lower speed and a lower arrival rate. The relation between crowdedness and speed (or arrival rate) can be expressed in a network fundamental diagram, or macroscopic fundamental diagram (MFD). Similar concepts have been shown for pedestrian and train traffic. In this paper, we extend the concept to three spatial dimensions. While simulations have explored some concepts, we present for the first time empirical results of the relation between the crowdedness in the air and the performance of the "network." We base our results on several months of data of airplanes around Amsterdam Schiphol Airport. Similar to car traffic, we observe a reduction in speeds as the number of airplanes in the area increases. However, even at the highest observed densities, we do not see a reduction in flows. This is because of active and intensive management (based on departure/landing possibilities), comparable to perimeter control in traffic, as well as a minimum airplane speed. This paper introduces an interesting concept of applying a MFD to three-dimensional (3D) spaces. We also show to what extent the performance reduction is caused by speed reduction and to what extent it is caused by less efficient routes. The MFD concept can eventually be used to also manage 3D airspaces for applications with less strict microscopic air traffic management than the current management around airports.