Eulerian network model of air traffic flow in congested areas

We derive an Eulerian network model applicable to air traffic flow in the National Airspace System. The model relies on a modified version of the Lighthill-Whitham-Richards (LWR) partial differential equation (PDE), which contains a velocity control term inside the divergence operator. We relate the PDE to aircraft count, which is a key metric in air traffic control. Using the method of characteristics, we construct an analytical solution to the LWR PDE for the case in which the control depends only on space (and not time). We validate our model against real air traffic data (ETMS data), by first showing that the Eulerian description enables good aircraft count predictions, provided a good choice of numerical parameters is made. Finally, we show some predictive capabilities of the model.