Multicommodity Eulerian–Lagrangian Large-Capacity Cell Transmission Model for En Route Traffic

Anewparadigm for building anEulerian–Lagrangian cell transmissionmodel for air trafficflow is developed. It is based on an aggregation of track data and is applied to the full National Airspace System in the United States. The Eulerian–Lagrangian model is based on a multicommodity network flow model constructed from historical air traffic data. The flow model is reduced to a linear time invariant dynamical system, in which the state is a vector of aggregate aircraft counts. This model is called a large-capacity cell transmission model in reference to the cell transmission model in highway traffic, which inspired this work. The predictive capabilities of the model are successfully validated against recorded air traffic data by showing an accurate match between predicted sector counts (based onfiledflight plans) andmeasured sector counts. The problemof controlling the sector aircraft count is posed as an integer program in which the dynamical system appears in the constraints. To improve the computational time for solving the problem, the integer program is relaxed to a linear program. The computational results show that a high portion of solutions of the linear program are integers, making this method appropriate for high-level traffic flow management.