MILP Control of Aggregate Eulerian Network Airspace Models

A new Eulerian model of airspace is derived and applied to high altitude traffic for a full air traffic control center of the National Airspace System. The Eulerian model is reduced to a linear time invariant dynamical system, in which the state is a vector of aggregate aircraft counts. The model is validated against ASDI data and applied to the Oakland airspace. The problem of controlling sector aircraft count is posed as an integer program, in which the dynamical system appears in the constraints. To improve the computational time of calculating the solution, the integer program is relaxed to a linear program, solved for instances with more than one million variables. The computational results show that a high proportion of solutions of the LP are integers. The computational time is satisfactory for two hour traffic flow management problems.