Abstract: Computer implemented methods and systems using a multidimensional Monotonic Lagrangian Grid (MLG) to sort and order locations of aircraft, are used for simulating, controlling, and optimizing aircraft traffic systems. The MLG is combined with algorithms for collision detection and resolution, separation assurance, and updating aircraft trajectories, and applied to test cases of the air transportation system. Physical locations describing aircraft traffic moving in complex paths are stored into a data structure of the multidimensional MLG algorithm. The moving aircraft traffic platforms are sorted and ordered on a grid structure in real space and in an indexing space, causing a monotonic mapping between indices of the grid structure and locations describing the plurality of moving aircraft. Computer operations using data stored in the multidimensional MLG determine control strategies for aircraft separation assurance and optimum routes to circumvent blockages in transport paths.

Abstract: Computer implemented methods and systems using a multidimensional Monotonic Lagrangian Grid (MLG) to sort and order locations of aircraft, are used for simulating, controlling, and optimizing aircraft traffic systems. The MLG is combined with algorithms for collision detection and resolution, separation assurance, and updating aircraft trajectories, and applied to test cases of the air transportation system. Physical locations describing aircraft traffic moving in complex paths are stored into a data structure of the multidimensional MLG algorithm. The moving aircraft traffic platforms are sorted and ordered on a grid structure in real space and in an indexing space, causing a monotonic mapping between indices of the grid structure and locations describing the plurality of moving aircraft. Computer operations using data stored in the multidimensional MLG determine control strategies for aircraft separation assurance and optimum routes to circumvent blockages in transport paths.