Computer-implemented methods, systems, and computer readable mediums for solving large systems of linear equations, such as for aircraft traffic control and analysis, are disclosed. A method for aircraft traffic control, includes receiving as input, airspace sector information and aircraft traffic information, configuring a homogeneous system of linear inequalities comprising a plurality of linear inequalities based upon the airspace sector information and the aircraft traffic information, and resolving the homogeneous linear system to determine a second airspace sector information and a second aircraft traffic information, wherein the second airspace sector information and the second aircraft traffic information are based upon a predetermined future point of time, and wherein the resolving includes at least one of reducing a maximum infeasibility of the homogeneous linear system and reducing a sum infeasibility of the homogeneous linear system.