Game-Theoretic Trajectory-Negotiation Mechanism for Merging Air Traffic Management

A novel trajectory-negotiation mechanism for fairly distributing the benefits of trajectory-based operations among all the stakeholders based on bargaining theory is advanced. The trajectory-negotiation mechanism is formulated as an n-player finite strategy game. The objective of each aircraft in the game is to minimize its cost of deviating from its desired trajectory, whereas the objective of the air traffic controller is to provide clearances that ensure fairness while preventing conflicts. To avoid the need to share competition-sensitive business logic employed by individual airlines, the utility function is formulated in terms of the percentage cost deviation reported by each aircraft. Penalty costs are defined based on the rules of the bargaining game, which are determined by the air traffic controllers based on the traffic situation. The final solution is chosen from the Nash equilibriums of the game, representing the best possible outcome for all the players in the game. The Nash equilibrium of the game is found using a binary mixed-integer linear programming algorithm. The feasibility and the performance of the proposed game-theoretic trajectory-negotiation mechanism are demonstrated in a merging arrival traffic situation. Numerical studies show that the proposed mechanism can reduce the total cost by 55.62% and improve fairness by 50.3% when compared with the current first-come/first-served approach in the selected traffic scenarios in the paper.