Lyapunov Drift-Plus-Penalty Method for Atco System Making Optimal Decisions

Air traffic management is a complex process influenced by conflicting user requirements, air navigation system limitations, and unpredictable weather. These factors disrupt traffic flow, requiring interventions such as air traffic flow control. When the Air Traffic Controller (ATC) system is overwhelmed, delays, in-flight holdings, rerouting, and economic penalties become inevitable, causing congestion and passenger dissatisfaction. The paper addresses the complexity of air traffic management, which is influenced by airspace conditions and different departure rates, leading to disruptions like delays and congestion. The goal is to minimize aircraft wait times before takeoff by optimizing schedules based on airspace conditions and congestion levels. The proposed model treats aircraft routes as channels and optimizes arrival, queue stacking, and departure scheduling. It dynamically manages aircraft arrivals and adjusts departure rates to stabilize queues and reduce delays. The model is based on stochastic network optimization and queuing theory, using a Lyapunov drift-plus-penalty approach to achieve stability and minimize delays. This method balances convex optimization with queuing control and requires minimal system knowledge, aiming for improved scheduling efficiency and reduced delays in air traffic management.