The increasing volume of traffic in the air transportation is leading to excessive workload on air traffic controllers. Developing automated air traffic management (ATM) tools is a critical technology in reducing the workload of air traffic controllers and hence increasing the airspace capacity. The existing approaches to automated ATM either use overly-simplified air traffic and aircraft dynamics models to reduce computational complexity or end up being computationally intractable for large-scale ATM scenarios. This paper presents a new hybrid system description of modeling the decision process of the air traffic controllers in en-route and approach operations. The model is based on the domain expertise provided by the State Airport Authority and Air Navigation Service Provider (ANSP) of Turkey. The emulation of air traffic controller decision process in the hybrid model provides realistic conflict resolution maneuvers and separation assurance in 3D, while being computationally tractable. The algorithm has polynomial iteration complexity in the number of waypoints of the aircraft, which makes it scalable to large-scale ATM scenarios with more than 100 aircraft. The algorithm is validated on the real air traffic data over the Istanbul region extracted from the ALLFT+ dataset provided by EUROCONTROL, which includes over 7000 flights in a 96-hour period. The developed algorithm is also integrated into a Boeing 737-800 flight deck simulator with a custom radar display to demonstrate the applicability to existing avionics systems.