Numerical Applications of Markov Chains in the Optimization and Forecasting of the Lisbon TMA Capacity

The air transport sector growth has been seen through the increase of clients’ interest and the number of aircraft operating simultaneously on different routes. This increase, despite being beneficial, represents one of the main current problems, the concern of the proper air traffic flow management near the airports’ terminal areas. This concern has triggered the development of numerous methodologies, techniques and tools with the aim of analyzing its complexity and the possibility of optimizing the TMAs capacity, allowing the achievement of an estimation of the occupancy of this capacity in the medium and/or long term and helping to anticipate the occurrence of congestion situations. The methodology selected for the analysis of this problem, in the particular case of the Lisbon TMA, was the Markov Chain Theory, with the objective of creating an algorithm that would enable the air traffic flow management, fighting against the imbalance between demand and supply and helping to optimize the limited TMA capacity. Through the analysis of the dynamic network created, it was possible to confirm the Lisbon TMA saturation, indicating the most worrying intervals and anticipating the future behavior of its capacity.