In the US, delays in the Air Traffic Management Systems (ATMS) are most often caused by weather events, which are stochastic in nature. In practice however, for complexity reasons, these stochastic obstacles are dealt with using overly conservative, deterministic strategies. This means avoiding en- tirely storm zones that have a very good chance of vanishing in the near future, which translates into lost airspace capacity and unnecessary delays. In Europe, the situation is slightly different. There, sector capacity constraints rather than weather are the key limiting factor in ATM. Again, these disturbances are stochastic in nature and there too, overly conservative deterministic routing strategies result in lost airspace. In this work we try to reduce the amount of wasted capacity by solving the optimal path planning problem in a framework that models both the weather patterns and the sector capacity constraints by a stationary Markov chain. If we assume that a priority order is given ranking the various aircraft priorities, our algorithm has a complexity that only grows linearly with the number of aircraft. In simulated examples, as weather and traffic intensity increase, we show a significant improvement over conservative routing strategies. We also study large-scale numerical performance on a simplified European airspace with a large number of aircraft.
["Alexandre d'Aspremont", 'Devan Sohier', 'Arnab Nilim', 'L. El Ghaoui', 'Vu Duong']
Optimal path planning for air traffic flow management under stochastic weather and capacity constraints