An efficient combinatorial optimization algorithm for optimal scheduling of aircraft arrivals at congested airports

Aircraft are often required to delay their landing/arrival time at an airport when they are approaching the terminal radar approach control (TRACON) area, due to airport capacity constraints. In regions like the Northeast (NE) corridor of the US the sectors are small, with shorter controllable time, and these areas involve very complex traffic flows. Hence, many sectors are needed to absorb the required delays and aircraft have to be delayed when they are far away from the airport. Over these long distances, the ability to accurately predict aircraft trajectories is not good enough to compute expected times of arrival with precision, due to uncertain winds and piloting techniques. The existent scheduling system - traffic management advisor-single center (TMA-SC) - ignores this uncertainty and schedules the aircraft in the predicted first come first served (FCFS) order. This can lead to inefficient aircraft sequences and scheduled times of arrival (STAs). Pilot-in-loop simulations have revealed that at such busy airports, a loosely coupled hierarchy of multiple single point dynamic schedulers, in which scheduling constraints at downstream scheduling points are passed upstream, would be beneficial, because it would eliminate exclusive reliance on distant trajectory estimates. This concept of coupling scheduling over a small region to the scheduling over a bigger outer region is at the core of the new multi center TMA (McTMA) system, currently in development at NASA Ames Research Center. However, in all the proposed algorithms for scheduling aircraft in McTMA no consideration has been given to optimizing the arrival aircraft sequences. In this paper, we work within such a hierarchial scheduling structure and develop a new efficient scheduling algorithm, which uses combinatorial optimization techniques to find the optimal arrival aircraft sequence and the optimal STAs for the aircraft at a certain reference point, given that the maximum number of position switches from the FCFS order is specified. Scheduling constraints and minimum separation requirements depending on the leading and trailing aircraft types, will be taken care of within the scheduling algorithm. The algorithm will also enable prioritization of aircraft according to airline preferences and it will distribute the allocated delays optimally among all the sectors that lie along the route of the aircraft