Separation-Compliant Time Advance in Terminal Area Arrivals: Modeling Tradeoff between Makespan and Fuel Burn

摘要

The current operational practice in scheduling air traffic arriving at an airport is to adjust flight schedules by delay, i.e. a postponement of an aircraft's arrival at a scheduled location, to manage safely the FAA-mandated separation constraints between aircraft. To meet the observed and forecast growth in traffic demand, however, the practice of time advance (speeding up an aircraft toward a scheduled location) is envisioned for future operations as a practice additional to delay. Time advance has three potential advantageous capabilities: to increase the throughput of the arriving traffic, to reduce the total traffic delay when the traffic sample is below saturation density, and to save total fuel consumption (though perhaps at the expense of increasing it for some individual aircraft). A cost associated with time advance is the fuel expenditure required by an aircraft to speed up. The contribution of this paper is a simplified optimal control model of air traffic arriving in a terminal area that gives, as a first step toward time advance, qualitative insight into the interdependence between two competing objectives: saving fuel (total, for the entire air traffic operation) and reducing the duration (makespan) of the operation. The numerical solutions provided here were obtained using, for convenience, a software packaged based on the Pseudospectral Method with Legendre-Gauss-Radau collocation.