Air traffic optimization models for aircraft delay and travel time minimization in terminal control areas

Abstract

This paper addresses the real-time aircraft routing and scheduling problem at a busy terminal control area (TCA) in case of traffic congestion. The problem of effectively managing TCA operations is particularly challenging, since there is a continuous growth of traffic demand and the TCAs are becoming the bottleneck of the entire air traffic control system. The resulting increase in airport congestion, economic and environmental penalties can be measured in terms of several performance indicators, including take-off and landing aircraft delays and energy consumption. This work addresses this problem via the development of mixed-integer linear programming formulations that incorporate the safety rules with high modeling precision and objective functions of practical interest based on the minimization of the total travel time and the largest delay due to potential aircraft conflicts. Computational experiments are performed on real-world data from Roma Fiumicino, the largest airport in Italy in terms of passenger demand. Traffic disturbances are generated by simulating sets of random landing/take-off aircraft delays. Near-optimal solutions of practical-size instances are computed in a short time via a commercial solver. The computational analysis enables the selection of those solutions offering the best compromise among the different objectives.

Appendix

Figure 3 presents a numerical example of traffic flows for FCO TCA. We consider two landing aircraft (named A and B) and a taking-off aircraft (named C). The following routes are considered by the solver. Aircraft A has two routes: 3-6-8-10-11-13 is the default route, and 3-6-8-11-12 is the alternative route. Aircraft B has the default route 1-4-7-10-11-13, while aircraft C has the default route 12.

The entrance (exit) due date of A is 40 (640), the entrance (exit) due date of B is 0 (640), the entrance (exit) due date of C is 630 (630). The release time of each aircraft is equal to the corresponding entrance due date time. The travel time of each aircraft in each resource is reported in Fig. 4.

Fig. 3

A numerical example for FCO TCA

Figure 4 a (b) gives the Gantt diagram of the optimal ATFM-TCA solution for the default (alternative) routes. In the case with default routes, the routes of aircraft A and B are conflicting and the optimal sequencing order is first B and then A. The consecutive delay of A is 46 at the entrance (a too small delay to consider half circles in the holding resource) and 95 at the runway. In the case with alternative routes, the routes of aircraft A and C are conflicting and the optimal sequencing order is first A and then C. Thus, the consecutive delay of C is 20.

Fig. 4

Gantt diagrams of the solutions with default routes (a) and alternative routes (b)