A new hierarchical architecture for Air Traffic Management: Optimisation of airway capacity in a Free Flight scenario

Abstract

We describe a new two-level hierarchical architecture for air traffic management problems with corresponding mathematical models. The first level represents the air route network, and its solutions provide the air traffic flows on each arc of the network. This level interacts with the second one, which represents the single airway and its own air traffic flows. This latter model allows us to assign the optimal air traffic route to each aircraft and to optimise the airway's capacity. Furthermore, for the airway optimisation model we have also carried out a computational analysis, providing both exact and heuristic solutions, for problem instances based on real data. These are obtained with the Cplex solver exploiting the mixed integer mathematical formulation and with a proposed heuristic algorithm for problems of larger size, respectively. The heuristic solutions obtained are within a maximum gap of 13% from the LP relaxation.

Introduction

The minimisation of delays due to congestion in air traffic networks has received a lot of attention both from aviation authorities and from the scientific research community. The additional costs caused by delays are substantial, and they are quantified by international organisation:

• Euro 5.73 billion/year produced by air traffic control delay (1999);

• $2 billion/year produced by longer trajectories due to the fixed airways network (in Europe);

• $10 billion/year due to air traffic control actions which generate deviations from optimal aircraft flight profiles.

In the past few years, many mathematical and simulation models have been developed in order to reduce the amount of congestion and to examine the possibility of introducing auxiliary systems which better support air traffic management. Models regarding either tactical or strategic control have been developed. For tactical models we can cite Bianco and Bielli [8], Bianco et al. [9], [10], and Zenios [21]. Andreatta et al. [2], [4], Andreatta and Brunetta [3], Bertsimas and Stock [7], Hoffman and Ball [15] and Vranas et al. [19] have proposed different models for the ground holding problem, which has been efficiently implemented in the United States airspace (see [17]). Many members of the aviation community feel current policies, procedures and technologies antiquated and inadequated, and are pushing toward the new concept of Free Flight. In 1995, Fearnsides [14] proposed the following definition of Free Flight: “A safe and efficient flight operating capability under instrument flight rules in which the operators have the freedom to select their path and speed in real time. Air traffic restrictions are only imposed to ensure separation, to preclude exceeding airport capacity, to prevent unauthorised flight through special use airspace, and to ensure safety of flight. Restrictions are limited in extent and duration to correct the identified problem. Any activity which removes restrictions represents a move toward Free Flight.” Aviation authorities have played an important role in the definition of this new paradigm. They have investigated the possibility of delegating air traffic control functions to the flight deck, allowing more freedom of movement to airspace users. In particular, Eurocontrol has developed the Free Route Experimental Encounter Resolution project [13], in order to investigate the feasibility of this concept and to see the possibility to involve the airspace users in the ATM loop.

More in general, the success of Free Flight will be measured by its ability to increase capacity, safety and efficiency [16].

In case of congestion, policies adopted in North America and Europe are different. In North America, collaborative processes between the Air Traffic Command Control, System Command Center and Airline Operational Control Centers are implemented. These initiatives belong to a wider framework called Collaborative Decision Making. This concept has been explored by several authors. We can cite Adams et al. [1], Ball et al. [6], Jenny [16] and Wambsganss [20].

In Europe, no such collaborative processes are implemented, since en-route airspace, and not only airports, is highly congested. This is due to both the airway system, built up by a fixed track system connecting airports, and to the existing air navigation and air traffic control rules. Nowadays, the minimum safe separation between aircraft is assured only by means of altitude and/or longitudinal separations. This type of structure represents a bottle-neck for air traffic flow with the increase of flight volume. Though some measures have been taken to reduce traffic congestion, much more is needed before air traffic can once again flow smoothly and efficiently. We are interested in the development of all decision methodologies which can make maximum use of airspace without violating safety constraints.

In this paper, we develop a new two-level hierarchical architecture for the Air Traffic Management problems with corresponding mathematical models. We envision the proposed architecture in a centralised air traffic flow management system, but it easily fits into the new concept of Free Flight, particularly with reference to the navigation area. It may be used as a tool for addressing the issue of the efficient use of the airspace, that is of considerable concern to the European air traffic control system.

Moreover, we carried out a computational analysis and evaluation of the mathematical model which describes the lower level of the architecture. To verify its validity, we used a series of different size test instances based on real data provided by ENAV (Italian Aviation Administration Agency). Smaller instances have been solved efficiently using the mathematical programming solver Cplex, which has provided exact solutions in a short computation time. Due to solution time restrictions, Cplex was not able to solve larger instances. A heuristic algorithm was employed to obtain “good” solutions, the quality of which has been tested using a lower bound computed by the linear relaxation, obtaining a maximum gap of 13%.

The paper is organised as follows: in Section 2 we describe the two-level hierarchical architecture with the corresponding mathematical model formulations, and the model integration. Section 3 discusses the computational analyses and the evaluation of the airway model. We present both exact and heuristic solutions for problem instances based on real data. Finally, Section 4 contains conclusions and future research.