Coordination of Strategic and Tactical Interventions for Reducing Air Traffic Delays: A Case Study Based on Heathrow Airport

As of September 2022, flight numbers in Europe have returned to 88% of the levels seen prior to the global outbreak of Covid-19, and major European hubs such as London Heathrow are again processing more than 1000 runway movements (i.e. landings or take-offs) per day on average. Large volumes of air traffic impose heavy demands on airport infrastructure, with runway capacity being the most critical bottleneck. Demand-capacity imbalances result in flight delays, which not only disrupt airline and passenger itineraries but also have serious financial consequences and environmental impacts.

In order to mitigate the risk of flight delays, various types of interventions are possible. "Strategic" interventions are those that are made far in advance of a particular day of operations, before any 'real-time' information (e.g. weather conditions, airline crew shortages) becomes known. These types of interventions typically involve restricting the numbers of arrivals and departures that can be scheduled per hour at an airport. On the other hand, "tactical" interventions are those that are made on a particular day of operations in response to events that unfold in real time. For example, air traffic controllers have knowledge of the latest positions and estimated arrival times of aircraft that are due to arrive in the terminal airspace and can use this information to plan the most efficient sequence of aircraft landings in order to maximise runway throughput rates and reduce expected airborne holding times.

In current practice, airport scheduling is carried out via a process known as "slot coordination". Airport schedules are required to comply with airport capacity declarations, which impose limits on hourly numbers of scheduled runway movements. However, even if an airport's schedule is consistent with its capacity declaration, there is no guarantee that the delays seen under that schedule will remain within `acceptable' limits - as, in reality, these delays depend on a range of stochastic factors (e.g. upstream delays, weather conditions) as well as the real-time tactical interventions implemented by air traffic controllers. We propose to develop a new framework for airport schedule optimisation which explicitly models airport delays through a high-fidelity, stochastic and dynamic model of air traffic control and aims to ensure that the final airport schedule results in a relatively low risk of delays exceeding 'acceptable' levels.

To elaborate further, our proposed optimisation framework consists of two separate (but related) modules:

1. First, we use a mixed integer linear programming (MILP) model to minimise schedule displacement, which is defined as the total amount of deviation between an airport schedule and an ideal 'baseline' scenario. This MILP formulation includes constraints that restrict the numbers of arrivals and departures that can be scheduled in different time slots.

2. The optimal schedule given by the MILP in Step 1 is regarded as a 'candidate' for the final airport schedule. In this step we use a stochastic, dynamic model of the airport sequencing problem to test whether or not the expected delays under the candidate schedule satisfy a set of delay-based performance criteria, which includes components based on punctuality and fuel emissions. This is a tactical optimisation problem in which aircraft sequencing decisions are made under continuously-evolving random conditions. If the performance criteria are satisfied, then the candidate schedule is accepted as the final schedule and the process is completed. Otherwise, we return to Step 1 and reformulate the constraints of the MILP, making them 'tighter' in order to further restrict the numbers of flights that can be scheduled in particular time slots. This process is repeated iteratively (reformulating the MILP constraints as many times as necessary) until a candidate schedule is found which satisfies the delay-based criteria.