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

截至2022年9月，欧洲的航班数量已恢复到全球疫情爆发前的88%，伦敦希思罗机场等欧洲主要枢纽平均每天处理1000多次跑道起降（即降落或起飞）。大量的空中交通对机场基础设施提出了沉重的要求，跑道容量是最关键的瓶颈。供需失衡导致航班延误，不仅扰乱航空公司和乘客的行程，还会造成严重的经济后果和环境影响。为了降低航班延误的风险，可以采取多种干预措施。“战略性”干预措施是在任何“实时”信息（如天气状况、航空公司机组人员短缺）已知之前，在特定运营日之前进行的干预措施。这些类型的干预措施通常包括限制机场每小时可安排的到达和离开的人数。另一方面，“战术”干预是指在某一天的行动中对实时展开的事件做出的反应。例如，空中交通管制员了解即将到达航站楼空域的飞机的最新位置和预计到达时间，并可以利用这些信息来规划最有效的飞机降落顺序，以最大限度地提高跑道吞吐量并减少预期的空中等待时间。在目前的实践中，机场调度是通过一个称为“机位协调”的过程进行的。机场的时间表必须符合机场容量声明，该声明对每小时预定的跑道起降次数加以限制。然而，即使机场的时间表与其容量声明一致，也不能保证该时间表下的延误将保持在“可接受”的范围内——因为，实际上，这些延误取决于一系列随机因素（例如上游延误、天气条件）以及空中交通管制员实施的实时战术干预。我们建议开发一个新的机场时间表优化框架，通过高保真度、随机和动态的空中交通管制模型明确地模拟机场延误，旨在确保最终的机场时间表导致延误超过“可接受”水平的风险相对较低。进一步详细说明，我们提出的优化框架由两个独立（但相关）模块组成：1。首先，我们使用混合整数线性规划（MILP）模型来最小化调度位移，它被定义为机场调度与理想“基线”场景之间的总偏差量。这个MILP公式包括限制在不同时间段内可以安排的到达和离开的数量的约束。将步骤1中MILP给出的最优时刻表作为最终机场时刻表的“候选”。在这一步中，我们使用机场排序问题的随机动态模型来测试候选计划下的预期延误是否满足一组基于延误的性能标准，其中包括基于正点率和燃油排放的组件。这是一个战术优化问题，其中飞机排序决策是在不断发展的随机条件下做出的。如果满足性能标准，则接受候选时间表作为最终时间表，并完成流程。否则，我们回到步骤1并重新制定MILP的约束，使它们“更紧”，以进一步限制可以在特定时隙安排的航班数量。这个过程迭代地重复（根据需要多次重新制定MILP约束），直到找到满足基于延迟的标准的候选时间表。

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.