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至2019冠状病毒病全球爆发前的88%水平，而伦敦希思罗机场等欧洲主要枢纽平均每天再次处理超过1000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。需求-能力不平衡导致航班延误，这不仅扰乱航空公司和乘客的行程，而且造成严重的财务后果和环境影响，为了减轻航班延误的风险，可以采取各种干预措施。“战略性”干预是指在某个特定的运营日之前，在任何“实时”信息（例如天气状况、机组人员短缺）变得已知之前，远远提前进行的干预。这类干预措施通常涉及限制机场每小时可安排的抵港和离港人数。另一方面，“战术性”干预是指在行动的某一天针对真实的事件进行的干预。例如，空中交通管制员知道飞机的最新位置和预计到达终端空域的时间，并且可以使用这些信息来规划最有效的飞机着陆顺序，以最大化跑道吞吐率并减少预期的空中等待时间。机场时刻表必须遵守机场容量声明，该声明对预定跑道运行的每小时次数规定了限制。然而，即使机场的时间表与其容量申报相一致，也不能保证该时间表下的延误将保持在“可接受”的限度内，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刻表优化框架，通过一个高保真度，随机和动态的空中交通控制模型，明确模拟机场延误，旨在确保最终的机场时刻表结果在一个相对较低的风险延误超过“可接受”的levels.To进一步阐述，我们提出的优化框架包括两个独立的（但相关的）模块：1。首先，我们使用一个混合整数线性规划（MILP）模型，以尽量减少时间表位移，这是定义为一个机场的时间表和一个理想的“基线”的情况之间的偏差的总量。该MILP公式包括限制可以在不同时间段安排的到达和离开的数量的约束。MILP在第一步中给出的最优时间表被视为最终机场时间表的“候选”。在这一步中，我们使用一个随机的，动态模型的机场排序问题，以测试是否在候选时间表下的预期延误满足一组基于延误的性能标准，其中包括组件的基础上准时和燃料排放。这是一个战术优化问题，其中飞机排序决策是在不断演变的随机条件下进行的。如果满足性能标准，则候选调度被接受为最终调度，并且该过程完成。否则，我们返回步骤1并重新制定MILP的约束，使其“更紧”，以进一步限制特定时段可以安排的航班数量。这个过程是重复迭代（重新制定MILP的约束，如有必要的次数），直到找到一个候选人的时间表，满足基于延迟的标准。

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.