## 1 Introduction  
Due to the growing number of flights, increasing delays and high-cost pressure on the whole aviation system, the provision of Air Navigation Services (ANS) has recently drawn increasing attention from both academics and policy decision-makers. A major challenge regarding ANS provision is \"planning under uncertainties\", e.g., as a result of volatile traffic demand in terms of movement numbers and flow patterns, which can significantly influence resource planning and allocation. Several factors could cause or increase volatility, e.g., weather, strikes, geopolitical factors, airline decisions and unexpected economic downturns [1]. Volatile traffic affects ANS planning on multiple time scales and operational levels [2]. Changes in traffic demand and flow patterns have a direct influence on pre-tactical and strategic capacity planning and on resulting delays, their associated costs and safety. Thus, traffic volatility and the associated airspace risk have become a daily concern for Europe's ANSPs and Functional Airspace Blocks (FABs), posing a complex challenge due to the size and extent of the problem. So much so that FABEC launched an interactive platform in 2018 to discuss this topic as part of an initiative addressing new developments in air traffic flow management. In the aftermath of the COVID-19 pandemic, the importance of addressing this issue has become even clearer: Although traffic in FABEC started to recover in 2021, the increase in demand was slow and accompanied by extreme volatility, as unplanned flights put pressure on airspace capacity and staff resources. Changes in traffic demand are not a new phenomenon. But there are at least two reasons that explain why this issue is taken seriously and why a more in-depth analysis of its causes and consequences is being undertaken [3]. On the one hand, volatility has shifted from being an isolated phenomenon to affecting the entire aviation system. On the other hand, recent years have been characterised by increasingly wide variations in the volume of flights and routes (and a high level of volatility in the rate of recovery of traffic levels across Europe following the COVID-19 pandemic). Figure 1 shows changes in air traffic relative to the base year of 1970 for different countries. Note that, in all cases, the tendency is for a steady increase as years go by. Surprisingly, in 2019, air traffic fell just prior to the general spread of the COVID-19 pandemic. COVID-19 affected the mobility of European air transport with a reduction of as much as 89% in the number of flights [4] and created an uncertain future for the aviation industry [5]. In any event, it must be noted that, in general, the air traffic pattern shows tremendous changes, mean reversion and jumps. ANSPs are constantly recruiting new personnel (controllers) and adapting capacity to demand to provide more flexibility. These solutions have proved effective in the short term [7], but as activity in the industry becomes even more unpredictable [8; 9], it is increasingly clear that new ways of setting targets, assessing performance plans in terms of profitability and ultimately measuring the impact of volatility on ANSP operations need to be found. Providing flexible air traffic services therefore requires new thinking to minimise  
Figure 1: Rate of change in air traffic relative to 1970. Source: Prepared by authors using data from ref. [6]. the impact of volatility on the travelling public, while at the same time providing the capacity to meet demand in the short- and long term. This means that efforts to understand what volatility is and propose ways to measure and estimate it are especially welcome in this topic. The complexity and scope of the industry offer a number of research opportunities from a variety of perspectives. For example, studies on volatility have focused on applying a few metrics [10] or [11] realise a survey on Artificial Intelligence (AI) in order to maintain aviation safety.