## 6 Conclusions  
Volatility in the number of flights poses a serious challenge to airspace management in all countries in the FABEC area. Every year, great efforts are put into trying to understand this and learning to anticipate how the number of flights may fluctuate at given times and on given days of the year. The analysis presented in this paper presents a sound mathematical method for estimating volatility in the near future based on past data. This volatility may differ \begin{table}
\begin{tabular}{l r r r r r r} \hline \hline \multirow{2}{*}{**Country**} & \multirow{2}{*}{**Hour**} & \multicolumn{3}{c}{**Values**} & \multicolumn{3}{c}{**Simulated**} \\ \cline{3-8}  & & **Mean** & **Alpha** & **Mean Simulated** & **95 th Percentile** & **ES (95\%)** \\ \hline Belgium & 9 & 179.34 & 0.002131 & 179.36 & 206 & 222 \\  & 10 & 208.33 & 0.000636 & 208.31 & 234 & 249 \\  & 11 & 191.57 & 0.001390 & 191.55 & 218 & 233 \\  & 12 & 192.45 & 0.000833 & 192.44 & 217 & 232 \\  & 13 & 205.38 & 0.000550 & 205.37 & 231 & 246 \\  & 14 & 196.22 & 0.001786 & 196.22 & 223 & 240 \\  & 15 & 178.67 & 0.000973 & 178.67 & 203 & 217 \\  & 16 & 178.43 & 0.001247 & 178.44 & 203 & 218 \\ Germany & 9 & 575.20 & 0.004061 & 575.22 & 649 & 693 \\  & 10 & 661.44 & 0.002289 & 661.44 & 730 & 771 \\  & 11 & 437.26 & 0.002441 & 437.29 & 488 & 517 \\  & 12 & 620.27 & 0.002760 & 620.23 & 689 & 730 \\  & 13 & 589.18 & 0.001910 & 589.14 & 648 & 683 \\  & 14 & 570.50 & 0.002354 & 570.49 & 632 & 668 \\  & 15 & 572.65 & 0.001920 & 572.64 & 630 & 665 \\  & 16 & 514.56 & 0.003658 & 514.58 & 579 & 618 \\ Netherlands & 9 & 206.89 & 0.001006 & 206.88 & 233 & 249 \\  & 10 & 254.77 & 0.001083 & 254.77 & 285 & 303 \\  & 11 & 236.42 & 0.001936 & 236.41 & 267 & 286 \\  & 12 & 276.40 & 0.000917 & 276.36 & 307 & 326 \\  & 13 & 226.71 & 0.000384 & 226.71 & 253 & 268 \\  & 14 & 222.44 & 0.000000 & 222.43 & 247 & 262 \\  & 15 & 237.46 & 0.00000 & 237.48 & 263 & 278 \\  & 16 & 203.65 & 0.000689 & 203.66 & 229 & 244 \\ France & 9 & 489.19 & 0.004175 & 489.16 & 554 & 593 \\  & 10 & 538.82 & 0.003457 & 538.83 & 605 & 644 \\  & 11 & 572.54 & 0.003336 & 572.50 & 641 & 682 \\  & 12 & 552.46 & 0.004130 & 552.51 & 624 & 667 \\  & 13 & 547.64 & 0.002843 & 547.60 & 610 & 648 \\  & 14 & 522.88 & 0.004047 & 522.85 & 591 & 632 \\  & 15 & 528.73 & 0.003186 & 528.78 & 592 & 630 \\  & 16 & 529.25 & 0.002619 & 529.25 & 589 & 624 \\ Switzerland & 9 & 175.15 & 0.002057 & 175.13 & 201 & 216 \\  & 10 & 196.31 & 0.000874 & 196.32 & 222 & 237 \\  & 11 & 229.38 & 0.000929 & 229.38 & 257 & 274 \\  & 12 & 209.94 & 0.001874 & 209.95 & 239 & 256 \\  & 13 & 211.18 & 0.001850 & 211.19 & 240 & 257 \\  & 14 & 169.67 & 0.004436 & 169.68 & 199 & 216 \\  & 15 & 182.47 & 0.002289 & 182.46 & 209 & 226 \\  & 16 & 180.39 & 0.002777 & 180.38 & 208 & 225 \\ Luxembourg & 9 & 38.50 & 0.000000 & 38.50 & 49 & 55 \\  & 10 & 31.79 & 0.000000 & 31.78 & 41 & 47 \\  & 11 & 41.36 & 0.000000 & 41.36 & 52 & 59 \\  & 12 & 28.83 & 0.003919 & 28.83 & 39 & 46 \\  & 13 & 41.74 & 0.018811 & 41.75 & 57 & 66 \\  & 14 & 33.82 & 0.016448 & 33.83 & 46 & 55 \\  & 15 & 44.03 & 0.008168 & 44.02 & 57 & 66 \\  & 16 & 41.91 & 0.000000 & 41.89 & 53 & 59 \\ \hline \hline \end{tabular}
\end{table} 
Table 6: Risk measures. depending on various factors, such as country, time and day of the week. This estimation effort then makes it possible to obtain the full distribution of expected flights at a given future time and, consequently, to estimate risk indicators in the form of ES and VaR. These indicators highlight situations in which the number of flights may exceed a given threshold and come to pose a risk for anyone who has to manage the airspace. The method is applied using actual data to estimate expected future flight numbers and volatilities for each period of interest in each country. Using the expected flights and variance calculated, the full distributions are obtained for those periods and the risk measures are calculated.