It appears that the European ATM system - considered as a whole - can be defined as resilient.
Fig. 6.9 (top-left panel) plots the two previously introduced metrics (µ+ and µ−) against each other for all the days available in the data set. It can be observed that all points lie above the diagonal (grey dotted line), for the exception of Wednesday 7th and Friday 16th of December. That means that for almost all days of the data set, there have been more negative delay generated than positive ones. But what happened on those two specific days so that the system looses its resilience? Tab. 6.3 reports all reported perturbations in the Network news section of the EUROCONTROL Network Operations Portal (NOP).
Indeed, December 16th seems to have been a particularly disturbed day, with the closure of
0 , 3 2 0 , 3 4 0 , 3 6 0 , 3 8
Figure 6.9: Characterisation of the system in the temporal domain. Top left panel represents the relationship between µ−and µ+at each day. The remaining graphs represent the fluctuation of the system’s daily response as a function of the number of flights (top right); the average delay at take-off (bottom left); and the day of the day (bottom right). In all, the red solid curves represent the best quadratic fit. The dashed blue line in bottom right panel represents the number of flights as a function of the day. Reprinted with permission from [BPZ16].
two important airports (Manchester and Stockholm) and strong wind reported at big airports (Heathrow, Charles de Gaulle Orly, Brussels, Munich, Rome, etc.). However, the high magni-tude of these perturbations, while not frequent, can occur on other days, as reported on the 23rd of November, without affecting the resilience of the system. Also, the perturbations suf-fered during the 7th of December seem much less important and still affected the resilience of the system, although it touched central airports like Madrid, Heathrow, Oslo or Amsterdam.
The resilience of the airborne phase of the system (during a day timeframe) thus appears to be uncoupled with the operational conditions encountered at the airports, though other factors as sectors congestion or closure - more implicated in the direct route of the flights - might be responsible for the non-resilient behaviour of the system on those particular days.
It is quite remarkable that not only most days appear to be resilient, but that - considering a day long of data - the system is able to recover positive delays7 whatever is the value of such
7This does not mean, of course, that airborne delays do not exist, nor that an individual flight cannot be
Date Airport(s) Perturbation
Table 6.3: List of perturbations for three days of 2011, as reported by the EUROCONTROL Network Operations Portal (NOP). Reprinted with permission from [BPZ16].
delays. In other words, the resilient ability of the system does no seem to saturate, and that is confirmed by the linear behaviour of the quadratic regression included in the top-left panel (red curve). Whilst lacking the data resources to study the cause behind the appearance of these delay generating events and the relationship behind their dynamics (as their proportional relationship leads to diverse question as whether positive events creates negatives ones; or whether the opposite is true, etc.), it can nevertheless be observed that the magnitude of the system’s reaction remains partly framed by the traffic and the average take-off delays of that day (see Fig. 6.9 top-right and bottom-left panels). The slight correlations highlighted
delayed: just that generated and recovered delays, on average and on a daily scale, cancel out.
Table 6.4: p-values for the Kolmogorov-Smirnov test, between the distributions of generated delays of the days of the week - see Fig. 6.9 (bottom right panel). Reprinted with permission from [BPZ16].
Mon. Tue. Wed. Thu. Fri. Sat. Sun.
Mon. 1.0 9.74· 10−1 4.78· 10−1 9.01· 10−1 7.62· 10−1 4.33· 10−5 1.06· 10−4
Figure 6.10: Characterisation of the system in the temporal domain as a function of the hour.
The dashed blue line represents the fraction of flights as a function of the hour of the day.
Reprinted with permission from [BPZ16].
with the linear regressions suggest that less traffic and more take-off delays are coupled with a stronger absorption of airborne delay; this is probably because take-off delays provide incentives to the pilot for asking the controllers for a shortening of the route - which is, in turn, much easier to provide when less traffic (i.e. more space in the sky) is observed. Such features remain insufficient to explain the general behaviour of the system’s airborne reactions without additional data; however, they bring insights to the understanding of the little fluctuations observable within the magnitude of the system’s response (i.e. to what is due the difference between µ− and µ+). This is furthermore confirmed by the bottom-right panel, where the difference between the positive and negative response of the system have been plotted as a function of the day of the week, and where a Kolmogorov-Smirnov test (see Tab. 6.4) confirms the stronger reaction of the system on weekends - that is when both the traffic and take-off delays are lower.
Finally, Fig. 6.10 resumes the evolution of both the creation of positive delays and the resilience of the system as a function of the hour of the day. It can be appreciated that the resilience is particularly high at the end of the day, while low in the early morning. The blue dashed line specifies the fraction of flights operating as a function of the hour of the day, notably suggesting that the lower proportion of flights during night shall wide up the interval confidence of the high and low resilience reported during the two phases of the night. However, this pattern can also be explained by the fact that flights on their landing and take-off phase are characterised with respectively high and low resilience (see further in Section 6.2.4). Specifically, the high resilience between 9 p.m. and midnight might be due to the higher proportion of landing flights; the low resilience between 1 a.m. and 6 a.m. to the higher proportion of departing flights; and finally, the equilibrium between take-offs and landings during the day generates a stable resilience.