Phase changes in delay propagation networks

📝 Abstract

The analysis of the dynamics of delays propagation is one of the major topics inside Air Transport Management research. Delays are generated by the elements of the system, but their propagation is a global process fostered by relationships inside the network. If the topology of such propagation process has been extensively studied in the literature, little attention has been devoted to the fact that such topology may have a dynamical nature. Here we differentiate between two phases of the system by applying two causality metrics, respectively describing the standard phase (i.e. propagation of normal delays) and a disrupted one (corresponding to abnormal and unexpected delays). We identify the critical point triggering the change of the topology of the system, in terms of delays magnitude, using a historical data set of flights crossing Europe in 2011. We anticipate that the proposed results will open new doors towards the understanding of the delay propagation dynamics and the mitigation of extreme events.

💡 Analysis

The analysis of the dynamics of delays propagation is one of the major topics inside Air Transport Management research. Delays are generated by the elements of the system, but their propagation is a global process fostered by relationships inside the network. If the topology of such propagation process has been extensively studied in the literature, little attention has been devoted to the fact that such topology may have a dynamical nature. Here we differentiate between two phases of the system by applying two causality metrics, respectively describing the standard phase (i.e. propagation of normal delays) and a disrupted one (corresponding to abnormal and unexpected delays). We identify the critical point triggering the change of the topology of the system, in terms of delays magnitude, using a historical data set of flights crossing Europe in 2011. We anticipate that the proposed results will open new doors towards the understanding of the delay propagation dynamics and the mitigation of extreme events.

📄 Content

Phase changes in delay propagation networks Seddik Belkoura, Massimiliano Zanin The INNAXIS Foundation & Research Institute Madrid, Spain {sb, mz}@innaxis.org

Abstract— The analysis of the dynamics of delays propagation is one of the major topics inside Air Transport Management research. Delays are generated by the elements of the system, but their propagation is a global process fostered by relationships inside the network. If the topology of such propagation process has been extensively studied in the literature, little attention has been devoted to the fact that such topology may have a dynamical nature. Here we differentiate between two phases of the system by applying two causality metrics, respectively describing the standard phase (i.e. propagation of normal delays) and a disrupted one (corresponding to abnormal and unexpected delays). We identify the critical point triggering the change of the topology of the system, in terms of delays magnitude, using a historical data set of flights crossing Europe in 2011. We anticipate that the proposed results will open new doors towards the understanding of the delay propagation dynamics and the mitigation of extreme events.

Keywords-delays; delays propagation; causality; functional networks I. INTRODUCTION In the last decade, the study of complex systems has shifted from the reductionist hypothesis towards an information processing approach, i.e. how information is distributed among, combined with, and modified by the different elements of the system [1]. Not only the constituting elements are important, but also their relationships; and understanding the complete system becomes tantamount to analyzing how information is processed within, and exchanged between, the individual elements. Examples span from the study of financial markets [2] to the human brain [3]. This information processing approach has recently been adapted to air transport, and specifically to the study of delays propagation. While delays are generated at a local scale (i.e. by individual aircraft), their propagation is a process that lies on a more global scale. Local metrics, as for instance “delay multipliers”, are useful to understand how delays are generated [4, 5]. Nevertheless, shedding light on how delays propagate, as the result of interactions between flights and airports, requires a more systemic approach, as the one provided by complex networks [6-8].
In recent years, complex networks have been used to characterize the structures created by delays propagation – see, for instance, [9-12]. Of special interest is the use of functional networks, i.e. networks in which nodes (in this case, airports) are connected by a link if a delay propagation process has been identified within the corresponding operational data. In other words, suppose one is to identify if a delay propagation happened between airports A and B. The solution entails obtaining two time series, for instance the average hourly delays in both A and B; for then calculating the presence of a correlation (or of a causality) between both time series. If a causality ! →! is detected, one can then conclude that the delays observed in B are (partly) the result of the delays observed in A.
The use of functional networks for the understanding of delays propagation presents some important advantages. First, networks yield a global view of the propagation process, beyond the dynamics of individual flights and airports. Second, they are reconstructed using only real operational data, and not a priori information; on the contrary, models of delays propagation can be useful, but their results are as good as the models themselves – if some processes are not correctly modeled, results may be misleading. Third, they are able to identify indirect propagations, i.e. propagations of delays between pairs of airports not connected by a direct fly. On the other hand, functional networks also entail an important problem: all available data are used in their reconstruction. In other words, if a causality is detected between two airports, it means that “on average” a propagation process is present. Let us state this the other way around: if an abnormal delay propagation only appears under certain conditions, such relation may be smoothed by the average process, thus yielding no statistically significant causality. In this contribution, we tackle this problem by comparing the results obtained through two causality metrics. First, the well-known Granger Causality (GC) [13-14], a metric that assesses whether a time series can be used to forecast a second one. This analysis is performed over all the available data, to provide a quantification of the average causality relation between the series. As such, GC suffers from the aforementioned problem of statistical smoothing. Second, a recently proposed causality of extreme events [15], which detects causa

This content is AI-processed based on ArXiv data.