New network metrics for complex interactions!
Author: Silvia Zaoli
Air traffic can naturally be described as a networked system, where nodes are the different elements of the airspace, e.g. airports, airlines, or arrival and departure managers, and the links between those nodes describe the interaction between them. Network metrics capture relevant information from these network, as the interconnection of system’s elements and the causal relations between them, representing the spreading channel for delays and costs.
Figure 1: Network where nodes are airports and links are flights.
Delays and cancellations disrupt connections in the network, affecting the airports’ connectivity. This is why we considered centrality metrics, which measure the “importance” of the node of a network in terms of its role in getting the network connected, to evaluate the impact of delays in different scenarios. Existing centrality metrics are not suited to the ATM system, because they do not consider the temporal dynamics of the network, where links (flights) appear and disappear. Therefore, we developed the Trip centrality metric, accounting for the time ordering of connections, and showed that it is able to tell apart situations where delays affect the network connectivity from situations where they do not.
Figure 2: A temporal network changes in time, as links (black arrows) appear and disappear. A walk on this network (green arrow) must respect the time ordering.
Delays propagate through the network by means of the interactions between elements, e.g. through flights due to reactionary delays. We proposed to identify the channels of delay propagation by detecting causal relations (in the statistical sense) between the state of delay of airports. The network where nodes are airports and links are causal relations (named causal network) informs us on the patterns of delay propagation. The denser the network is, the more delay propagates. Therefore, we suggested the use of the density of links and feedback patterns in the causal network to assess the impact of innovations on the propagation of delay. Furthermore, to account for non-linearity in the propagation of delay, we proposed to use a method of causality detection which focuses on extreme delay events.
These new network metrics developed by Domino to assess the impact of innovations on the ATM system were presented at the SESAR Innovation Days in Salzburg! Download the paper and the presentation for more information about these exciting new metrics!
Follow our future updates to see the applications of the metrics to the results of the Agent Based Model in different scenarios!