The “Mathematical Models and Methods in Earth and Space Sciences” Conference will be held on 19-22 March 2019 in Rome. Our Salvatore Micciché of University of Palermo is one of the invited speakers. He will speak about “A percolation approach for the detection of bottlenecks in air traffic networks”.
Here is the abstract of the speech of Salvatore Micciché.
Our main aim is detecting critical links in air traffic networks by using a percolation approach.
While the percolation approach has already been considered in other model complex systems, to our
knowledge it is the first time that an empirical study using this methodology is performed at the level of the
network that originates from the navigation points that appear in the aircraft flight plans. In our network,
the navigation points are the nodes and we set a link between two nodes whenever there is a flight
In general, percolation is a random process exhibiting a phase transition. In the simplest setting percolation
is investigated in simple geometrical systems such as regular lattices covering a 2D surface. Even in the
simplest setting there are different variants of the percolation problem. Specifically, one speaks about bond
percolation when a link between two neighbouring sites is present with probability q and its absence is
observed with probability (1-q). In this variant all sites are present in the system and links between any pair
of them may or may not be present. In the other variant of node percolation the links of the lattice are
always present between two occupied sites, but each site is occupied with probability q and empty with
probability (1-q). In our context, percolation refers to probabilistic, network-wide emergent behaviour,
between sites or sub-systems (clusters). Specifically, percolation refers to the phenomenon by which,
according to the value of q, which play the role of an order parameter, the network shows a transition from
a phase where all nodes are connected in a unique giant connected component to a phase where nodes
belong to clusters of elements not connected between each others, i.e. the network gets fragmented.
As such while in the first case it is always possible to reach any point in the network starting from any other
point, as soon as q increase the network gets fragmented into smaller pieces, which prevents a potential
user to reach any point in the network starting from any other point.
The investigations we have so far performed, although preliminary, yet clearly shows that percolation
occurs in the navigation point network generated starting from the aircraft trajectories flying over the ECAC
airspace in a cartain day and this approach is therefore able to detect links, characterized by certain q
values, which carry a potential risk of disruption in the network.
We will also discuss the implications of our results at the level of air traffic sectors. These are the
elementary blocks in which the airspace is partitioned for the purpose of a better management of the
aircraft trajectories when performing conflict detection and resolution. One key parameter characterizing
sectors is capacity, i.e. the maximal number of aircraft present in the sectors in a certain time-interval. We
will specifically discuss the role of capacity in relation to the value qc of the order parameter q that
characterizes the critical links.