  In this work we present a model of an air transportation traffic system from
the complex network modelling viewpoint. In the network, every node corresponds
to a given airport, and two nodes are connected by means of flight routes. Each
node is weighted according to its load capacity, and links are weighted
according to the Euclidean distance that separates each pair of nodes. Local
rules describing the behavior of individual nodes in terms of the surrounding
flow have been also modelled, and a random network topology has been chosen in
a baseline approach. Numerical simulations describing the diffusion of a given
number of agents (aircraft) in this network show the onset of a jamming
transition that distinguishes an efficient regime with null amount of airport
queues and high diffusivity (free phase) and a regime where bottlenecks
suddenly take place, leading to a poor aircraft diffusion (congested phase).
Fluctuations are maximal around the congestion threshold, suggesting that the
transition is critical. We then proceed by exploring the robustness of our
results in neutral random topologies by embedding the model in heterogeneous
networks. Specifically, we make use of the European air transportation network
formed by 858 airports and 11170 flight routes connecting them, which we show
to be scale-free. The jamming transition is also observed in this case. These
results and methodologies may introduce relevant decision making procedures in
order to optimize the air transportation traffic.
