مقایسه مدل سازی انتشار تاخیر در شبکه های ترافیکی هوایی ایالات متحده و اروپا   Comparing the modeling of delay propagation in the US and European air traffic networks

1. Introduction Among all the different means of transport, air transportation is the one that has experienced the fastest growth in the last century (Heppenheimer, 1995). According to the World Bank, in 2014 the number of domestic and international air passengers summed up 3.21 billions worldwide (World Bank, 2015), and it is expected to increase by 6.3% this year (ICAO, 2015). The rapid increase in demand comes at a high price, causing the transport network to become congested (Lan et al., 2006) (see also the evolution of the delays in Europe from the CODA digests of Eurocontrol since 1998 until the present (CODA). It is therefore of great importance to understand the interplay between the various components of the system. Delays are one of these components and have a great economic impact, a study for the US found that the costs imputable directly or indirectly to delays were around 40.7 billion dollars (US Congress, 2008). Delay related direct costs in Europe may look modest in comparison (1.25 billion euros) but still high (Cook and Tanner, 2011; Note). The intricacy and interaction between the elements that compose the air-traffic system qualifies it as a Complex System. Complexity is not used just to refer to complicated phenomena within Science; it emphasizes the notion of emergent behavior at the system level that surges from the interaction between its components. During the last decade, the scientific community has extensively studied these systems under the light of Network Science. In this context, air-traffic systems can be represented as networks whose vertices represent airports and its edges direct flights during a fixed period of time (Barrat et al., 2004; Li and Cai, 2004; Guimer a et al., 2005; Burghouwt and de Wit, 2005; Balcan et al., 2009; Gautreau et al., 2009). Several aspects of the air traffic network have been studied. The first works (Barrat et al., 2004; Guimera et al., 2005 ) were focused on a topological description of the network structure. The results showed a high heterogeneity in the number of connections that bear each node (the so-called degree of a node) and the traffic sustained by each connection, finding a non-linear relation between the node degree and the fluxes of passengers in a given route (Barrat et al., 2004). The Air Transportation Network can also be understood as the backbone where different dynamical processes take place. A story of notable success was the modeling and forecasting of disease spreading using air traffic data (Balcan et al., 2009). Delay propagation dynamics can be also studied within this framework (Fleurquin et al., 2013, 2013b; 2014, 2014b; Campanelliet al., 2014, 2015). Since airlines operate in an interconnected network, they are subject to propagation effects. A disruption in one flight or airport can quickly spread and multiply in cascade affecting other parts of the air transport network (Beatty et al., 1998; Allan et al., 2001; AhmadBeygi et al., 2008; Belobaba et al., 2009). The delay between flights may propagate due to several mechanisms: aircraft rotations, passengers and crew connections, or airport congestion. These factors are at the basis of the models developed to reproduce delay propagation.