This paper presents a propagation dynamics model for congestion propagation in complex networks of airspace. It investigates the application of an epidemiology model to complex networks by comparing the similarities and differences between congestion propagation and epidemic transmission. The model developed satisfies the constraints of actual motion in airspace, based on the epidemiology model. Exploiting the constraint that the evolution of congestion cluster in the airspace is always dynamic and heterogeneous, the SIR epidemiology model (one of the classical models in epidemic spreading) with logistic increase is applied to congestion propagation and shown to be more accurate in predicting the evolution of congestion peak than the model based on probability, which is common to predict the congestion propagation. Results from sample data show that the model not only predicts accurately the value and time of congestion peak, but also describes accurately the characteristics of congestion propagation. Then, a numerical study is performed in which it is demonstrated that the structure of the networks have different effects on congestion propagation in airspace. It is shown that in regions with severe congestion, the adjustment of dissipation rate is more significant than propagation rate in controlling the propagation of congestion.

In order to alleviate flight delay it is important to understand how air traffic congestion evolves or propagates. In this context, this paper focusses on the aggravation of airport congestion by the accumulation of delayed departure flights. We start by applying a heterogeneous network model that takes congestion connection/degree into consideration to predict departure congestion clusters. This is on the basis of the fact that, from a micro perspective, the connection between congestion and discrete clusters can be embodied in models. However, the results show prediction to be of high accuracy and time consuming due to the complexities in capturing the connection in congested flights. The problem of being highly time consuming is resolved in this paper by improving the models by stages. Stage partitioning based on the variation of delay clusters is similar to the typical infectious cycle. For heterogeneous networks the model can describe the congestion propagation and its causes at the different stages of operation. If the connection between flights is homogeneous, the model can describe a more indicative process or trend of congestion propagation. In particular, for single source congestion, the simplified multistage models enable short-term prediction to be fast. Furthermore, for the controllers, the accuracy of prediction using simplified models can be acceptable and the speed on the prediction is significantly increased. The simplified models can help controllers to understand congestion propagation characteristics at different stages of operation, make a fast and short-term prediction of congestion clusters, and facilitate the formulation of traffic control strategies.

To be different from the traditional concept of congestion, congestion propagation based on the correlation between aircraft is given. And the main resource shared and competed for in airspace is the air route network, especially the intersection linking the multiroute. The system composed of congestion propagation units operates in airspace network, which is limited by the network geometry and the correlation between aircraft. This paper presents models based on the congestion and propagation characteristics in complex network, predicting the trend of congestion propagation and the peak of congestion size. By analyzing the relationships between system parameters and congestion propagation and accounting for the effects of propagation across networks, this paper enhances the current dynamics models of congestion propagation in airspace. Firstly, a heterogeneous network model is introduced to reveal the propagation process of aircraft with different degrees of correlation. This is followed by the specification of two simplified models for short-term prediction, just taking the sector capacity, propagation rate, and dissipation rate into account. And the propagation rate and dissipation rate depend on the sector geometry and aircraft distribution. Using them (sector capacity, propagation rate, and dissipation rate), the prediction models are accurate in predicting the evolution of congestion peak and propagation trend in comparison with the sample data of intersections in the sector. Of them, the model with capacity limitation is more accurate on busy hour. And on non-busy hour, capacity is insensitive in predicting congestion clusters. Furthermore, the computing method of propagation rate and dissipation rate is given in our paper. Finally, a numerical analysis is performed, in which it is demonstrated that system capacity, propagation rate, and dissipation rate have different effects on congestion propagation in airspace. The results show that low propagation and high dissipation rates not only are nonlinear but also decrease the level of congestion in the propagation of congestion. In particular, of the three parameters, system capacity affects the rate of convergence, with a low-capacity system reaching a stable state quickly and therefore providing a basis for sector partitioning. The method proposed in this paper should enable air traffic controllers to better understand the characteristics of congestion and its propagation for the benefits of both congestion management and improvement of efficiency. Significantly, airspace designers can take congestion propagation into consideration for optimizing the airspace structure in the future.

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A multilayer network approach to model and analyze air traffic networks is proposed. These networks are viewed as complex systems with interactions between airports, airspaces, procedures, and air traffic flows (ATFs). A topology-based airport-airspace network and a flight trajectory network are developed to represent critical physical and operational characteristics. A multilayer traffic flow network and an interrelated traffic congestion propagation network are also formulated to represent the ATF connection and congestion propagation dynamics, respectively. Furthermore, a set of analytical metrics, including those of airport surface (AS), terminal controlled airspace (TCA), and area-controlled airspace (ACA), is introduced and applied to a case study in central and south-eastern China. The empirical results show the existence of a fundamental diagram of the airport, terminal, and intersections of air routes. Moreover, the dynamics and underlying mechanisms of congestion propagation through the AS-TCA-ACA network are revealed and interpreted using the classical susceptible-infectious-removed model in a hierarchical network. Finally, a high propagation probability among adjacent terminals and a high recovery probability are identified at the network system level. This study provides analytical tools for comprehending the complex interactions among air traffic systems and identifies future developments and automation of layered coupled air traffic management systems.