# An Attention-Based Deep Convolution Network for Mining Airport Delay Propagation Causality
###### Abstract
The stochastic dynamic queuing model treats each airport in the network as a single-server queuing system whose arrival rate obeys negative exponential distribution and service rate obeys Erlang distribution to calculate delays. Approximate network delay models are computationally fast, able to quickly calculate delays due to localized congestion at individual airports and capture the \"ripple effects\" of delay propagation. Applying the model to a network of 34 of the busiest airports in the United States shows that delay propagation tends to \"smooth out\" daily airport demand and push more demand into late night hours. [PERSON] et al. [28] displayed the generated delays and the propagated delays on a two-dimensional graph and grouped airports/routes according to the delay characteristics. [PERSON] et al. [29] considered controlling the distribution of ATFM delays to minimize the likelihood of delays propagating to subsequent flights. Therefore, they propose a two-layer mixed-integer optimization model to solve the unbalanced problem of route demand and capacity. Minimizing delay propagation by solving the demand and capacity imbalance problem of routes is the first level, and increasing the connectivity of flight slots without increasing delays is the second level. In recent years, the research community has begun to analyze the delay propagation mechanism from the aspect of airport delay propagation causality mining [15]. Airport delay propagation causality can describe the degree of the direct impact of delays at one airport on another airport. Building an airport delay propagation causal network will help managers understand key nodes in the airport network so that targeted measures can be taken in advance to alleviate air traffic congestion. In addition, the current delay prediction model based on correlation cannot guarantee the robustness of the model. Constructing delay prediction models based on causality is more interpretable and can predict which factors are responsible for the results and when the prediction model will stop working, resulting in more robust predictions. As the airport network is a highly complex dynamic network, it is difficult to study the impact of one airport's delay on other airports by means of human intervention. Fortunately, the delay time series implies the law of delay propagation causality, which has been preliminarily explored by some researchers. Some researchers use Granger causality [30] to construct the airport delay propagation network. [PERSON] et al. [15] regarded the Chinese airport network as a complex network, and used the method of Granger causality tests to study the delay time series between two airport pairs. If the delay time series of airport A is more helpful to predict the delay time series of airport B than the delay time series of airport B itself, it is considered that the delay of airport A is the cause of the delay of airport B. Similarly, [PERSON] et al. [31] also established a delay causal network based on Granger causality, and studied the airport delay propagation mechanism by analyzing the topological properties of the network. The causal mining of airport delay propagation based on the Granger causality method can only capture the linear dependence of two airport delay time series. [PERSON] et al. [32] used transfer entropy to analyze the causal relationship between two airport delay time series, and then quantitatively expressed the degree of influence of one airport's delay on another airport's delay. Causal relationship mining based on transfer entropy belongs to a class of nonparametric models that can discover linear and nonlinear dependencies, but cannot handle nonstationary time series. The airport network is a network composed of a large number of airports passing through the airline network. Due to the dynamic changes of flight information and environmental information, and the nonlinear interaction between airports, the airport network can be regarded as a dynamic and nonlinear complex network system.