Basic parameters of virtual airport networks.

In this work, we established a density equation for delayed airports to investigate the horizontal propagation mechanism of delays among airports in an airport network. We explored the critical conditions, steady-state features, and scale of the delay propagation, and designed a simulation system to verify the accuracy of the results. The results indicated that, due to the no-table scale-free feature of an airport network, the critical value of delay propagation is extremely small, and delays are prone to propagate among airports. Furthermore, as delay propagation reaches a steady state in an aviation network, the degree value of the node becomes highly correlated with its delay state. Hub airports with high degree values are the most prone to being affected by delay propagation. In addition, the number of airports that are initially delayed influences the time required for delay propagation to reach a steady state. Specifically, if there are fewer initially delayed airports, a longer time is required to reach a steady state. In the steady state, the delay ratios of airports with different degree values in the network converge to a balance point. The delay degree of the node is highly positively correlated with the delay propagation rate in the network, but negatively related to the degree distribution index of the network.本研究针对延误机场构建了密度方程，旨在探究机场网络内各机场间延误的横向传播机制。本研究探究了延误传播的临界条件、稳态特征与传播规模，并设计了仿真系统以验证研究结果的准确性。研究结果表明，由于机场网络具备显著的无标度(scale-free)特征，延误传播的临界值极低，机场间极易发生延误传播。此外，当延误传播在航空网络中达到稳态时，节点的度值(degree)与其延误状态呈现高度相关性。度值较高的枢纽机场，最易受到延误传播的影响。此外，初始延误机场的数量会影响延误传播达到稳态所需的时长。具体而言，初始延误机场的数量越少，达到稳态所需的时长越长。在稳态下，网络中不同度值机场的延误占比会收敛至一个平衡点。节点的延误程度与网络内的延误传播速率呈高度正相关，却与网络的度分布指数呈负相关。