Sustainability and its component resilience have become an important issue that cannot be neglected in airspace planning and development. Resilience, as an emerging system concept, is critical to sustainability in many fields. With the rapidly growing demand in China’s air transportation sector, airspace congestion and flight delays have become a major issue in the fast development of this sector, and threatens the sustainability and resilience of air traffic control (ATC) systems such as waste of resources, air pollution, etc. Sectors, the basic units of an ATC system, play a significant role in ensuring the safe and smooth operations of day-to-day flights. In this paper, we apply the complex network theory to establish a model of China’s air sector network (CASN) and examine a series of characteristic parameters with an empirical analysis on its vulnerability and resilience. Through a simulation-based approach, the CASN’s resilience was quantitatively assessed with a resilience indicator (RI) in different scenarios to identify the optimal recovery strategy for building higher system resilience. The results show that the CASN has a lengthy average shortest path and a small clustering coefficient, which demonstrates a hybrid topological feature. We have also found that betweenness has the greatest impact on the resilience and has managerial implications to understand the relationship between vulnerability and resilience in CASN, so as to achieve the resilience and sustainability of CASN.

The increased number of severe weather events caused by global warming in recent years is a major turbulence factor for airport operation and results in more irregular flights. Quantifying the system response status towards turbulence is critical, in order for airports to deal with severe weather. For this reason, we propose a resilience framework that is in compliance with resilience theory to evaluate airport flight operations. In this framework, the departure rate (DPR), normal weather baseline (NWB), and nonnegative general resilience (NGR) were defined and used. Meanwhile, the whole process is divided into five phases before and after disturbance, and the system capacities of susceptibility, absorption, adaptation, and recovery are assessed. In order to clarify the performance of the framework towards various severe weather conditions, an analysis was conducted at Beijing Capital Airport in China based on a dataset that includes both the meteorological terminal aviation weather report (METAR) and flight operations from January to July 2021. The results show that the newly proposed resilience framework can commendably reflect airport flight operation performance. The airport flight operation resilience characteristic is different with severe weather. Compared to sandstorms and snow, airport flight operation with stronger robustness was observed during thunderstorm events. The study also confirms that, as the weather warning level increases, the disruption time increases and response time decreases accordingly. The above results could assist researchers and policy makers in clearly understanding the real-world resilience of airport flight operation, in both theory and practice, and responding to emergent disruptive events effectively.

Airspace sectorization is an effective approach to balance increasing air traffic demand and limited airspace resources. It directly impacts the efficiency and safety of airspace operations. Traditional airspace sectorization methods are often based on fixed spatial scales, failing to fully consider the complexity and interrelationships of airspace partitioning across different spatial scales. This makes it challenging to balance large-scale airspace management with local dynamic demands. To address this issue, a multi-scale airspace sectorization framework is proposed, which integrates a multi-resolution grid system and a hierarchical deep reinforcement learning algorithm. First, an airspace grid model is constructed using Quaternary Triangular Mesh (QTM), along with an efficient workload calculation model based on grid encoding. Then, a sector optimization model is developed using hierarchical deep Q-network (HDQN), where the top-level and bottom-level policies coordinate to perform global airspace control area partitioning and local sectorization. The use of multi-resolution grids enhances the interaction efficiency between the reinforcement learning model and the environment. Prior knowledge is also incorporated to enhance training efficiency and effectiveness. Experimental results demonstrate that the proposed framework outperforms traditional models in both computational efficiency and workload balancing performance.

The siphon effect between airports has amplified the polarization in passenger throughput, undermining the balanced development and sustainability of airport clusters. The airport siphon effect occurs when one airport attracts a disproportionate share of passengers, concentrating traffic at the expense of others, which affects the overall resilience of the entire airport cluster. To address this issue, this study proposes a siphon index, expands the range of ground transportation options for passengers, and establishes a zero-siphon model to assess the impact of siphoning on the resiliency of airport clusters. Using this framework, four major airport clusters in China were selected as research subjects, with regional aviation accessibility serving as a measure of resilience. The results showed that among the four airport clusters, the siphon effect is most pronounced in the Guangzhou region. To explore the implications of this effect further, three airport disruption scenarios were simulated to assess the resilience of the Pearl River Delta airport cluster. The results indicated that the intensity and timing of disruptive events significantly affect airport cluster resilience, with hub airports being particularly sensitive. This study analyzes the risks associated with excessive route concentration, providing policymakers with critical insights to enhance the sustainability, equity, and resilience of airport clusters. The proposed strategies facilitate coordinated infrastructure development, optimized air–ground intermodal connectivity, and risk mitigation. These measures contribute to building more sustainable and adaptive aviation networks in rapidly urbanizing regions.

The split feasibility problem models inverse problems arising from phase retrievals problems and intensity-modulated radiation therapy. For solving the split feasibility problem, Xu proposed a relaxed CQ algorithm that only involves projections onto half-spaces. In this paper, we use the dual variable to propose a new relaxed CQ iterative algorithm that generalizes Xu’s relaxed CQ algorithm in real Hilbert spaces. By using projections onto half-spaces instead of those onto closed convex sets, the proposed algorithm is implementable. Moreover, we present modified relaxed CQ algorithm with viscosity approximation method. Under suitable conditions, global weak and strong convergence of the proposed algorithms are proved. Some numerical experiments are also presented to illustrate the effectiveness of the proposed algorithms. Our results improve and extend the corresponding results of Xu and some others.