Air travel is crucial for global connectivity, yet it faces increasing challenges due to rising air traffic volumes and complex operational demands. Mathematical modeling has emerged as a transformative solution in air traffic control (ATC), enhancing efficiency and safety across the aviation sector. This review delves into the application and outcomes of mathematical models in ATC by analyzing recent literature that incorporates various computational techniques for optimizing air traffic flow, predicting and mitigating conflicts, and improving decision-making processes. In order to attain this, we thoroughly searched scholarly articles from well-known databases, for instance, Scopus as well as IEEE articles published in the last decade, focusing on studies that demonstrated clear numerical results regarding the effectiveness of mathematical modeling in ATC operations. The flow of the study is based on the PRISMA framework. By analyzing a comprehensive selection using an advanced searching approach on Scopus and IEEE database found (n=22), the final primary data was analyzed. The review highlights significant advancements, such as the development of algorithms capable of optimizing flight paths, reducing airspace congestion, and enhancing fuel efficiency, which collectively contributes to more sustainable aviation practices. The findings are divided into four themes, which are (1) optimization of ATC operations, (2) route and flight scheduling optimization, (3) resilience and robustness in atm systems, and (4) technological advances and their integration in air traffic management (ATM). Conclusively, mathematical models have proven indispensable for maximizing ATC efficiency and are pivotal in guiding strategic planning and policy-making to accommodate future air traffic growth while maintaining high safety standards.
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