The rapid growth of the civil aviation industry has placed significant pressure on limited airport runway resources, leading to increased taxiing delays and excessive fuel consumption. These challenges are exacerbated by the constant rise in air traffic, which necessitates more efficient management of airport operations. To mitigate these issues, this study proposes a flexible management approach that categorizes busy periods based on airport traffic density, taking into account the fluctuating load demand at different times of the day. This approach ensures that resource allocation aligns with actual traffic conditions, optimizing operational efficiency. Additionally, leveraging the existing dynamic pushback control framework, this research develops a cosine-based dynamic pushback control model, which incorporates parking stand waiting penalties. This model aims to reduce departure costs by dynamically adjusting the pushback rate according to congestion levels. To further optimize the model, a novel genetic algorithm combined with continuous Markov chains is introduced. This algorithm is designed to determine the optimal control thresholds for different congestion levels throughout the day, ensuring that resources are used effectively while minimizing delays. Simulations conducted using actual operational data from Beijing Capital International Airport demonstrate the effectiveness of the proposed approach. Compared to the uncontrolled pushback method, the cosine-based dynamic pushback control method significantly reduces average taxiway waiting times by 42.92%. Furthermore, this method also reduces fuel consumption and emissions associated with taxiing delays, offering a more sustainable solution to managing airport congestion. This research provides a comprehensive strategy for improving airport operations in high-density air traffic environments.