Airport and terminal area traffic congestion is a growing concern of the air traffic management (ATM) system. A major step towards mitigating the impacts of congestion is understanding the fluctuating arrival and departure process at airports. Exploring the intrinsic time-varying nature of the arrival and departure process enhances this understanding, hence, is instrumental in formulating operational policies for managing airport capacity and delays. This paper presents a data-driven statistical framework to investigate, understand, and model the time-varying fluctuations in the aircraft arrival and departure process. We have considered one-month data obtained from Chennai international airport operations for this study. The dynamic evolution and fluctuation characteristics of arrivals and departures are conducted using Seasonality and Multifractal Detrended Fluctuation Analysis. Six theoretical probability distributions were used to fit the observed aircraft arrivals and departures at different temporal scales using the maximum likelihood estimation method. This study also develops a G1(t)/G2(t)/KFirst Come First Serve dynamic queuing model for a day’s arrival and departure process. The results suggest that arrival and departure processes exhibit weak but visible multifractal characteristics. Fluctuations are higher at a smaller temporal scale compared to a larger scale, and the probability distributions of arrival and departure are also time-varying. The framework has universal applicability, and the insights have important implications for operational policies on the air transportation workforce and infrastructure management.