A Complexity-Aware Course–Speed Model Integrating Traffic Complexity Index for Nonlinear Crossing Waters

We propose a complexity-aware extension of the Course–Speed (CS) model that integrates an AIS-derived Traffic Complexity Index (TCI) based on change in speed (ΔV) and course (Δθ) to quantify maneuvering complexity in nonlinear crossing waters. The framework consists of: (i) data preprocessing and gating to ensure navigationally valid AIS samples; (ii) CS index computation using distribution-aware statistics; (iii) TCI estimation from variability in speed and course along intersecting flows; and (iv) an integrated CS–TCI for interpretable mapping and ranking. Using one year of AIS data from a high-density crossing area near the Korean coast, we show that the integrated index reveals crossing hotspots and small-vessel maneuvering burdens that are not captured by spatial regularity metrics alone. The results remain robust across reasonable parameter ranges (e.g., speed filter and σ-based weighting), and they align with operational observations in vessel traffic services (VTS). The proposed CS–TCI offers actionable decision support for port and coastal operations by jointly reflecting traffic smoothness and complexity; it can complement collision-risk screening and efficiency-oriented planning (e.g., energy and emission considerations). The approach is readily transferable to other crossing waterways and can be integrated with real-time monitoring to prioritize control actions in complex marine traffic environments.