MATRIX: A multidimensional maritime traffic complexity evaluation framework

Maritime traffic complexity (MTC) is a key metric of navigational difficulty. Existing MTC models share a common limitation: they assess complexity almost exclusively through vessel-interaction geometry derived from Automatic Identification System (AIS) data, neglecting the environmental and operational conditions that shape real navigational difficulty. This paper introduces multidimensional maritime traffic complexity (MDMTC) and MATRIX, the framework that operationalises it. MATRIX decomposes complexity into three conceptually distinct dimensions, geometrical, environmental, and traffic-characteristic, resolved into twelve normalised sub-indices and combined, through a weighted quadratic mean, into a single spatially resolved index on the unit interval. The weights couple the Analytic Network Process, elicited from seventeen experts with inter-criteria dependencies, with Shannon entropy weighting from a large empirical sample. Three seven-day case studies on real AIS and environmental data demonstrate the framework: introducing offshore wind farms as the only manipulated variable raises the mean index from 0.33 to 0.52 through the constraint sub-index alone, while a severe-weather episode drives an area to a critical state that a geometry-only model would miss. Against twenty deck officers rating twenty scenarios, the index agrees strongly with expert judgement (Spearman ρ = 0.90 ), a convergent, perception-based validation. MATRIX supports vessel traffic services, offshore-infrastructure assessment, and autonomous navigation.