Spectral Analysis of Delay Propagation in Air-Rail Intermodal Networks: A Case Study at Paris CDG Hub

Intermodal transportation networks integrating air and rail systems are critical for efficient and sustainable pas- senger mobility, yet their performance is often challenged by cascading disruptions originating from delays at key hubs. This paper presents a novel application of Graph Signal Processing (GSP) techniques to analyze delay propagation and characterize unexpected disruptions within a large-scale air-rail intermodal network. Using real flight data and simulated rail delay data for the Paris Charles de Gaulle (CDG) hub, we model the network of transportation legs as a graph where edges represent Pearson correlation coefficients of delay patterns. We introduce spectral metrics such as total variation and total energy derived from the graph Laplacian to quantify the spatial smoothness and irregularity of delay distributions. The spectral decomposition via the Graph Fourier Transform (GFT) enables identification of distinct delay patterns associated with both expected and irregular states of the network. Our results reveal that, while most days exhibit smooth and predictable delay propagation consistent with historical correlations, select days demonstrate significantly high total variation, indicating unexpected disruption dynamics. This methodological framework provides transport operators with actionable insights to detect, characterize, and potentially mitigate complex disruption scenarios in multimodal hubs.