Multi-state Modeling of Delay Evolution in Suburban Rail Transports

Train delays are a persistent issue in railway systems, particularly in suburban networks where operational complexity is heightened by frequent services and high passenger volumes. Traditional delay models often overlook the temporal and structural dynamics of real delay propagation. This work applies continuous-time multi-state models to analyze the temporal evolution of delay on the S5 suburban line in Lombardy, Italy. Using detailed operational, meteorological, and contextual data, the study models delay transitions while accounting for observable heterogeneity. The findings reveal how delay dynamics vary by travel direction, time slot, and route segment. Covariates such as station saturation and passenger load are shown to significantly affect the risk of delay escalation or recovery. The study offers both methodological advancements and practical results for improving the reliability of rail services.