Understanding Long-Term Dynamics of Individual Metro Usage: A Hidden Semi-Markov State Framework with Survival Analysis

2026-06-16

AI Summary

Existing research struggles to characterize the dynamic life cycle of individual metro travel behavior over multi-year horizons, often limited to static clustering or short-term behavioral analysis. This study proposes a state-based life cycle framework that integrates a hidden semi-Markov model (HSMM) with discrete-time survival analysis, jointly modeling state evolution and system entry/exit events for the first time. Leveraging four years of smart card data from Shanghai Metro, the framework identifies five robust travel states and reveals that exit risk depends solely on the current state, whereas re-entry risk decays sharply with increasing inactivity duration, exhibiting asymmetric temporal dynamics. The approach not only constructs a directed hierarchy of state transitions centered on occasional usage but also provides theoretical grounding and empirical support for targeted user retention strategies.

Abstract

Understanding how individual metro usage evolves over multi-year horizons is essential for transit planning and passenger retention. However, existing approaches typically characterize mobility patterns as static clusters or short-term variability, leaving the lifecycle dynamics of transit participation underexplored. This study proposes a state-based lifecycle modeling framework that integrates Hidden Semi-Markov Models (HSMM) with discrete-time survival analysis to characterize the evolution of individual metro mobility. The HSMM infers latent mobility states with explicit duration distributions and a transition matrix governing regime changes, while the survival component models exit and re-entry events via state-dependent hazard functions conditioned on mobility-state trajectories and behavioral history. Applied to four years of smart card data from the Shanghai metro system (2021-2024), the framework enables the identification of interpretable mobility states, the characterization of transition dynamics, and the quantification of state-dependent exit and re-entry processes. The analysis reveals five robust mobility states with a directional transition hierarchy centered on an occasional-usage gateway state, and fundamentally different temporal mechanisms governing disengagement and return: exit hazard is state-dependent but duration-independent, whereas re-entry hazard decays sharply with inactivity length. These findings provide a methodological foundation for lifecycle-oriented mobility analysis and practical guidance for transit operators to identify at-risk users and time retention interventions.

Problem

• metro usage
• long-term dynamics
• lifecycle modeling
• individual mobility
• transit participation

Innovation

• Hidden Semi-Markov Model
• Survival Analysis
• Mobility Lifecycle
• State-Dependent Hazard
• Smart Card Data