Understanding bus network delay propagation: Integration of causal inference and complex network theory

Bus transport, characterized by a complex network of routes and stops, frequently experiences delays that can affect the entire system's reliability, passenger satisfaction, and operational efficiency. Existing research on bus delay propagation predominantly focuses on the route level. They lack a broader network-level perspective, which is essential for fully understanding the complex interactions and delay propagation. Additionally, previous studies typically rely on correlation-based analysis, which may not adequately uncover the underlying causal mechanisms of bus delay propagation. To understand bus delay propagation in the Public Transport System (PTS), this study employs a causality-based model instead of traditional correlation-based analysis to identify causal relationships between bus stops. We introduce a time-series causal discovery model that integrates temporal and spatial features of stop delays to generate a delay propagation causal graph (DPCG). Then, complex network theory and metrics are used to perform topological analysis on the DPCG and identify key bus stops. The case study is conducted using real-time GTFS data from Stockholm, Sweden. The results indicate that stops with more connections significantly influence delay propagation, and the network displays a distinct community structure with mixed connectivity. Moreover, bus stops exhibit different delay propagation patterns during various time periods. During the morning peak, delays primarily propagate to stops in the inner city due to the commuting surge. In the evening peak, however, delays are more widely distributed across central and suburban areas, reflecting the diversity of after-work travel patterns. The study also reveals that delay propagation extends beyond a single route and affects multiple routes.