Integrating track layout into urban rail vulnerability envelope assessment: A case of Hong Kong rail transit network

Vulnerability envelope is a recently proposed systematic tool for analyzing transportation network vulnerability, which evaluates the lower and upper bounds of vulnerability and reveals the possible range of network performance degradations under various disruption severities. However, in urban transit systems, vulnerability envelopes are typically evaluated using a simplified node-link topology. While this approach captures service resilience through train rescheduling, flexible stops and short turnaround times enabled by redundant tracks, it often overlooks the critical role of track layout in train operations during disruptions. Moreover, it may fail to accurately reflect system behavior, as operators might close rail sections to maintain service efficiency, preventing turnback operations. This article integrates track layout into vulnerability envelope analysis for urban rail transit networks. The proposed method is demonstrated using the urban rail transit network in Hong Kong, comparing vulnerability envelopes derived from track-based and link-based approaches. By considering both physical infrastructure and operational strategies, it enhances the realism of vulnerability assessments and provides actionable insights for decision-making.