Resilience modeling of transportation infrastructure and network based on the semi-Markov process considering resource dependency

Resilience quantification for transportation systems remains challenging due to complex interdependencies between infrastructure degradation and network functional evolution. This study presents probabilistic resilience models of transportation infrastructures and networks, which integrate resource-dependent semi-Markov processes with cascading failure mechanisms to address this problem. Specifically, unlike conventional models treating physical and functional failures in isolation, the proposed models explicitly couple infrastructure-level fragility with network-level traffic redistribution dynamics by cascading failure modeling. With respect to the functional recovery modeling, the core innovation of this study lies in the modified semi-Markov recovery model, which integrates the semi-Markov process and the Bayesian-updated resource dependency model to address both recovery strategy selection and the effect of the available recovery resource on the recovery time distribution. Further, the procedure and simulation-based algorithm of the resilience models are provided. A case study is then carried out for a real-world transportation network to illustrate the applicability of the proposed resilience models. Case analysis results demonstrate that recovery strategy selection drives 84% variability in infrastructure-level resilience and 74% divergence in network-wide resilience metrics, while severe resource constraints degrade infrastructure-level resilience by 71% compared to optimal availability. Crucially, conventional criticality-based allocation prolongs network recovery efficiency by 50% versus functionality-loss-prioritized strategies. It indicates the necessity of multi-criteria including functionality loss severity, topological importance, and on-site construction limitations. Methodologically, it unifies infrastructure physics failure with network flow dynamics evolution for urban transport decision-making. The framework enables adaptive recovery via real-time capacity predictions and resource-strategy optimization, providing stakeholders with actionable insights.