The increasing interconnectedness of urban infrastructure networks presents significant challenges in managing unforeseen disruptions, especially those caused by extreme weather events linked to climate change. Understanding and enhancing the resilience of these interconnected systems is crucial for effective disruption management. This research focuses on the resilience-by-design approach, emphasizing the inherent properties of the system's design rather than solely relying on post-disaster interventions. The study utilizes Hong Kong as a case study, given its heavy reliance on a multimodal public transportation network (MPTN). The central research question is how the resilience of a multimodal public transportation network changes as different modes are interconnected. The study contrasts the resilience-by-design approach with the resilience-by-intervention approach, highlighting their complementary nature. While resilience-by-intervention focuses on improving individual systems or introducing new ones, the resilience-by-design approach centers on creating a system inherently capable of withstanding disruptions. The researchers aim to quantify how interconnectedness enhances the resilience of the MPTN using network science principles, specifically focusing on the concept of 'safe-to-fail' systems.

Existing research on infrastructure resilience has largely focused on either resilience-by-design or resilience-by-intervention. Resilience-by-design emphasizes system design and immediate responses, while resilience-by-intervention involves conventional responses such as enhancing capacity and community support. Previous studies have examined the resilience of individual transportation modes, but there's a lack of understanding on how resilience changes when multiple modes are interconnected. While some studies have acknowledged the need for multimodal system analysis, a quantitative demonstration of interconnectedness' impact on network resilience is missing. This study aims to bridge this gap by focusing on the interconnectedness of different public transportation modes within a multimodal system and examining the resulting changes in resilience. The study also incorporates geospatial factors in modeling the interconnected MPTN, considering both multiplex networks (same nodes connected by different edge types) and interconnected networks (different node sets connected via interlayer edges). The concept of interconnection is broadened beyond physical interchanges to include passenger transfer behavior and accessibility, measured geospatially using walkability.

This research uses a real-world case study of Hong Kong's public transportation system, encompassing six modes: Mass Transit Railway (MTR), light rail (LR), franchised buses (FB), green minibuses (GMB), ferries (FERRY), and trams (TRAM). The study models each transportation mode as a directed graph, using nodes to represent stations/stops and edges to represent transportation links. The MPTN is represented as a directed multilayer graph, including both intra-modal edges and intermodal edges representing transfers between modes. The research employs a topology-based resilience framework with three indicators: preparedness, robustness, and interoperability. Preparedness is measured by the Gini index, reflecting the homogeneity of node criticality. Robustness is assessed by the area under the curve (AUC) of the network degradation curve during simulations of random failures and targeted attacks. Interoperability is quantified by the relocation rate of stranded passengers to the nearest alternative service, considering walkability (measured using Haversine distance). A null model, integrating the Erdős-Rényi model with geospatial constraints, is used to benchmark the results and account for network scale effects. The study integrates the subsystems sequentially, comparing the resilience indicators in isolated versus interconnected states for various intermodal transfer distances. Z-scores are calculated to compare the resilience metrics of the interconnected MPTN against the null model.

The study demonstrates that interconnectedness significantly enhances the resilience of Hong Kong's MPTN. Specifically: 1. **Improved Robustness:** Interconnectedness significantly improves network robustness under random disruptions and targeted attacks. The MPTN shows higher tolerance to attacks, particularly on high-degree nodes (hubs). This improvement is validated using Z-scores against a null model, demonstrating the superiority of the interconnected network compared to a random network. 2. **Enhanced Interoperability:** All subsystems exhibit improved relocation capabilities when interconnected, with MTR and Ferry showing the most significant improvements. The global average relocation rate reaches 0.93 at a 750-meter relocation distance limit, indicating high interoperability. 3. **Integration of Vulnerable Systems:** Integrating vulnerable systems (like GMB and TRAM) through interconnection can surprisingly improve overall network robustness, highlighting the potential of strategic integration to strengthen resilience. 4. **Marginal Benefit of Intermodal Transfer:** Enhancing intermodal transfer improves robustness, particularly at short distances. The marginal benefit diminishes as the transfer distance increases, suggesting that prioritizing improvements in short-distance transfers offers the most cost-effective way to improve robustness. 5. **Slight Centralization:** Interconnectedness leads to a slightly more centralized network structure, potentially increasing the difficulty and cost of preparedness measures. This finding suggests the need for a balanced approach between interconnectedness and the 'safe-to-fail' principle. The Gini coefficient analysis shows only slight increases in heterogeneity with interconnection, indicating that the benefits outweigh the costs. The results are presented in tables and figures showing the changes in topological properties and resilience indicators during the sequential integration of subsystems under different intermodal transfer distance scenarios (0m and 100m).

The findings address the research question by demonstrating the substantial benefits of interconnectedness in enhancing the resilience of multimodal public transportation networks. The improved robustness and interoperability resulting from interconnectedness support the 'safe-to-fail' design philosophy. The study highlights the potential of strategically integrating even vulnerable systems to increase overall network robustness. The analysis of intermodal transfer distances reveals that focusing on short-distance transfers yields significant improvements in robustness with relatively lower costs. This contrasts with conventional resilience-by-intervention approaches which focus on enhancing individual systems. The results provide valuable insights for transportation planners, suggesting that promoting interconnectedness can be a highly effective resilience-by-design strategy, especially in systems with poorly interconnected modes. The findings are relevant to other network-like infrastructures aiming to improve their resilience through design.

This study demonstrates the significant benefits of interconnectedness in enhancing the resilience of multimodal public transportation networks. The findings highlight the importance of considering network topology and intermodal transfer distances in resilience-by-design approaches. Focusing on short-distance intermodal transfers provides a cost-effective means of improving robustness and interoperability. Future research could explore weighted systems, considering factors like demand and capacity, and investigate the impact of inter-sectoral connections and interdependencies.

The study uses a simplified graph model, assuming uniform weights on edges and focusing on topological properties. Real-world complexities, such as varying passenger demands and capacity constraints, are not fully incorporated. The analysis also relies on Haversine distance for walkability, which may not perfectly capture actual pedestrian travel times. Future research should address these limitations by using more detailed, weighted network models and incorporating factors like actual travel times and real-world constraints.