Terminal reliability of road networks with multiple destination options

Neumann, Thorsten; Behrisch, Michael · 2018 · Crossref

DOI: 10.2495/safe-v8-n3-426-437

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Summary

This paper addresses the vulnerability of road networks during crisis situations, such as natural disasters, where maintaining connectivity to critical supply nodes (e.g., hospitals, fire departments) is essential. The authors focus on quantifying the risk that a specific node in a network becomes isolated from all available supply nodes of a given type, assuming multiple such nodes exist within the network. The primary research questions involve determining the probability of isolation for any given node based on network topology and link failure probabilities, and identifying which network links are most critical to overall connectivity. To solve this, the authors adapt the concept of terminal reliability, which traditionally assesses connectivity between a single origin and destination pair. They introduce a graph modification technique that combines all supply nodes of a specific type into a single "virtual" supply node. This transformation allows the application of standard terminal reliability methods to determine if a regular node remains connected to at least one original supply node. The methodology involves identifying all minimal paths and minimal cut sets in the modified graph. A recursive algorithm is presented to systematically detect these minimal cut sets. To manage computational complexity, the authors employ a clustering approach combined with Boolean algebra to calculate the system reliability ($R_{sys}$), which represents the probability that a node remains connected. This approach simplifies calculations by grouping disjoint paths and factoring out common links. The study demonstrates these methods using an illustrative artificial road network with ten regular nodes and two supply nodes. Results show that system reliability varies significantly across nodes depending on their topological position. Nodes with multiple disjoint paths to supply nodes exhibit much lower isolation risks compared to nodes with single-path dependencies. For instance, nodes I and J, which rely on single links for access, show isolation risks nearly equal to the link failure probability, whereas central nodes with alternative routes have risks orders of magnitude lower. The analysis also identifies critical links by counting their appearance in minimal cut sets; links 3, 5, and 10 were found to be the most critical in the example network, while central links 6 and 7 were less critical despite their central location. The significance of this work lies in providing a quantitative framework for crisis management and infrastructure resilience planning. By identifying critical links and quantifying isolation risks, planners can prioritize maintenance and reinforcement efforts. The authors conclude that while the proposed method is effective for small to medium networks, scalability remains a challenge for large-scale applications due to the computational cost of expanding structure functions. Future work should address correlated link failures, multiple types of supply nodes, and the potential failure of supply nodes themselves.

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