Identifying the critical road combination in urban roads network under multiple disruption scenarios

The promising approach to ensure the robustness of the road network is to identify the critical roads. Previous researches mainly focus on the identification of single critical road. Nevertheless, the impact of one road seems to be limited, and the more practical problem is to figure out the critical road combination wherein multiple roads failures may lead to the serious collapse of a road network. This paper develops a rigorous, extensible, mathematical model to identify the critical combination of roads in urban road networks for multiple disruption scenarios. Specifically, we propose a bi-level mixed-integer nonlinear problem (MINLP) model, which is challenging to solve due to its NP-hard characters. Then the transformation and linearization of constraints help simplify the formula into a single-level mixed-integer linear problem (MILP) formula. Finally, the Nguyen and Sioux Falls networks are sufficiently tested under multiple scenarios with different levels of disruption rate and travel demand. The results confirmed the validity and superiority of the proposed model. From the numerical results, it is more practical to measure the robustness of the road network than topological analysis. Besides, the most critical combination with multiple-link failures is not simply the combination of most critical roads with single-link failure, and these roads are not necessarily connected or in the neighborhood of each other. The results also correctly evaluate the impact of disconnection, which could provide advice for managers with preferences for accessibility and travel time.