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Vulnerability analysis is crucial in strategic planning and highway maintenance to ensure a robust transportation system. Owing to the characteristics of network-modeling framework, traditional vulnerability analyses may not be able to realistically model the impacts of network degradations. This paper presents an application of the continuum traffic equilibrium model for network vulnerability analysis that aims to resolve the critical issues faced by the network-modeling framework. The continuum traffic equilibrium model treats the road system as a continuum over which the demands are continuously dispersed. In this study, a bi-level model is set up for finding the most vulnerable location(s) in the study region. At the lower-level model, a set of differential equations is constructed to describe the traffic equilibrium problem under capacity degradation. In the upper-level model, a constrained minimization problem is set up to find the most vulnerable location(s) that minimizes the accessibility index of the study region. A sensitivity-based solution algorithm that adopts the finite element method (FEM) is proposed to solve the bi-level model. Numerical examples are presented to demonstrate the characteristics of the proposed continuum vulnerability analysis and the efficiency of the proposed solution algorithm

A Continuum Modeling Approach for Network Vulnerability Analysis at Regional Scale