Evaluating the Resilience of Urban Road Networks Against Recurrent Disruptions: A Hysteretic Approach

Performance-based resilience measures arise from the need to quantify the dynamic response of transportation systems to extreme disruptive events, where recovery is central. Extending the scope of these measures to recurrent events demands a proper assessment of the disruptive stage, which exhibits a progressive behavior determined by cascading failure. To account for both disruptive and recovery stages, we propose a hysteretic model built upon standard traffic microsimulation data, where the arriving flow is described by a three-stage Ornstein-Uhlenbeck stochastic process. By relating its deterministic component to the solution of a differential equation analogous to a mass-spring system, we construct a hysteresis curve that describes system resilience as a unified process, covering both the disruptive and recovery stages, whereas its enclosed area represents performance loss. Finally, we propose a new quantitative resilience measure, the normalized hysteretic resilience (NHR), associated with the hysteresis loop. The methodology is demonstrated for the case study of the influence area of a bus rapid transit (BRT) terminal when a critical segment is blocked by a traffic accident. Findings show that the NHR measure is suitable to quantify the nonlinear behavior of traffic flows and consistent with existing resilience measures.