A Recovery Model for Faulty Networked System

In this article, we introduce a novel optimization formulation able to capture the main aspects of a networked system affected by faults that reduce the efficiency in terms of flow transmission, as well as to optimize response teams in charge of restoring the subsystems from faults. We propose a nonlinear optimization problem based on the max-flow formulation, which merges, in a comprehensive framework, the aspects related to 1) the flow management; 2) the fault propagation and its impact in terms of network efficiency; 3) the scheduling of response teams interventions with the aim to restore the nominal behavior of the network. Finally, with the aim to reduce the computational effort required to solve such a problem, we provide a linearized optimization formulation. The results, computed on a test-case network, confirm the model's applicability in real-time restoration process planning; moreover, our methodology is sufficiently general to be applicable in a multitude of emergency scenarios such as crowd evacuation or critical infrastructure under domino effect propagation.