A modeling framework for system restoration from cascading failures

System restoration from cascading failures is an integral part of the overall defense against catastrophic breakdown in networked critical infrastructures. From the outbreak of cascading failures to the system complete breakdown, actions can be taken to prevent failure propagation through the entire network. While most analysis efforts have been carried out before or after cascading failures, restoration during cascading failures has been rarely studied. In this paper, we present a modeling framework to investigate the effects of in-process restoration, which depends strongly on the timing and strength of the restoration actions. Furthermore, in the model we also consider additional disturbances to the system due to restoration actions themselves. We demonstrate that the effect of restoration is also influenced by the combination of system loading level and restoration disturbance. Our modeling framework will help to provide insights on practical restoration from cascading failures and guide improvements of reliability and resilience of actual network systems.