Network endurance against cascading overload failure

Network endurance can be regarded as the upper limit of survival time before the system's complete breakdown, which is highly related to system resilience. Although network endurance against overload failure is critical for network design and operational management, the definition and corresponding evaluation method still remain challenging. In this paper, based on the load-dependent overload model, we define network endurance as the cascade duration at criticality before the complete network breakdown and develop an approach for endurance evaluation. We find that network endurance highly depends on initial disturbance intensity and cascade intensity. The network endurance with a uniform initial load distribution usually monotonically increases with decreasing initial disturbance intensity, while for other initial load distributions endurance behaviors are more complicated. We also provide theoretical analysis for the network endurance. Our findings may help to understand the network reliability mechanism against cascading overload failures and design a highly reliable network.