Operational Lifetime-Stress Model for Complex Networks

While a number of network systems are running under certain stress with a limited lifetime, it is still unknown how to predict the lifetime-stress relation of complex systems. We develop a percolation-based approach to build an operational lifetime-stress model for complex networks, which captures the spatial and temporal reliability characteristics of the system. In this article, the general analytical expression for the entire operational lifetime-stress relation has been presented, which suggests that the load stress and the number of nodes in the network impact the operational lifetime in the same manner. The size effect found here in the lifetime-stress relation is observed for the first time, to our best knowledge. For 2-D lattices, we show that the lifetime-stress relation can be regarded as the combination of two parts - an approximately linear region for small stress, and nonlinear region for large stress. We also analyze the lifetime-stress function of Beijing road network and the western United States power grid. Our article might help to develop acceleration testing methods, which will facilitate better design of reliable complex systems.