Theory and applications of an integrated model for capacitated-flow network reliability analysis

To evaluate the performance of engineering systems, this study acts as a bridge between the theories of classical and capacitated-flow network reliabilities and helps integrate them. Unlike existing works, in which a deterministic probability distribution was used for arcs in a network, in this study, the time-dependent reliability function is applied for components in arcs. In particular, the proposed model applies an arbitrary reliability function to evaluate reliability. In arc-level reliability analysis, the components in an arc are characterized by a reliability function, and such components comprise a capacitated-flow arc. Therefore, a certain number of components can be derived from the probability distribution of the capacity provided by an arc. In system-level reliability analysis, an algorithm is used to generate the minimal component vectors (MCV) for the given demand and time constraints. The system reliability can be calculated in terms of the MCVs using the derived capacity probability distribution. Based on the reliability analysis, a maintenance issue with two policies is discussed. Examples, including a large-scale case study of the Taiwan Academic Network, are discussed to validate the correctness, applicability, and scalability of the proposed model.