Reliability Evaluation of Multicommodity Limited-Flow Networks with Budget Constraints

Reliability is an important performance indicator in the planning, designing, and operation of a real-world system. Traditionally, it is assumed that the system under study is represented by a probabilistic graph in a binary-state model, and the system operates successfully if there exists one or more paths from the source node s to the sink node t. In such a case, reliability is considered as a matter of connectivity only and so it does not seem to be reasonable as a model for some realworld systems. Many physical systems such as manufacturing systems, transportation systems, and logistics/distribution systems can be regarded as flow networks in which arcs have independent, finite, and integer-valued random capacities. To evaluate the system reliability of such a flow network, different approaches have been presented [7, 9, 14-23, 26-28]