Subset Cut Enumeration of Flow Networks with Imperfect Nodes

A general assumption made in evaluation of flow network reliability is perfectly reliable nodes. Under such assumption, network reliability is evaluated through subset cut or composite path set approaches. This paper presents a simple approach to account for node failures in reliability evaluation of flow networks using subset cut approach. The proposed approach starts with generating combinations of nodes of the network and utilizes subset cuts (with perfect nodes) to find the valid additional subset cuts due to imperfect nodes. These additional subset cuts consist of only nodes or nodeslinks combinations. To illustrate efficacy of the proposed approach, computational results on various benchmarks networks are provided. The proposed method is applicable to evaluate additional minimal cut sets due to imperfect nodes from minimal cut sets (with perfect nodes) for networks considering only connectivity as the success criteria or additional subset cut set for networks with multiple node pair capacity requirements.