Abstract
Many real-world multi-state systems can be modeled as multistate flow networks (MFN) such that the net flow into and out of a node (excluding the source and target nodes) is equal to zero, e.g., distribution systems and supply chains. The quickest path (QP) reliability problem is to evaluate the probability, i.e., $R_{(d, t)\hbox{-}{\rm QP}}$ , that at least $d$ units of data can be sent from the source node to the sink node through a single special minimal path (MP) within $t$ units of time in an MFN. Such a special MP is called a $(d, t)\hbox{-}{\rm QP}$ here. In this study, a novel algorithm based on depth-first-search (DFS) is proposed to search for all $(d, t)\hbox{-}{\rm QPs}$ without solving two NP-hard problems: finding all minimal paths (MPs) in advance, and removing all infeasible $(d, t)\hbox{-}{\rm QPs}$ candidates. The correctness of the proposed Depth-First-Search (DFS)-based algorithm is proven, and an example is provided to illustrate the generation of all $(d, t)\hbox{-}{\rm QPs}$ . Furthermore, the analysis of the algorithm's computational complexity and computer experiments indicate that it is more efficient than known algorithms.
Published Version
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