A New Method for Verifying d-MC Candidates

Abstract: Network reliability modeling and calculation is a very important study domain in reliability engineering. It is also a popular index for validating and measuring the performance of real-world multi-state flow networks (MFNs), e.g., the applications in internet of things, social networks, clouding computing, and 5G. The d-MC is a vector, the maximum flow of whose related network is d, and any vector less than the d-MC is not a d-MC in MFNs. The MFN reliability can be calculated in terms of d-MCs. Hence, the d-MC is one of the most popular tools for evaluating the MFN reliability. The method to find all d-MCs is through the mathematical programming whose solutions are called d-MC candidates, and all d-MCs are selected from these candidates. In this study, a novel and simple algorithm is proposed to filter out d-MCs from these d-MC candidates after removing duplicates. The time complexity of the proposed algorithm is analyzed along with the demonstration using an example. An experiment with 200 random networks is outlined to compare the proposed, traditional, and best-known algorithms used for verifying d-MC candidates.