Efficient Enumeration of d-Minimal Paths in Reliability Evaluation of Multistate Networks

Abstract

A number of real-world complex networks can be modeled as multistate networks for performance analysis. A multistate network consists of multistate components and possesses multiple different performance levels. For such a network, reliability is concerned with the probability of the network capacity level greater than or equal to a predetermined demand level d. One major method for multistate network reliability evaluation is using d-minimal paths. This paper proposes an efficient algorithm to find d-minimal paths. First, a new concept of qualified state vector is defined so as to fix a relatively smaller search space of d-minimal paths, and a sufficient and necessary condition for a qualified state vector to be d-minimal path is established. Then, the max-flow algorithm and the enumeration algorithm are integrated to search for d-minimal paths in the determined search space that is recursively divided into subspaces such that the searching efficiency can be increased as much as possible. Both analytical and numerical results show that the proposed algorithm is more efficient in finding all d-minimal paths. In addition, a case study related to power transmission network is performed to demonstrate the implication of network reliability.

Cut-Set Based Method to Determine the Maximum Demand Accommodated by a Multi-State Network

“…All of these methods assumed that all minimal paths (Chen and Lin, 2012;Yeh, 2016) to be known in advance. Other methods are presented to improve searching the d-MPS with knowing MPS in advance or without (Yeh, 1998;2002;2018;Lin, 2001a;Bai et al, 2015;Chen, 2014;Chen and Lin, 2016;Lin and Chen, 2017;Xu et al, 2019). Also, many algorithms presented to evaluate Rd in terms of Minimal Cuts (MCS) vectors to a given demand d, d-MCS based, (Jane et al, 1993;Lin, 2001b;2003a;Jane and Laih, 2010;Yeh et al, 2015).…”