Search for all d-MPs for all d levels in multistate two-terminal networks

Bai, Guanghan; Zuo, Ming J.; Tian, Zhigang

doi:10.1016/j.ress.2015.04.013

Cited by 69 publications

(42 citation statements)

References 27 publications

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“…Duplicate MPs increase computation complexity, and must therefore be removed before calculating network reliability [16], [34], [35]. The following property confirms that there are no duplicate MPs, i.e., no such burden, in the proposed convolution-based MP sets.…”

Section: Node Labels and Convolution-based Mp Setsmentioning

confidence: 58%

A Novel Convolution-Based Algorithm for the Acyclic Network Symbolic Reliability Function Problem

Zhang

Yeh

et al. 2020

IEEE Access

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Acyclic (binary-state) networks are commonly implemented in many diverse disciplines and applications, including information systems, processes management, project management. These networks owe their popularity to the fact that they do not use directed cycles. Network reliability is the most commonly used tool for evaluating and managing systems modeled on acyclic networks, and minimal paths (MPs) play a significant role in evaluating this reliability. This study therefore proposes a new algorithm based on a novel convolution concept for evaluating acyclic network reliability. The proposed algorithm is able to find all convolution-based MP sets within polynomial time, and then obtain the symbolic function of the acyclic network reliability in terms of those convolution-based MP sets based on the pivotal decomposition. Its total time complexity is O(2 n), which is the best among all existing MP algorithms which are at least O(2 |P|), where O(|P|) = O(2 n), and n and |P| are the number of nodes and MPs, respectively. The correctness and time complexity of the proposed algorithm is proven and examined. An example is used to display the novel convolution-based algorithm is implemented to solve the acyclic network reliability problem.

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Section: Node Labels and Convolution-based Mp Setsmentioning

confidence: 58%

A Novel Convolution-Based Algorithm for the Acyclic Network Symbolic Reliability Function Problem

Zhang

Yeh

et al. 2020

IEEE Access

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“…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).…”

Section: Introductionmentioning

confidence: 99%

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

Monsef¹,

Abdou²

2020

American Journal of Engineering and Applied Sciences

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The reliability of a multi-state network is defined as the probability that the network can successfully send d (demand) units of data from the source to the sink. To predict the value of maximum demand (dmax) that could be accommodated by a network, a cut-set based approach is presented in this study. The presented approach is simple and easy to implement. The proposed method was applied to many examples studied in literature to illustrate its efficiency. The results show that the reliability value at maximum demand (max d R) is less than any Rd.

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“…For such a network, an interesting question is to evaluate its reliability defined as the probability of the network capacity level greater than or equal to a predetermined demand level . Researchers have presented various algorithms to evaluate the reliability of multistate networks, including direct algorithm [22][23][24] and indirect algorithm [25][26][27][28][29][30][31][32][33]. Indirect algorithm is often called 2 Complexity network-based algorithm established in terms of minimal paths or minimal cuts.…”

Section: Introductionmentioning

confidence: 99%

“…Indirect algorithm is often called 2 Complexity network-based algorithm established in terms of minimal paths or minimal cuts. One common indirect method for reliability computation of multistate networks is based on minimal path vectors to level d (d-minimal paths for short) [25][26][27][28][29][30][31][32][33]. And, all of these methods pay attention to the enumeration of d-minimal paths.…”

Section: Introductionmentioning

confidence: 99%

“…Following the literature in [25,26,[28][29][30][31][32][33], this paper considers four assumptions: (1) the state/capacity of each arc is a nonnegative integer random variable following a Complexity 3 [34], and generally speaking, it represents the ability of a network to achieve its intended function within a given environment. For a multistate network, the reliability index is defined as the probability that at least units of flow can be sent from the source node to the sink node or the probability that the network capacity level is greater than or equal to a predetermined demand level d, that is = Pr{ | ( ) ≥ }.…”

Section: Introductionmentioning

confidence: 99%

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

Niu

2019

Complexity

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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.

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Search for all d-MPs for all d levels in multistate two-terminal networks

Cited by 69 publications

References 27 publications

A Novel Convolution-Based Algorithm for the Acyclic Network Symbolic Reliability Function Problem

A Novel Convolution-Based Algorithm for the Acyclic Network Symbolic Reliability Function Problem

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

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

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