Enumeration of Minimal Cutsets for Directed Networks with Comparative Reliability Study for Paths or Cuts

Mishra, Rajesh; Saifi, Mohd Ashraf; Chaturvedi, Sanjay K.

doi:10.1002/qre.1772

Cited by 23 publications

(7 citation statements)

References 34 publications

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“…Our solution strategy follows a divide-andconquer paradigm. We identify the two most prominent cutsets (involving the smallest numbers of links) of the flow network using any of the methods for minimal cut enumeration [40][41][42]. Let these two cutsets be denoted by , where = 1, 2.…”

Section: Proposed Methodsmentioning

confidence: 99%

Reliability Evaluation of Multi-State Flow Networks Via Map Methods

Rushdi

Alsalami

2020

JERR

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This paper examines two simple (albeit useful) methods used to evaluate the reliability of two-terminal multistate flow networks. These two methods involve two Karnaugh map versions, namely the Variable-Entered Karnaugh Map (VEKM) and the Multi-Valued Karnaugh Map (MVKM). These two versions are crucial in providing not only the visual insight necessary to write better future software but also adequate means of verifying such software. We assess these two versions of map methods versus the exhaustive search method, which guarantees conceptual clarity at the expense of lack of computational efficiency. Our target is the evaluation of the probability mass function (pmf) in a wide array of cases, in which we consider flow from a source node to a sink node in a capacitated network with a multistate capacity model for the links. Each network link has a varying capacity, which is assumed to exist in a mutually exclusive sense. The reliability of the system is wholly dependent on its ability to successfully transmit at least a certain required system flow from the source (transmitter) to the sink (receiver) station. The max-flow min-cut theorem is critical in obtaining all successful states. To demonstrate the proposed methods applicability, two demonstrative examples are given with ample details.

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Section: Proposed Methodsmentioning

confidence: 99%

Reliability Evaluation of Multi-State Flow Networks Via Map Methods

Rushdi

Alsalami

2020

JERR

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“…While there were no previous algorithms found in the literature to identify these MLSs, an algorithm was developed to enumerate the complement to MLSs, MCSs. Mishra et al (2015) proposed an algorithm to identify MCSs that used the connectivity matrix of a graph to check the connection between nodes in a network as nodes are progressively removed. The largest system that this algorithm was tested on in the study contained 21 nodes and 26 links.…”

Section: Performance Compared To Prior Approachesmentioning

confidence: 99%

Framework for Probabilistic Vulnerability Analysis of Interdependent Infrastructure Systems

Applegate

Tien

2019

J. Comput. Civ. Eng.

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Critical infrastructure systems are deteriorating and experiencing increased cascading failures. In this paper, we propose a new probabilistic framework for modeling interdependent infrastructure networks. As part of this framework, we present our modeling approach and the accompanying sets of algorithms that enable the computationally efficient probabilistic modeling of large infrastructure systems considering interdependencies between networks. The proposed method creates a representative Bayesian network (BN) of the system, which provides exact inferences over the network compared to simulation-based approximations. With the traditional computational limitations of BNs to tens of parent component nodes per child system node, our generalized framework enables computationally efficient BN modeling of systems of, for example, hundreds of component nodes, including component-level performance and interdependent connections across networks. Our approach requires only simple inputs based on the basic component characteristics of location, type, connectivity, and initial failure probabilities. We modeled three types of interdependencies across the system-service provision, geographic, and access for repair. We combined a minimum link set (MLS) formulation with the idea of supercomponents in order to reduce network complexity without any approximating assumptions. We present algorithms to efficiently identify MLSs and supercomponents, as well as to identify and remove any cyclic dependencies that arise across the network. Once the BN was constructed, we were able to perform exact inference analyses over a range of component state and hazard event scenarios in order to identify vulnerabilities across the network. The main novelty of the paper is to enable the probabilistic assessment of large, complex, interdependent infrastructure systems. We were able to consider performance from the component level and model hundreds of component nodes in a computationally efficient manner without approximating assumptions. We accounted for interdependencies between systems with exact inference results. The model can be used to investigate the potential for cascading failures and to prioritize critical components for repair, replacement, or reinforcement. We applied the proposed methodology and algorithms to the water distribution network in Atlanta, Georgia, and its dependencies with the power system. We validated the model using the results from a recent interdependent outage event.

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“…Efficient methods for enumerating all minimal paths are presented in [14,17,18]. To compute the network reliability R s−t based on (2), the well-known rule of sum of disjoint products is recommended:…”

Section: Considerations On Network Reliability Evaluationmentioning

confidence: 99%

Approximate Method to Evaluate Reliability of Complex Networks

Caşcaval

2018

Complexity

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This paper deals with the issue of reliability evaluation in complex networks, in which both link and node failures are considered, and proposes an approximate method based on the minimal paths between two specified nodes. The method requires an algorithm for transforming the set of minimal paths into a sum of disjoint products (SDP). To reduce the computation burden, in the first stage, only the links of the network are considered. Then, in the second stage, each term of the set of disjoint link-products is separately processed, taking into consideration the reliability values for both links and adjacent nodes. In this way, a reliability expression with a one-to-one correspondence to the set of disjoint products is obtained. This approximate method provides a very good accuracy and greatly reduces the computation for complex networks.

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Enumeration of Minimal Cutsets for Directed Networks with Comparative Reliability Study for Paths or Cuts

Cited by 23 publications

References 34 publications

Reliability Evaluation of Multi-State Flow Networks Via Map Methods

Reliability Evaluation of Multi-State Flow Networks Via Map Methods

Framework for Probabilistic Vulnerability Analysis of Interdependent Infrastructure Systems

Approximate Method to Evaluate Reliability of Complex Networks

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