Reliability Evaluation of Imperfect K-Terminal Stochastic Networks using Polygon-to Chain and Series-parallel Reductions

Rebaiaia, Mohamed-Larbi; Ait-Kadi, Daoud

doi:10.1145/2815317.2815336

Cited by 4 publications

(7 citation statements)

References 10 publications

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“…Now, we remark that Equation (26) is valid if and only if the relations (27), (28) and (29) are respected.…”

Section: R G P P P P R G E E P P R G E Ementioning

confidence: 98%

“…The reduction by factorization is based on the factoring theorem of Moore & Shannon theorem [33], which is considered by several authors as the basis for a class of algorithms for computing K-terminal reliability [27] [31]. It consists of decomposing a graph by making assumptions about the state of a component (edge/node) until a simple configuration is obtained.…”

Section: The Factoring Principlementioning

confidence: 99%

“…In this paper we propose an algorithm which combines the reduction polygon-to-chain using the works of Theologou and Carlier [22], those of Satyanarayana and Wood [21], Simard [14] and Rebaiaia and Ait-Kadi [27], in the sense that a combination of Satyanarayana and Wood [21] and of Theologou and Carlier [22] are provided. We find the work of Theologou and Carlier [22] …”

Section: Polygon-to-chain Reductionmentioning

confidence: 99%

“…However, most of these solutions are very effective but unfortunately do not allow taking into account the complexity of systems and networks' architecture. The problem is that, in practice, there is no general and unified mathematical expression that can represent the reliability from which an exact value can be determined, except for some specific architecture, such as parallel, series, series-parallel, standby, k-from-n, and others as discussed in the literature (see [27]). …”

Section: Introductionmentioning

confidence: 99%

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System Reliability Evaluation for Imperfect Networks Using Polygon-to-Chain Reduction

Rebaiaia¹,

Ait-Kadi²

2017

AJOR

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The purpose of this paper is to propose a computational technique for evaluating the reliability of networks subject to stochastic failures. In this computation, a mathematical model is provided using a technique which incorporates the effect of the factoring decomposition theorem using polygonto-chain and series-parallel reductions. The algorithm proceeds by identifying iteratively one of seven polygons and when it is discovered, the polygon is immediately removed and replaced by a simple chain after having changed the individual values of the reliability of each edge and each node of the polygon. Theoretically, the mathematical development follows the results presented by Satyanarayana & Wood and Theologou & Carlier. The computation process is recursively performed and less constrained in term of execution time and memory space, and generates an exact value of the reliability.

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“…Now, we remark that Equation (26) is valid if and only if the relations (27), (28) and (29) are respected.…”

Section: R G P P P P R G E E P P R G E Ementioning

confidence: 98%

Section: The Factoring Principlementioning

confidence: 99%

Section: Polygon-to-chain Reductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

System Reliability Evaluation for Imperfect Networks Using Polygon-to-Chain Reduction

Rebaiaia¹,

Ait-Kadi²

2017

AJOR

Self Cite

View full text Add to dashboard Cite

show abstract

“…In Migov and Shakhov, factoring method has been utilized to evaluate the reliability of MANETs. A polygon‐to‐chain and series‐parallel reduction approach for evaluating the reliability of MANETs has been employed in Rebaiaia and Ait‐Kadi . In Ahmad and Mishra, a critical node detection‐based approach for the reliability evaluation of large scale MANETs has been proposed.…”

Section: Related Workmentioning

confidence: 99%

On computing the reliability of opportunistic multihop networks with Mobile relays

Khanna

Chaturvedi

Soh

2019

Quality & Reliability Eng

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Opportunistic multihop networks with mobile relays recently have drawn much attention from researchers across the globe due to their wide applications in various challenging environments. However, because of their peculiar intrinsic features like lack of continuous connectivity, network partitioning, highly dynamic behavior, and long delays, it is very arduous to model and effectively capture the temporal variations of such networks with the help of classical graph models. In this work, we utilize an evolving graph to model the dynamic network and propose a matrix‐based algorithm to generate all minimal path sets between every node pair of such network. We show that these time‐stamped‐minimal‐path sets (TS‐MPS) between each given source‐destination node pair can be used, by utilizing the well‐known Sum‐of‐Disjoint Products technique, to generate various reliability metrics of dynamic networks, ie, two‐terminal reliability of dynamic network and its related metrics, ie, two‐terminal reliabilities of the foremost, shortest, and fastest TS‐MPS, and Expected Hop Count. We also introduce and compute a new network performance metric−Expected Slot Count. We use two illustrative examples of dynamic networks, one of four nodes, and the other of five nodes, to show the salient features of our technique to generate TS‐MPS and reliability metrics.

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Reliability analysis for command‐and‐control systems based on edge extension diagram and binary decision diagram

Huang

Zhang

et al. 2022

Quality & Reliability Eng

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As the central nervous system of modern information warfare, the command‐and‐control network becomes the brain of command and the strategic target of the enemy's primary attack during the operation. In this paper, a method based on edge extension diagram (EED) and binary decision diagram (BDD) is proposed to evaluate the reliability of connectivity within the basic command post of command‐and‐control network, which is solving the problem that the conventional methods failed to model failure probabilities of node links and with low calculation efficiency. First, graph simplification of network topology, extension of nodes under reliable state, construction of path functions, replacement of associated edges, variable sorting, construction of binary decision graphs, and recursive calculation to evaluate the reliability of the connection between the two ends of the command‐and‐control network. Then, further analyze and sort the variable importance of the command‐and‐control network and analyze the sensitivity of the network topology. This paper contributes to the reliability assessment of command‐and‐control network system, the identification and maintenance of key network nodes, and the design of network topology structure.

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Reliability Evaluation of Imperfect K-Terminal Stochastic Networks using Polygon-to Chain and Series-parallel Reductions

Cited by 4 publications

References 10 publications

System Reliability Evaluation for Imperfect Networks Using Polygon-to-Chain Reduction

System Reliability Evaluation for Imperfect Networks Using Polygon-to-Chain Reduction

On computing the reliability of opportunistic multihop networks with Mobile relays

Reliability analysis for command‐and‐control systems based on edge extension diagram and binary decision diagram

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