Methods of Speeding up of Diameter Constrained Network Reliability Calculation

Migov, Denis A.; Nesterov, Sergei N.

doi:10.1007/978-3-319-21407-8_9

Cited by 7 publications

(3 citation statements)

References 15 publications

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“…The pivotal link

e

is here uniformly chosen at random. The reader can find a comparison among different link selection heuristics in . The optimal choice from a computational point of view is still an open problem in the diameter‐constrained context.…”

Section: Factorization Algorithmmentioning

confidence: 99%

Factorization and exact evaluation of the source‐terminal diameter‐constrained reliability

2017

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In classical network reliability, the system under study is a network with perfect nodes and imperfect links that fail randomly and independently. The probability that a given subset K of terminal nodes belongs to the same connected component is called classical or K ‐Terminal reliability. Although (and because) the classical reliability computation belongs to the class of N P‐Hard problems, the literature offers many methods for this purpose, given the importance of the models. This article deals with diameter‐constrained reliability, where terminal nodes are further required to be connected by d hops or fewer ( d is a given strictly positive parameter of the metric called its diameter). This metric was defined in 2001, inspired by delay‐sensitive applications in telecommunications. Factorization theory is fundamental for the classical network reliability evaluation, and today it is a mature area. However, its extension to the diameter‐constrained context requires at least the recognition of irrelevant links, which is an open problem. In this article, irrelevant links are efficiently determined in the most used case, where |K|=2, thus providing a first step toward a Factorization theory in diameter‐constrained reliability. We also analyze the metric in series‐parallel and composition graphs. The article closes with a Factoring algorithm and a discussion of trends for future work. © 2017 Wiley Periodicals, Inc. NETWORKS, Vol. 70(4), 283–291 2017

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“…The pivotal link

e

Section: Factorization Algorithmmentioning

confidence: 99%

Factorization and exact evaluation of the source‐terminal diameter‐constrained reliability

2017

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“…Pseudocode of the method proposed for the DCR bounds cumulative updating [27], which is based on CPFM, is presented below:…”

Section: System Reliabilitymentioning

confidence: 99%

“…In our previous studies [25][26][27], we have obtained such methods which can calculate the DCR faster. These methods are the analogue of the well-known series-parallel transformation for CPFM, and the pivot edge selection strategy.…”

Section: System Reliabilitymentioning

confidence: 99%

Obtaining and Using Cumulative Bounds of Network Reliability

Rodionov¹,

Migov²

2017

System Reliability

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In this chapter, we study the task of obtaining and using the exact cumulative bounds of various network reliability indices. A network is modeled by a non-directed random graph with reliable nodes and unreliable edges that fail independently. The approach based on cumulative updating of the network reliability bounds was introduced by Won and Karray in 2010. Using this method, we can find out whether the network is reliable enough with respect to a given threshold. The cumulative updating continues until either the lower reliability bound becomes greater than the threshold or the threshold becomes greater than the upper reliability bound. In the first case, we decide that a network is reliable enough; in the second case, we decide that a network is unreliable. We show how to speed up cumulative bounds obtaining by using partial sums and how to update bounds when applying different methods of reduction and decomposition. Various reliability indices are considered: k-terminal probabilistic connectivity, diameter constrained reliability, average pairwise connectivity, and the expected size of a subnetwork that contains a special node. Expected values can be used for unambiguous decision-making about network reliability, development of evolutionary algorithms for network topology optimization, and obtaining approximate reliability values.

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