Improvements in the Efficiency of Cumulative Updating of All-Terminal Network Reliability

Rodionov, Alexey S.; Migov, Denis A.; Rodionova, Olga

doi:10.1109/tr.2012.2196172

Cited by 28 publications

(14 citation statements)

References 4 publications

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“…However, our results on using an arbitrary node cut for all-terminal reliability calculation were published only in Russian [18,19], and only the two-node cut case was presented in English [16,20]. Maybe, this is the reason that these results are not so widely known, and therefore, the same ideas were proposed again by Juan Manuel Burgos and Franco Robledo Amoza [23,24] in 2016.…”

Section: The Usage Of Two-node Cutsmentioning

confidence: 98%

“…Our methods named chain branching (CB) and chain reduction (CR) [15] could be used [16] .as a basis for two kinds of the ATR bound updating (UAB) algorithms named UAB based on CB (UAB_CB), and UAB based on CR (UAB_CR). These methods can be used if a network contains a chain, that is, a sequence of adjacent two-degree nodes.…”

Section: System Reliability 96mentioning

confidence: 99%

“…The CB reduces the calculation of ATR for calculating the ATRs of networks obtained from G by removing a pivot chain, or removing it and contracting its terminal nodes, while CR reduces it for calculating the ATR of the network G R , in which, this chain is substituted by a single edge. Let a chain C consist of k edges, its terminal nodes are s and t, and let an edge e st has a reliability p st , then [16] …”

Section: System Reliability 96mentioning

confidence: 99%

“…Proof of the statement can be found in [16], as well as the algorithm with the use of cutnodes (UAB_C).…”

Section: The Usage Of Cutnodesmentioning

confidence: 99%

“…The total number of these networks is 2*B W , where B W is the Bell number and W is the number of nodes in the cut. A particular case of two-node cut along with numerical experiments to demonstrate the efficiency for the ATR calculation was presented in [16,20], and in [21]-for the k-terminal reliability calculation. Despite the fact that the method from [17] presents a graph transformation for further factoring, and the method from [20] presents an expression for the network reliability, both of them practically lead to similar calculations of the same complexity.…”

Section: The Usage Of Two-node Cutsmentioning

confidence: 99%

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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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