An Approach to Structural Analysis Using Moore-Shannon Network Reliability

Nath, Madhurima; Ren, Yihui; Eubank, Stephen

doi:10.1007/978-3-030-05411-3_44

Cited by 3 publications

(2 citation statements)

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“…Today, networks are ubiquitous starting from roads, railways [4,30] , and power lines [8] to internet [29], telecommunications [27] and wireless sensor networks [7,20,21] , and even models of infectious diseases epidemiology [33,34] , so reliability polynomials can be applied to a plethora of different networks, generating lots of research. However, the seminal work of Moore and Shannon [31] was intended for computation (rather than communications) networks, proposing a very practical redundancy scheme for circuit design.…”

Section: Introductionmentioning

confidence: 99%

Markov Chain Method for Computing the Reliability of Hammock Networks

Jianu¹,

Ciuiu²,

Dăuş³

et al. 2020

Prob. Eng. Inf. Sci.

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In this paper, we develop a new method for evaluating the reliability polynomial of a hammock network. The method is based on a homogeneous absorbing Markov chain and provides the exact reliability for networks of width less than 5 and arbitrary length. Moreover, it produces a lower bound for the reliability polynomial for networks of width greater than or equal to 5. To investigate how sharp this lower bound is, we compare our method with other approximation methods and it proves to be the most accurate in terms of absolute as well as relative error. Using the fundamental matrix, we also calculate the average time to absorption, which provides the mean length of a network that is expected to work.

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Section: Introductionmentioning

confidence: 99%

Markov Chain Method for Computing the Reliability of Hammock Networks

Jianu¹,

Ciuiu²,

Dăuş³

et al. 2020

Prob. Eng. Inf. Sci.

View full text Add to dashboard Cite

show abstract

“…In order to improve the reliability of such networks, they introduced a new type of reliability enhancement scheme called brick-wall (or hammock) network. In the last few years, the interest regarding the work of Moore and Shannon has been growing (see [2], [4], [8], [9]), not only from theoretical point of view, but also because of its applicability in various fields ranging from biology/medicine to engineering and even social sciences.…”

Section: Introductionmentioning

confidence: 99%