Why Reliability for Computing Needs Rethinking

Beiu, Valeriu; Drăgoi, Vlad; Beiu, Roxana-Mariana

doi:10.1109/icrc2020.2020.00006

Cited by 9 publications

(7 citation statements)

References 28 publications

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“…The first argument follows on the steps used by Moore and Shannon for hammocks: a square MMN is one which is neither too serial (which depends on

l

) but also not too parallel either (which depends on

w

), so obviously the most natural choice for achieving a balance is

w = l

. Another argument is given in [5,16], where several FOMs have been proposed: the steepness of the reliability polynomials, and their variation in a symmetric interval with respect to

p_{0} = 0.5

. The simulations reported there, as well as fresh simulations [6], have shown that square MMNs are able to come “closer” to

θ (p - 0.5)

than nonsquare ones. Still, such simulations have covered only small values of

l

and

w

. Finally, suppose that one would randomly choose from the set of all MMNs of size

n

.…”

Section: Most Reliable Mmnsmentioning

confidence: 93%

“…Firstly, the reliability polynomials are efficiently computable (for compositions of series and parallel). Secondly, there are series and parallel compositions which are comparable to hammocks (with respect to several different metrics for reliability) [6]. Thirdly, the reliability polynomials of compositions have compact forms and are sparser than the ones for hammocks [16].…”

Section: Introductionmentioning

confidence: 99%

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Fast reliability ranking of matchstick minimal networks

Drăgoi

Beiu

2021

Networks

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In this article, we take a closer look at the reliability of large minimal networks constructed by repeated compositions of the simplest possible networks. For a given number of devices n=2m we define the set of all the possible compositions of series and parallel networks of two devices. We then define several partial orders over this set and study their properties. As far as we know the ranking problem has not been addressed before in this context, and this article establishes the first results in this direction. The usual approach when dealing with reliability of two‐terminal networks is to determine existence or nonexistence of uniformly most reliable networks. The problem of ranking two‐terminal networks is thus more complex, but by restricting our study to the set of compositions we manage to determine and demonstrate the existence of at least a graded poset.

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“…The first argument follows on the steps used by Moore and Shannon for hammocks: a square MMN is one which is neither too serial (which depends on

l

) but also not too parallel either (which depends on

w

), so obviously the most natural choice for achieving a balance is

w = l

. Another argument is given in [5,16], where several FOMs have been proposed: the steepness of the reliability polynomials, and their variation in a symmetric interval with respect to

p_{0} = 0.5

. The simulations reported there, as well as fresh simulations [6], have shown that square MMNs are able to come “closer” to

θ (p - 0.5)

than nonsquare ones. Still, such simulations have covered only small values of

l

and

w

. Finally, suppose that one would randomly choose from the set of all MMNs of size

n

.…”

Section: Most Reliable Mmnsmentioning

confidence: 93%

Section: Introductionmentioning

confidence: 99%

Fast reliability ranking of matchstick minimal networks

Drăgoi

Beiu

2021

Networks

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“…. , 9: L (x) = 4.4602 − 0.11725x−0.0096x 2 +0.02393x 3 − −0.00847x 4 +0.00083x 5 −0.00003x 6 The smooth curve defined by r(x) = (x, L(x), P (x, L(x))), x ∈ [1,9], belongs to Pascal's surface and is interconnecting the points (x i , y i , N i ), i = 3, 4, . .…”

Section: Reliability Polynomialsmentioning

confidence: 99%

“…It is in this context that we have started to revisit results on network reliability [54,55], by looking into consecutive [5,23] and hammock networks [22]. That is how we slowly realized that the original goal of Moore and Shannon-of finding networks for enhancing the reliability of computations-has been slowly shifting over time towards networks for reliable communications [6]. Still, with scaling, both computations and communications are being affected by variations [8], so a deeper understanding of reliability polynomials should in the end prove beneficial, and Pascal's surface seems to be providing a different view which starts from their coefficients.…”

Section: Introduction and Motivationsmentioning

confidence: 99%

Approximating the Level Curves on Pascal’s Surface

Dăuş

Jianu

Nagy

et al. 2022

INT J COMPUT COMMUN, Int. J. Comput. Commun. Control

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It is well-known that in general the algorithms for determining the reliability polynomial associated to a two-terminal network are computationally demanding, and even just bounding the coefficients can be taxing. Obviously, reliability polynomials can be expressed in Bernstein form, hence all the coefficients of such polynomials are fractions of the binomial coefficients. That is why we have very recently envisaged using an extension of the classical discrete Pascal’s triangle (which comprises all the binomial coefficients) to a continuous version/surface. The fact that this continuous Pascal’s surface has real values in between the binomial coefficients makes it appealing as being a mathematical concept encompassing all the coefficients of all the reliability polynomials (which are integers, as resulting from counting processes) and more. This means that, the coefficients of any reliability polynomial can be represented as discrete steps (on level curves of integer values) on Pascal’s surface. The equation of this surface was formulated by means of the gamma function, for which quite a few approximation formulas are known. Therefore, we have started by reviewing many of those results, and have used a selection of those approximations for the level curves problem on Pascal’s surface. Towards the end, we present fresh simulations supporting the claim that some of these could be quite useful, as being both (reasonably) easy to calculate as well as fairly accurate.

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“…Lately, the relentless scaling of CMOS transistors [7] has been the driving force calling for reliability enhancements of complex digital systems affected by noises and variations [8,9]. These have inspired us to investigate consecutive systems [10,11] and, more recently, hammocks [12], as well as other particular two-terminal networks [13].…”

Section: Introductionmentioning

confidence: 99%

On a Surface Associated with Pascal’s Triangle

et al. 2022

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An open problem in reliability theory is that of finding all the coefficients of the reliability polynomial associated with particular networks. Because reliability polynomials can be expressed in Bernstein form (hence linked to binomial coefficients), it is clear that an extension of the classical discrete Pascal’s triangle (comprising all the binomial coefficients) to a continuous version (exhibiting infinitely many values in between the binomial coefficients) might be geometrically helpful and revealing. That is why we have decided to investigate the geometric properties of a continuous extension of Pascal’s triangle including: Gauss curvatures, mean curvatures, geodesics, and level curves, as well as their symmetries.

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Why Reliability for Computing Needs Rethinking

Cited by 9 publications

References 28 publications

Fast reliability ranking of matchstick minimal networks

Fast reliability ranking of matchstick minimal networks

Approximating the Level Curves on Pascal’s Surface

On a Surface Associated with Pascal’s Triangle

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