Nancy: An efficient parallel Network Calculus library

Zippo, Raffaele; Stea, Giovanni

doi:10.1016/j.softx.2022.101178

Cited by 8 publications

(10 citation statements)

References 17 publications

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“…We run our experiments on a desktop PC equipped with an Intel Core i9-9900, 16 GB of DRAM @3200 MHz, Windows 10. Our publicly available NC library, called Nancy [31], [32] is written in C# (. NET 6), and can exploit the PLINQ framework to easily parallelize and scale the algorithms in multicore processors.…”

Section: A Computational Resultsmentioning

confidence: 99%

“…However, the latter only reports functional comparisons (i.e., discusses the capabilities of each tool), and does not address performance issues. To the best of our knowledge, there seems to be no other open NC tool that is able to deal with UPP functions, beside ours [31], [32]. Most of the existing public tools, e.g., CyNC [47], NC-Maude [48], DiscoDNC [49], DEBORAH [50], [51], CATS [52] restrict the implementation of NC operators to the case of CPL functions.…”

Section: Related Workmentioning

confidence: 99%

“…Our arithmetics is based instead on rational numbers, hence computations are always exact. Moreover, it seems that RTC loops infinitely in several cases -which are not challenging, performance-wise [31].…”

Section: Related Workmentioning

confidence: 99%

See 2 more Smart Citations

Computationally Efficient Worst-Case Analysis of Flow-Controlled Networks With Network Calculus

Zippo

Stea²

2023

IEEE Trans. Inform. Theory

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Networks with hop-by-hop flow control occur in several contexts, from data centers to systems architectures (e.g., wormhole-routing networks on chip). A worst-case endto-end delay in such networks can be computed using Network Calculus (NC), an algebraic theory where traffic and service guarantees are represented as curves in a Cartesian plane. NC uses transformation operations, e.g., the min-plus convolution, to model how the traffic profile changes with the traversal of network nodes. NC allows one to model flow-controlled systems, hence one can compute the end-to-end service curve describing the minimum service guaranteed to a flow traversing a tandem of flow-controlled nodes. However, while the algebraic expression of such an end-to-end service curve is quite compact, its computation is often intractable from an algorithmic standpoint: data structures tend to grow quickly to unfeasibly large sizes, making operations intractable, even with as few as three hops.In this paper, we propose computational and algebraic techniques to mitigate the above problem. We show that existing techniques (such as reduction to compact domains) cannot be used in this case, and propose an arsenal of solutions, which include methods to mitigate the data representation space explosion as well as computationally efficient algorithms for the minplus convolution operation. We show that our solutions allow a significant speedup, enable analysis of previously unfeasible case studies, and -since they do not rely on any approximation -still provide exact results.

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Section: A Computational Resultsmentioning

confidence: 99%

Section: Related Workmentioning

confidence: 99%

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Computationally Efficient Worst-Case Analysis of Flow-Controlled Networks With Network Calculus

Zippo

Stea²

2023

IEEE Trans. Inform. Theory

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“…At the end of this section, we report the necessary information for the alert reader to retrace the steps exposed hereafter to include these two corner cases. We remark that the Nancy software library [29] computes pseudo-inverses of generic (non-decreasing) UPP functions, including UC and wUI ones.…”

Section: Properties Of Pseudo-inverses Of Upp Functionsmentioning

confidence: 99%

“…Last, we exemplify our findings on a comprehensive proof of concept, showing how to compute the per-flow service curve of [24, Theorem 1], which makes use of all the findings in this paper. The algorithms described in this paper, together with those for known NC operators, are implemented in the Nancy open-source toolbox [29], which, to the best of our knowledge, is the only public one to implement UPP algorithms.…”

Section: Introductionmentioning

confidence: 99%

Extending the Network Calculus Algorithmic Toolbox for Ultimately Pseudo-Periodic Functions: Pseudo-Inverse and Composition

Zippo

Nikolaus

Stea

2022

Preprint

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Network Calculus (NC) is an algebraic theory that represents traffic and service guarantees as curves in a Cartesian plane, in order to compute performance guarantees for flows traversing a network. NC uses transformation operations, e.g., min-plus convolution of two curves, to model how the traffic profile changes with the traversal of network nodes. Such operations, while mathematically well-defined, can quickly become unmanageable to compute using simple pen and paper for any nontrivial case, hence the need for algorithmic descriptions. Previous work identified the class of piecewise affine functions which are ultimately pseudo-periodic (UPP) as being closed under the main NC operations and able to be described finitely. Algorithms that embody NC operations taking as operands UPP curves have been defined and proved correct, thus enabling software implementations of these operations. However, recent advancements in NC make use of operations, namely the lower pseudo-inverse, upper pseudo-inverse, and composition, that are well defined from an algebraic standpoint, but whose algorithmic aspects have not been addressed yet. In this paper, we introduce algorithms for the above operations when operands are UPP curves, thus extending the available algorithmic toolbox for NC. We discuss the algorithmic properties of these operations, providing formal proofs of correctness.

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Extending the network calculus algorithmic toolbox for ultimately pseudo-periodic functions: pseudo-inverse and composition

Zippo,

Nikolaus,

Stea

2023

Discrete Event Dyn Syst

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Network Calculus (NC) is an algebraic theory that represents traffic and service guarantees as curves in a Cartesian plane, in order to compute performance guarantees for flows traversing a network. NC uses transformation operations, e.g., min-plus convolution of two curves, to model how the traffic profile changes with the traversal of network nodes. Such operations, while mathematically well-defined, can quickly become unmanageable to compute using simple pen and paper for any non-trivial case, hence the need for algorithmic descriptions. Previous work identified the class of piecewise affine functions which are ultimately pseudo-periodic (UPP) as being closed under the main NC operations and able to be described finitely. Algorithms that embody NC operations taking as operands UPP curves have been defined and proved correct, thus enabling software implementations of these operations. However, recent advancements in NC make use of operations, namely the lower pseudo-inverse, upper pseudo-inverse, and composition, that are well-defined from an algebraic standpoint, but whose algorithmic aspects have not been addressed yet. In this paper, we introduce algorithms for the above operations when operands are UPP curves, thus extending the available algorithmic toolbox for NC. We discuss the algorithmic properties of these operations, providing formal proofs of correctness.

show abstract

Nancy: An efficient parallel Network Calculus library

Cited by 8 publications

References 17 publications

Computationally Efficient Worst-Case Analysis of Flow-Controlled Networks With Network Calculus

Computationally Efficient Worst-Case Analysis of Flow-Controlled Networks With Network Calculus

Extending the Network Calculus Algorithmic Toolbox for Ultimately Pseudo-Periodic Functions: Pseudo-Inverse and Composition

Extending the network calculus algorithmic toolbox for ultimately pseudo-periodic functions: pseudo-inverse and composition

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