Improved Delay Bound for a Service Curve Element With Known Transmission Rate

Mohammadpour, Ehsan; Stai, Eleni; Boudec, Jean-Yves Le

doi:10.1109/lnet.2019.2927143

Cited by 18 publications

(29 citation statements)

References 10 publications

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“…and min. packet length and all links have same rate, then all flows have the same delay jitter bound and d i is a single number; else the delay may depend on the input port and the packet sizes, hence depends on the flow, not just the output port i [9]. For J ⊂ I, d J denotes the collection of all d i for i ∈ J; in particular, d I is the collection of all delay jitter bounds.…”

Section: System Modelmentioning

confidence: 99%

Equivalent Versions of Total Flow Analysis

Plassart¹,

Boudec²

2021

Preprint

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Total Flow Analysis (TFA) is a method for conducting the worst-case analysis of time sensitive networks without cyclic dependencies. In networks with cyclic dependencies, Fixed-Point TFA introduces artificial cuts, analyses the resulting cyclefree network with TFA, and iterates. If it converges, it does provide valid performance bounds. We show that the choice of the specific cuts used by Fixed-Point TFA does not affect its convergence nor the obtained performance bounds, and that it can be replaced by an alternative algorithm that does not use any cut at all, while still applying to cyclic dependencies.

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Section: System Modelmentioning

confidence: 99%

Equivalent Versions of Total Flow Analysis

Plassart¹,

Boudec²

2021

Preprint

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“…• the computation of a tighter delay bound within nodes by implementing the aforementioned result, as well as recent work in network calculus [22], and • an extension of the algorithm to topologies with cyclic dependencies by using an iterative fixed point described in [11, Chap. 12].…”

Section: Fp-tfa: a Novel Algorithm For Small Delay Bounds In Netwmentioning

confidence: 99%

“…In this subsection, we combine the aforementioned burstiness improvement with recent work in network calculus [22] and present the delay computations within the lowest layer in Figure 12. We are interested in the delay suffered by the flows within output port n of the device model in Figure 5.…”

Section: B Delay Within a Nodementioning

confidence: 99%

“…with R n the service rate of the scheduler n and T n its latency. The algorithm then applies the delay bound improvement of Mohammadpour et al, achieved when an output port n is followed by a line with transmission rate c n [22]:…”

Section: B Delay Within a Nodementioning

confidence: 99%

“…• We propose low-cost acyclic network (LCAN), an algorithm that finds the optimum number of regulators for breaking all cyclic dependencies; • We provide another algorithm, fixed-point total-flow analysis (FP-TFA), for computing small end-to-end delay bounds for general topologies, i.e., with and without cyclic dependencies. This algorithm is based on the most recent work in network calculus [22] and takes advantage of our improved bound for the burstiness increase within packetizers.…”

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

On Cyclic Dependencies and Regulators in Time-Sensitive Networks

Thomas

Boudec

Mifdaoui

2019

2019 IEEE Real-Time Systems Symposium (RTSS)

Self Cite

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For time-sensitive networks, as in the context of IEEE TSN and IETF Detnet, cyclic dependencies are associated with certain fundamental properties such as improving availability and decreasing reconfiguration effort. Nevertheless, the existence of cyclic dependencies can cause very large latency bounds or even global instability, thus making the proof of the timing predictability of such networks a much more challenging issue. Cyclic dependencies can be removed by reshaping flows inside the network, by means of regulators. We consider FIFO-per-class networks with two types of regulators: perflow regulators and interleaved regulators (the latter reshape entire flow aggregates). Such regulators come with a hardware cost that is less for an interleaved regulator than for a perflow regulator; both can affect the latency bounds in different ways. We analyze the benefits of both types of regulators in partial and full deployments in terms of latency. First, we propose Low-Cost Acyclic Network (LCAN), a new algorithm for finding the optimum number of regulators for breaking all cyclic dependencies. Then, we provide another algorithm, Fixed-Point Total Flow Analysis (FP-TFA), for computing end-to-end delay bounds for general topologies, i.e., with and without cyclic dependencies. An extensive analysis of these proposed algorithms was conducted on generic grid topologies. For these test networks, we find that FP-TFA computes small latency bounds; but, at a medium to high utilization, the benefit of regulators becomes apparent. At high utilization or for high line transmission-rates, a small number of per-flow regulators has an effect on the latency bound larger than a small number of interleaved regulators. Moreover, interleaved regulators need to be placed everywhere in the network to provide noticeable improvements. We validate the applicability of our approaches on a realistic industrial timesensitive network.

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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.

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Improved Delay Bound for a Service Curve Element With Known Transmission Rate

Cited by 18 publications

References 10 publications

Equivalent Versions of Total Flow Analysis

Equivalent Versions of Total Flow Analysis

On Cyclic Dependencies and Regulators in Time-Sensitive Networks

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

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