Guaranteeing accurate worst-case bounds on the end-to-end delay that data flows experience in communication networks is required for a variety of safety-critical systems , for instance in avionics . Deterministic Network Calculus (DNC) is a widely used method to derive such bounds. The DNC theory has been advanced in recent years to provide ever tighter delay bounds, though this turned out a hard problem in the general feed-forward network case. Currently, the only analysisto achieve tight delay bounds, i. e. , best possible ones, is based on an optimization formulation instead of the usual algebraic DNC analysis. However, it has also been shown to be NP-hard and was accompanied by a similar, yet relaxed optimization that trades tightness against computational effort. In our article, we derive a novel , fast algebraic delay analysis that nevertheless retains a high degree of accuracy . We show in extensive numerical experiments that our solution enables the analysis of large-scale networks by reducing the computation time by several orders of magnitude in contrast to the optimization analysis. Moreover, in networks where optimization is still feasible, our delay bounds stay within close range, deviating on average by only 1.16\% in our experiments .
Networks are integral parts of modern safety-critical systems and certification demands the provision of guarantees for data transmissions . Deterministic Network Calculus (DNC) can compute a worst-case bound on a data flow's end-to-end delay. Accuracy of DNC results has been improved steadily, resulting in two DNC branches: the classical algebraic analysis and the more recent optimization-based analysis. The optimization-based branch provides a theoretical solution for tight bounds. Its computational cost grows, however, (possibly super-)exponentially with the network size. Consequently, a heuristic optimization formulation trading accuracy against computational costs was proposed. In this paper, we challenge optimization-based DNC with a new algebraic DNC algorithm. We show that: (i) no current optimization formulation scales well with the network size and (ii) algebraic DNC can be considerably improved in both aspects, accuracy and computational cost. To that end, we contribute a novel DNC algorithm that transfers the optimization's search for best attainable delay bounds to algebraic DNC. It achieves a high degree of accuracy and our novel efficiency improvements reduce the cost of the analysis dramatically. In extensive numerical experiments , we observe that our delay bounds deviate from the optimization-based ones by only 1.142\% on average while computation times simultaneously decrease by several orders of magnitude .
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Guaranteeing accurate worst-case bounds on the end-to-end delay that data flows experience in communication networks is required for a variety of
Networks are integral parts of modern
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, for instance in avionics
and certification demands the provision of guarantees for data transmissions
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is a widely used method to derive such bounds. The DNC theory has been advanced in recent years to provide ever tighter delay bounds, though this turned out a hard problem in the general feed-forward network case. Currently, the only analysisto achieve tight delay bounds, i. e. , best possible ones, is based on an optimization formulation instead of the usual algebraic DNC analysis. However, it has also been shown to be NP-hard and was accompanied by a similar, yet relaxed optimization that trades tightness against computational effort. In our article, we derive a novel , fast algebraic delay analysis that nevertheless retains
can compute a worst-case bound on a data flow's end-to-end delay. Accuracy of DNC results has been improved steadily, resulting in two DNC branches: the classical algebraic analysis and the more recent optimization-based analysis. The optimization-based branch provides a theoretical solution for tight bounds. Its computational cost grows, however, (possibly super-)exponentially with the network size. Consequently, a heuristic optimization formulation trading accuracy against computational costs was proposed. In this paper, we challenge optimization-based DNC with a new algebraic DNC algorithm. We show that: (i) no current optimization formulation scales well with the network size and (ii) algebraic DNC can be considerably improved in both aspects, accuracy and computational cost. To that end, we contribute a novel DNC algorithm that transfers the optimization's search for best attainable delay bounds to algebraic DNC. It achieves
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. We show in
and our novel efficiency improvements reduce the cost of the analysis dramatically. In
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that our solution enables the analysis of large-scale networks by reducing the computation time
, we observe that our delay bounds deviate from the optimization-based ones by only 1.142\% on average while computation times simultaneously decrease
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in contrast to the optimization analysis. Moreover, in networks where optimization is still feasible, our delay bounds stay within close range, deviating on average by only 1.16\% in our experiments