# H-Mitigators: Improving Your Stochastic Network Calculus Output Bounds

Paul Nikolaus
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Jens Schmitt
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Lia Schütze
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DOI
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DBLP
Giving tight estimates for output bounds is key to an accurate network analysis using the stochastic network calculus (SNC) framework. In order to upper bound the delay for a flow of interest in the network, one typically has to calculate output bounds of cross-traffic flows several times. Thus, an improvement in the output bound calculation pays off considerably. In this paper, we propose a new output bound calculation in the SNC framework by making use of Jensen’s inequality. It consists of inserting a convex function \(h\) into the bound, the so-called \(h\)-mitigator. We prove the bound’s validity and also show that, by choosing \(h\) as the power function, that it is always at least as accurate as the state-of-the-art method. Numerical evaluations demonstrate that even in small heterogeneous two-server topologies, our approach can improve a delay bound’s violation probability by a factor of over 135. For a set of randomly generated parameters, the bound is still decreased by a factor of 1.23 on average. Furthermore, our approach can be easily integrated in existing end-to-end analyses. Last but not least, we investigated another variant for \(h\), the exponential function and showed numerically that this approach is mostly disadvantageous