H-Mitigators: Improving Your Stochastic Network Calculus Output Bounds

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