Bounded-Variance Network Calculus: Computation of Tight Approximations of End-to-End Delay

Currently, the most advanced framework for stochastic network calculus is the min-plus algebra, providing bounds for the end-to-end delay in networks. The bounds calculated with the min-plus algebra are tight, if compared with previous methods, but we still observe a significant degradation of the tightness of bounds as the number of nodes crossed by flows increases. Moreover, even if the calculations are greatly simplified relatively to previous methods, they are still complicated as numerical optimizations are necessary. In this paper, we propose a novel framework for the approximated calculation of end-to-end delay: the bounded-variance network calculus, by which we provide two important results. Firstly, we obtain an evaluation of end-to-end delay significantly tighter than that offered by the min-plus algebra. Secondly, the calculations needed to compute our approximations of delay are much simpler and we show that in a typical application scenario used to test the accuracy of the frameworks for network calculus, our approximations are obtained in a closed analytical form, as opposed to the numerical bounds of the other methods. These two advantages constitute an important progress in the direction of evolving statistical network calculus into a practical tool for network analysis.