In feed-forward time-sensitive networks with Deficit Round-Robin (DRR), worst-case delay bounds were obtained by combining Total Flow Analysis (TFA) with the strict service curve characterization of DRR by Tabatabaee et al. The latter is the best-known single server analysis of DRR, however the former is dominated by Polynomial-size Linear Programming (PLP), which improves the TFA bounds and stability region, but was never applied to DRR networks. We first perform the necessary adaptation of PLP to DRR by computing burstiness bounds per-class and per-output aggregate and by enabling PLP to support non-convex service curves. Second, we extend the methodology to support networks with cyclic dependencies: This raises further dependency loops, as, on one hand, DRR strict service curves rely on traffic characteristics inside the network, which comes as output of the network analysis, and on the other hand, TFA or PLP requires prior knowledge of the DRR service curves. This can be solved by iterative methods, however PLP itself requires making cuts, which imposes other levels of iteration, and it is not clear how to combine them. We propose a generic method, called PLP-DRR, for combining all the iterations sequentially or in parallel. We show that the obtained bounds are always valid even before convergence; furthermore, at convergence, the bounds are the same regardless of how the iterations are combined. This provides the best-known worst-case bounds for time-sensitive networks, with general topology, with DRR. We apply the method to an industrial network, where we find significant improvements compared to the state-of-the-art.
翻译:在与 " 缺陷 " 圆环-路滨(DRR)连接到对时间敏感的网络中,最坏的延迟界限是通过将 " 总体流动分析 " (TFA)与Tabababeee等人对DRR的严格服务曲线定性相结合获得的。 后者是减少灾害风险最著名的单一服务器分析,然而,前者则由多面尺寸的线性编程(PLP)主导,它改进了TFA的界限和稳定性区域,但从未适用于DRR网络。我们首先通过计算每类和每产出总合的防爆界限并使PLPF支持DR的严格服务曲线来对DRR进行必要的调整。 其次,我们扩展了支持网络使用周期依赖性单一的单一服务器分析方法:一方面,DRR的严格的服务曲线取决于网络内部的交通特征,而另一方面,TFA或PLPLP要求事先对DR服务曲线进行最差的改进。 这一点可以通过迭接方法加以解决,然而,PLPLP本身则需要不断进行合并。