Network calculus (NC), particularly its min-plus branch, has been extensively utilized to construct service models and compute delay bounds for time-sensitive networks (TSNs). This paper provides a revisit to the fundamental results. In particular, counterexamples to the most basic min-plus service models, which have been proposed for TSNs and used for computing delay bounds, indicate that the packetization effect has often been overlooked. To address, the max-plus branch of NC is also considered in this paper, whose models handle packetized traffic more explicitly. It is found that mapping the min-plus models to the max-plus models may bring in an immediate improvement over delay bounds derived from the min-plus analysis. In addition, an integrated analytical approach that combines models from both the min-plus and the max-plus NC branches is introduced. In this approach, the max-plus $g$-server model is extended and the extended model, called $g^{x}$-server, is used together with the min-plus arrival curve traffic model. By applying the integrated NC approach, service and delay bounds are derived for several settings that are fundamental in TSNs.
翻译:网络演算(NC),特别是其最小加分支,已被广泛应用于构建时间敏感网络(TSN)的服务模型并计算时延界。本文重新审视了其基础性结论。具体而言,针对TSN所提出并用于时延计算的最简最小加服务模型的反例表明,分组化效应常被忽略。为此,本文同时考虑了NC的最大加分支,该分支的模型能更显式地处理分组化流量。研究发现,将最小加模型映射至最大加模型可立即改善基于最小加分析得出的时延界。此外,本文提出了一种结合最小加与最大加NC分支模型的综合分析方法。在该方法中,对最大加$g$-服务器模型进行了扩展,并将扩展后的模型(称为$g^{x}$-服务器)与最小加到达曲线流量模型联合使用。通过应用这种综合网络演算方法,推导出了TSN中若干基础设置下的服务界与时延界。