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Deficit Round-Robin: A Second Network Calculus Analysis
arXiv - CS - Performance Pub Date : 2021-06-02 , DOI: arxiv-2106.01034
Seyed Mohammadhossein Tabatabaee, Jean-Yves Le Boudec

Deficit Round-Robin (DRR) is a widespread scheduling algorithm that provides fair queueing with variable-length packets. Bounds on worst-case delays for DRR were found by Boyer et al., who used a rigorous network calculus approach and characterized the service obtained by one flow of interest by means of a convex strict service curve. These bounds do not make any assumptions on the interfering traffic hence are pessimistic when the interfering traffic is constrained by some arrival curves. For such cases, two improvements were proposed. The former, by Soni et al., uses a correction term derived from a semi-rigorous heuristic; unfortunately, these bounds are incorrect, as we show by exhibiting a counter-example. The latter, by Bouillard, rigorously derive convex strict service curves for DRR that account for the arrival curve constraints of the interfering traffic. In this paper, we improve on these results in two ways. First, we derive a non-convex strict service curve for DRR that improves on Boyer et al. when there is no arrival constraint on the interfering traffic. Second, we provide an iterative method to improve any strict service curve (including Bouillard's) when there are arrival constraints for the interfering traffic. As of today, our results provide the best-known worst-case delay bounds for DRR. They are obtained by using the method of the pseudo-inverse.

中文翻译:

赤字循环:第二次网络演算分析

赤字循环 (DRR) 是一种广泛使用的调度算法,它为可变长度数据包提供公平排队。Boyer 等人发现了 DRR 最坏情况延迟的界限,他们使用了一种严格的网络演算方法,并通过凸严格的服务曲线来表征由一个感兴趣的流获得的服务。这些边界不对干扰流量做出任何假设,因此当干扰流量受到某些到达曲线的约束时是悲观的。对于这种情况,提出了两项​​改进。前者由 Soni 等人提出,使用源自半严格启发式的修正项;不幸的是,这些界限是不正确的,正如我们通过展示一个反例所展示的那样。后者,由 Bouillard,严格导出 DRR 的凸严格服务曲线,该曲线考虑了干扰流量的到达曲线约束。在本文中,我们通过两种方式改进这些结果。首先,我们为 DRR 推导出了一个非凸的严格服务曲线,该曲线在 Boyer 等人的基础上有所改进。当干扰流量没有到达约束时。其次,当干扰流量存在到达约束时,我们提供了一种迭代方法来改进任何严格的服务曲线(包括 Bouillard 曲线)。截至今天,我们的结果为 DRR 提供了最著名的最坏情况延迟界限。它们是通过使用伪逆的方法获得的。当干扰流量没有到达约束时。其次,当干扰流量存在到达约束时,我们提供了一种迭代方法来改进任何严格的服务曲线(包括 Bouillard 曲线)。截至今天,我们的结果为 DRR 提供了最著名的最坏情况延迟界限。它们是通过使用伪逆的方法获得的。当干扰流量没有到达约束时。其次,当干扰流量存在到达约束时,我们提供了一种迭代方法来改进任何严格的服务曲线(包括 Bouillard 曲线)。截至今天,我们的结果为 DRR 提供了最著名的最坏情况延迟界限。它们是通过使用伪逆的方法获得的。
更新日期:2021-06-03
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