赤字循环：第二种网络演算分析
Deficit Round-Robin: A Second Network Calculus Analysis
摘要：
缺陷轮循（DRR）是一种广泛使用的调度算法，它提供可变长度分组的公平调度。Boyer等人发现了DRR最差情况延迟的界限，他使用了严格的网络演算方法，并通过凸严格服务曲线来表征由一个感兴趣的流获得的服务。这些边界没有对干扰业务做任何假设，因此当干扰业务受到某些到达曲线的约束时，这些边界是悲观的。对于这种情况，提出了两项改进建议。前者，由Soni等人，使用来自半严格启发式的校正项;不幸的是，这些界限是不正确的，正如我们展示的反例。后者，由Bouillard，严格推导出凸严格的服务曲线DRR帐户的到达曲线的干扰流量的限制。在本文中，我们从两个方面改进了这些结果。首先，我们推导出一个非凸的严格的服务曲线DRR，提高博耶等人。当没有到达的干扰流量的限制。其次，我们提供了一个迭代法，以改善任何严格的服务曲线（包括Bouillard的）时，有到达的干扰流量的限制。到目前为止，我们的研究结果提供了DRR最著名的最坏情况下的延迟界限。它们是用伪逆方法得到的。
英文摘要：
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.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
