基于网络演算的流控网络计算高效最坏情况分析
Computationally Efficient Worst-Case Analysis of Flow-Controlled Networks with Network Calculus
AI总结：
本文针对流控网络中端到端服务曲线计算易因数据爆炸而不可行的问题，提出数据表示压缩方法和高效最小加卷积算法，在保持精确结果的同时显著提升计算效率。
摘要：
具有逐跳流控制的网络出现在多种场景中，从数据中心到系统架构（例如芯片上的虫洞路由网络）。此类网络中的最坏情况端到端延迟可以使用网络演算（Network Calculus，NC）进行计算，这是一种代数理论，其中流量和服务保证被表示为笛卡尔平面中的曲线。NC使用变换操作（例如最小加卷积）来建模流量剖面如何随网络节点的遍历而变化。NC允许对流控系统进行建模，因此可以计算端到端服务曲线，该曲线描述了流经串联流控节点的流所获得的最小服务保证。然而，尽管这种端到端服务曲线的代数表达式相当紧凑，但从算法角度看，其计算往往难以处理：数据结构往往会迅速增长到不可行的大尺寸，使得操作难以处理，即使只有三跳也是如此。在本文中，我们提出了计算和代数技术来缓解上述问题。我们表明现有技术（例如缩减到紧凑域）在此情况下无法使用，并提出了一系列解决方案，其中包括缓解数据表示空间爆炸的方法以及用于最小加卷积操作的计算高效算法。我们表明，我们的解决方案能够显著加速，使以前不可行的案例研究得以分析，并且由于它们不依赖任何近似，因此仍然提供精确结果。
英文摘要：
Networks with hop-by-hop flow control occur in several contexts, from data centers to systems architectures (e.g., wormhole-routing networks on chip). A worst-case end-to-end delay in such networks can be computed using Network Calculus (NC), an algebraic theory where traffic and service guarantees are represented as curves in a Cartesian plane. NC uses transformation operations, e.g., the min-plus convolution, to model how the traffic profile changes with the traversal of network nodes. NC allows one to model flow-controlled systems, hence one can compute the end-to-end service curve describing the minimum service guaranteed to a flow traversing a tandem of flow-controlled nodes. However, while the algebraic expression of such an end-to-end service curve is quite compact, its computation is often intractable from an algorithmic standpoint: data structures tend to grow quickly to unfeasibly large sizes, making operations intractable, even with as few as three hops. In this paper, we propose computational and algebraic techniques to mitigate the above problem. We show that existing techniques (such as reduction to compact domains) cannot be used in this case, and propose an arsenal of solutions, which include methods to mitigate the data representation space explosion as well as computationally efficient algorithms for the min-plus convolution operation. We show that our solutions allow a significant speedup, enable analysis of previously unfeasible case studies, and -- since they do not rely on any approximation -- still provide exact results.
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。
