Motivated by recent concerns that queuing delays in the Internet are on the rise, we conduct a performance evaluation of Compound TCP (C-TCP) in two topologies: a single bottleneck and a multi-bottleneck topology, under different traffic scenarios. The first topology consists of a single bottleneck router, and the second consists of two distinct sets of TCP flows, regulated by two edge routers, feeding into a common core router. We focus on some dynamical and statistical properties of the underlying system. From a dynamical perspective, we develop fluid models in a regime wherein the number of flows is large, bandwidth-delay product is high, buffers are dimensioned small (independent of the bandwidth-delay product) and routers deploy a Drop-Tail queue policy. A detailed local stability analysis for these models yields the following key insight: smaller buffers favour stability. Additionally, we highlight that larger buffers, in addition to increasing latency, are prone to inducing limit cycles in the system dynamics, via a Hopf bifurcation. These limit cycles in turn cause synchronisation among the TCP flows, and also result in a loss of link utilisation. For the topologies considered, we also empirically analyse some statistical properties of the bottleneck queues. These statistical analyses serve to validate an important modelling assumption: that in the regime considered, each bottleneck queue may be approximated as either an $M/M/1/B$ or an $M/D/1/B$ queue. This immediately makes the modelling perspective attractive and the analysis tractable. Finally, we show that smaller buffers, in addition to ensuring stability and low latency, would also yield fairly good system performance, in terms of throughput and flow completion times.

中文翻译：

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正确的缓冲区大小很重要：一些关于复合 TCP 的动态和统计研究

由于最近对 Internet 中排队延迟上升的担忧，我们在两种拓扑中对复合 TCP (C-TCP) 进行了性能评估：单瓶颈拓扑和多瓶颈拓扑，在不同的流量场景下。第一个拓扑由单个瓶颈路由器组成，第二个由两组不同的 TCP 流组成，由两个边缘路由器调节，馈入公共核心路由器。我们专注于底层系统的一些动态和统计特性。从动力学的角度来看，我们在流数量大、带宽延迟乘积高、缓冲区尺寸小（与带宽延迟乘积无关）和路由器部署 Drop-Tail 队列策略的情况下开发流体模型。对这些模型进行详细的局部稳定性分析可得出以下关键见解：较小的缓冲区有利于稳定性。此外，我们强调，除了增加延迟之外，更大的缓冲区还容易通过 Hopf 分叉在系统动力学中引入极限循环。这些限制周期反过来导致 TCP 流之间的同步，并且还导致链路利用率的损失。对于所考虑的拓扑，我们还根据经验分析了瓶颈队列的一些统计特性。这些统计分析用于验证一个重要的建模假设：在所考虑的机制中，每个瓶颈队列可以近似为 $M/M/1/B$ 或 $M/D/1/B$ 队列。这立即使建模视角具有吸引力并且分析变得易于处理。最后，我们展示了较小的缓冲区，除了确保稳定性和低延迟外，还会产生相当好的系统性能，