在速率控制协议（RCP）中，我们需要两种形式的反馈吗？
Do we need two forms of feedback in the Rate Control Protocol (RCP)?
摘要：
网络社区对显式拥塞控制有相当大的兴趣，因为它可以允许设计公平、稳定、低损耗、低延迟和高利用率的网络。速率控制协议（RCP）是这样的拥塞控制协议的示例。RCP的当前设计建议它应该采用两种形式的反馈，即速率失配和队列大小，以管理其流量控制算法。RCP中一个突出的设计问题是，给定基于速率不匹配的反馈，队列大小反馈的存在是否有用。在本文中，我们解决这个问题，使用控制和分岔理论的工具。我们线性化实际的非线性系统，并分析了局部渐近稳定性，鲁棒稳定性和收敛速度的设计选择，即，有和没有队列大小反馈。但是，这样的分析并没有提供明确的设计建议，是否队列反馈是有用的或没有。这激发了分叉理论分析，其中我们必须考虑非线性项，这有助于了解RCP系统的其他动力学特性。特别是，我们着手分析两个非线性性质，即Hopf分支的类型和分支极限环的渐近稳定性。分析结果表明，在RCP中的队列反馈的存在下，可以诱导一个亚临界的Hopf分岔，这可能会导致不良的系统行为。而在无队列反馈的情况下，系统的Hopf分岔总是超临界的，分岔极限环是稳定的，且幅值很小。数值计算和一些数据包级的模拟，以及证实了分析。基于我们的工作，RCP的建议是在协议的设计中只包括基于速率失配的反馈。
英文摘要：
There is considerable interest in the networking community in explicit congestion control as it may allow the design of a fair, stable, low loss, low delay, and high utilization network. The Rate Control Protocol (RCP) is an example of such a congestion control protocol. The current design of RCP suggests that it should employ two forms of feedback; i.e. rate mismatch and queue size, in order to manage its flow control algorithms. An outstanding design question in RCP is whether the presence of queue size feedback is useful or not, given feedback based on rate mismatch. In this paper, we address this question using tools from control and bifurcation theory. We linearize the actual non-linear system and analyze the local asymptotic stability, robust stability and rate of convergence of both the design choices, i.e., with and without queue size feedback. But such analyses do not offer clear design recommendations on whether the queue feedback is useful or not. This motivates a bifurcation-theoretic analysis where we have to take non-linear terms into consideration, which helps to learn additional dynamical properties of the RCP system. In particular, we proceed to analyze two non-linear properties, namely, the type of Hopf bifurcation and the asymptotic stability of the bifurcating limit cycles. Analytical results reveal that the presence of queue feedback in RCP can induce a sub-critical Hopf bifurcation, which can lead to undesirable system behavior. Whereas, in the absence of queue feedback, the Hopf bifurcation is always super-critical where the bifurcating limit cycles are stable and of small amplitude. The analysis is corroborated by numerical computations and some packet-level simulations as well. Based on our work, the suggestion for RCP is to only include feedback based on rate mismatch in the design of the protocol.
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