Stability analysis of QCN: the averaging principle.

Data Center Networks have recently caused much excitement in the industry and in the research community. They represent the convergence of networking, storage, computing and virtualization. This paper is concerned with the Quantized Congestion Notification (QCN) algorithm, developed for Layer 2 congestion management. QCN has recently been standardized as the IEEE 802.1Qau Ethernet Congestion Notification standard. We provide a stability analysis of QCN, especially in terms of its ability to utilize high capacity links in the shallow-buffered data center network environment. After a brief description of the QCN algorithm, we develop a delay-differential equation model for mathematically characterizing it. We analyze the model using a linearized approximation, obtaining stability margins as a function of algorithm parameters and network operating conditions. A second contribution of the paper is the articulation and analysis of the Averaging Principle (AP)---a new method for stabilizing control loops when lags increase. The AP is distinct from other well-known methods of feedback stabilization such as higher-order state feedback and lag-dependent gain adjustment. It turns out that the QCN and the BIC-TCP (and CUBIC) algorithms use the AP; we show that this enables them to be stable under large lags. The AP is also of independent interest since it applies to general control systems, not just congestion control systems.