Since its inception, control of data congestion on the Internet has been based on stochastic models. One of the first such models was Random Early Detection. Later, this model was reformulated as a dynamical system, with the average queue sizes at a router’s buffer being the states. Recently, the dynamical model has been generalized to improve global stability. In this paper we review the original stochastic model and both nonlinear models of Random Early Detection with a two-fold objective: (i) illustrate how a random model can be “smoothed out” to a deterministic one through data aggregation and (ii) how this translation can shed light into complex processes such as the Internet data traffic. Furthermore, this paper contains new materials concerning the occurrence of chaos, bifurcation diagrams, Lyapunov exponents and global stability robustness with respect to control parameters. The results reviewed and reported here are expected to help design an active queue management algorithm in real conditions, that is, when system parameters such as the number of users and the round-trip time of the data packets change over time. The topic also illustrates the much-needed synergy of a theoretical approach, practical intuition and numerical simulations in engineering.

中文翻译：

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互联网拥塞控制：从随机模型到动态模型

从一开始，互联网上的数据拥塞控制就一直基于随机模型。最早的此类模型之一是随机早期检测。后来，这个模型被重新表述为一个动态系统，路由器缓冲区的平均队列大小就是状态。最近，动态模型已被推广以提高全局稳定性。在本文中，我们回顾了具有双重目标的原始随机模型和随机早期检测的两个非线性模型：（i）说明如何通过数据聚合将随机模型“平滑”为确定性模型，以及（ii）如何这种翻译可以揭示复杂的过程，例如互联网数据流量。此外，本文还包含有关混沌发生、分岔图、Lyapunov 指数和关于控制参数的全局稳定性鲁棒性。这里审查和报告的结果有望帮助设计一种实际条件下的主动队列管理算法，即当系统参数（如用户数量和数据包的往返时间）随时间变化时。该主题还说明了工程中理论方法、实践直觉和数值模拟急需的协同作用。