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arXiv cs/0609014cs.NImath.PR
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利用TCP平均场模型计算RED的简单稳定性条件

A simple stability condition for RED using TCP mean-field modeling

Julien Reynier

摘要:

互联网拥塞是一个老问题,但仍然是一个深入研究的主题。TCP协议及其AIMD(加法增加和乘法减少)行为隐藏了非常具有挑战性的问题;其中之一是了解大量用户之间的交互与延迟反馈。本文将重点讨论TCP的两个建模问题,在实现[Baccelli McDonald Reynier 02]中提出的模型时,这两个问题对于解决具体场景非常重要,首先是最大TCP窗口大小的建模:在许多实际情况下可以快速达到这个最大值;其次是延迟结构:当排队延迟可变时,通常的Little-like公式表现得很差,并且可能显著地改变预测队列大小的演变,这使得研究drop-tail或RED(随机早期检测)机制是无用的。在提出的TCP建模改进中,我们能够看到一个具体的例子,其中RED应该在FIFO路由器中使用,而不是让默认的drop-tail发生。我们研究了RED算法窗口大小分布的数学不动点和局部稳定性。一个有趣的情况是,当RED在拥塞开始时以极限运行时,它避免了不必要的带宽损失和延迟变化。

英文摘要:

Congestion on the Internet is an old problem but still a subject of intensive research. The TCP protocol with its AIMD (Additive Increase and Multiplicative Decrease) behavior hides very challenging problems; one of them is to understand the interaction between a large number of users with delayed feedback. This article will focus on two modeling issues of TCP which appeared to be important to tackle concrete scenarios when implementing the model proposed in [Baccelli McDonald Reynier 02] firstly the modeling of the maximum TCP window size: this maximum can be reached quickly in many practical cases; secondly the delay structure: the usual Little-like formula behaves really poorly when queuing delays are variable, and may change dramatically the evolution of the predicted queue size, which makes it useless to study drop-tail or RED (Random Early Detection) mechanisms. Within proposed TCP modeling improvements, we are enabled to look at a concrete example where RED should be used in FIFO routers instead of letting the default drop-tail happen. We study mathematically fixed points of the window size distribution and local stability of RED. An interesting case is when RED operates at the limit when the congestion starts, it avoids unwanted loss of bandwidth and delay variations.

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。

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