网络拥塞中的非线性现象与控制

Nonlinear Behaviors and its Control in Internet Congestion

由于Internet通信量的快速增长和爆炸式膨胀,拥塞控制在当今正日益变得重要。Internet拥塞控制又存在着固有的、非常复杂的非线性动态问题。在本文中,我们利用随机早期检测算法(RED)研究了TCP的非线性现象,如RED的分叉、混沌以及鲁棒稳定性,同时考虑了线性和非线性的丢包函数。我们还证明了RED和PD-RED算法控制混沌与分叉的稳定性。仿真结果清楚展现以下两个算法结果的有效性。

Congestion control is becoming increasingly important nowadays due to explosive expansion and rapid growth of traffic in the Internet. They are inherently very complex nonlinear dynamic problems. In this article we in-vestigate nonlinear behaviors of TCP with random early detection(RED)gateways such as bifurcation, chaos as well as robust stability of RED. Both linear and nonlinear drop functions are considered. We also deduce the stability con-ditions of adaptive RED and proportional derivative RED algorisms controlling bifurcations and chaos. Simulation re-sults explicitly manifest the effective outcomes of above two algorisms.