Hopf bifurcation and oscillations in a communication network with heterogeneous delays

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• 作者：Huibing Yin ; Paul Wang ; Tansu Alpcan ; Prashant G. Mehta
• 关键词：Communication networks ; Nonlinear analysis ; Perturbation analysis ; Time delay ; Dynamic stability
• 刊名：Automatica
• 出版年：2009
• 出版时间：October 2009
• 年：2009
• 卷：45
• 期：10
• 页码：2358-2367
• 全文大小：3456 K

文摘

In this paper, we investigate stability, bifurcation and oscillations arising in a single-link communication network model with a large number of heterogeneous users adopting a Transmission Control Protocol (TCP)-like rate control scheme with an Active Queue Management (AQM) router. In the system considered, different user delays are known and fixed but taken from a given distribution. It is shown that for any given distribution of delays, there exists a critical amount of feedback (due to AQM) at which the equilibrium loses stability and a limit cycling solution develops via a Hopf bifurcation. The nature (criticality) of the bifurcation is investigated with the aid of Lyapunov–Schmidt perturbation method. The results of the analysis are numerically verified and provide valuable insights into dynamics of the AQM control system.