Stability analysis of multiple-bottleneck networks

Lijun Wang, Lin Cai, Xinzhi Liu, Xuemin (Sherman) Shen, Junshan Zhang

Research output: Contribution to journalArticlepeer-review

31 Scopus citations


A TCP/RED (Transmission Control Protocol/Random Early Detection) system with multiple-bottleneck links could be unstable even if its system parameters are set the same as those in a stable single-bottleneck system [D. Bauso, L. Giarre, G. Neglia, Active queue management stability in multiple bottleneck networks, IEEE ICC'04, vol. 4, June 2004, pp. 2267-2271]. In this paper, we study the stability of more general AIMD (Additive Increase and Multiplicative Decrease)/RED system with multiple bottlenecks that may incur non-negligible packet losses. We develop a general mathematical model to analyze network stability for both delay-free and delayed AIMD/RED systems. Sufficient conditions for the asymptotic stability of multiple-bottleneck systems with heterogeneous delays are derived by appealing to Lyapunov stability theory with Lyapunov-Razumikhin conditions, and these conditions can be easily assessed by using LMI (Linear Matrix Inequality) Toolbox. Numerical results with Matlab and simulation results with NS-2 are given to validate the analytical results.

Original languageEnglish (US)
Pages (from-to)338-352
Number of pages15
JournalComputer Networks
Issue number3
StatePublished - Feb 27 2009


  • AIMD/RED system
  • Lyapunov function
  • Multiple-bottleneck networks
  • Stability analysis

ASJC Scopus subject areas

  • Computer Networks and Communications


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