Brief paper: Hopf bifurcation and oscillations in a communication network with heterogeneous delays

  • Authors:

  • Huibing Yin;Paul Wang;Tansu Alpcan;Prashant G. Mehta

  • Affiliations:

  • Department of Mechanical Science & Engineering and the Coordinated Science Laboratory, University of Illinois at Urbana-Champaign, 1206 W. Green Street, Urbana, IL 61801, United States;Department of Mechanical Science & Engineering and the Coordinated Science Laboratory, University of Illinois at Urbana-Champaign, 1206 W. Green Street, Urbana, IL 61801, United States;Deutsche Telekom Laboratories, Ernst-Reuter-Platz 7, 10587, Germany;Department of Mechanical Science & Engineering and the Coordinated Science Laboratory, University of Illinois at Urbana-Champaign, 1206 W. Green Street, Urbana, IL 61801, United States

  • Venue:
  • Automatica (Journal of IFAC)
  • Year:
  • 2009

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Abstract

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.