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Summary: Hopf Bifurcation and Oscillations in Homogeneous
Communication Networks
Huibing Yin Paul Wang Tansu Alpcan Prashant G. Mehta
Coordinated Science Laboratory,
Department of Mechanical Science and Engineering,
University of Illinois at Urbana-Champaign,
1206 W. Green Street, Urbana, IL 61801.
yin3,paulwang,mehtapg@uiuc.edu
Deutsche Telekom Laboratories, Ernst-Reuter-Platz 7, 10587 Germany
tansu.alpcan@telekom.de
Abstract: In this paper, we investigate stability and bifurcation arising in a communication network
model with a large number of homogeneous (symmetric) users and a single bottleneck AQM queue. We
carry out bifurcation analysis to study the effect of user delay and strength of feedback. It is shown that
for any given delay, there exists a critical amount of feedback (due to AQM) at which the equilibrium
loses stability and a limit cycling solution develops via a super-critical Hopf bifurcation. The conclusion
is verified both numerically and analytically.
1. INTRODUCTION
Communication networks such as the Internet exhibit a wide
variety of complex dynamic behavior. Examples of such com-
plex behavior include dynamic synchronization of the flows
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