Congestion avoidance and control
SIGCOMM '88 Symposium proceedings on Communications architectures and protocols
Random early detection gateways for congestion avoidance
IEEE/ACM Transactions on Networking (TON)
Analysis and design of an adaptive virtual queue (AVQ) algorithm for active queue management
Proceedings of the 2001 conference on Applications, technologies, architectures, and protocols for computer communications
The Mathematics of Internet Congestion Control (Systems and Control: Foundations and Applications)
The Mathematics of Internet Congestion Control (Systems and Control: Foundations and Applications)
Proceedings of the 2004 conference on Applications, technologies, architectures, and protocols for computer communications
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In this paper we analyze a fluid model of TCP with an approximation of drop tail using tools from control and bifurcation theory. The focus of our analysis and experiments lies in a regime where the buffer sizes are small, as recently advocated by Appenzeller, Keslassy and McKeown [G. Appenzeller, I. Keslassy, N. McKeown, Sizing router buffers, in: Proceedings of ACM SIGCOMM, 2004]. We find that to ensure local stability of TCP with drop tail it is necessary and sufficient that the arrival rate be greater than capacity by a certain factor, which does not depend on the round-trip time. This factor is found to be 1.1415. The next natural question to ask is: what if these conditions of local stability are just violated? This entails conducting a local bifurcation theoretic analysis (at the point of linear instability), from which we conclude that the corresponding nonlinear system undergoes a supercritical Hopf bifurcation. So as stability of the equilibrium is just lost, it is regained by a stable limit cycle. The analysis is complemented by simulations at the packet level performed using the Network Simulator, ns2.