This work develops a discrete time feedback system model for a simplified TCP (Transmission Control Protocol) network with RED (Random Early Detection [2]) control. The model involves sampling the buffer occupancy variable at certain instants. The dynamical model is used to analyze the TCP-RED operating point and its stability with respect to various RED controller and system parameters. Bifurcations are shown to occur as various system parameters are varied. These bifurcations, which involve emergence of oscillatory and/or chaotic behavior, may provide an explanation for the parameter sensitivity observed in practice. The bifurcations arise due to the presence of a nonlinearity in the characteristics of TCP throughput as a function of drop probability at the gateway. Among the bifurcations observed in the system are the period-doubling bifurcation and border collision bifurcations. The bifurcations are studied analytically, numerically, and experimentally.
|
1825
|
Congestion avoidance and control
– Jacobson
- 1988
|
|
1738
|
Random Early Detections Gateways for Congestion Avoidance
– Floyd, Jacobson
- 1993
|
|
877
|
Rate control in communication networks: shadow prices, proportional fairness and stability
– Kelly, Maulloo, et al.
- 1995
|
|
629
|
Nonlinear Oscillations, Dynamical Systems, and Bifurcations of Vector Fields
– Guckenheimer, Holmes
- 1986
|
|
434
|
TCP and Explicit Congestion Notification
– Floyd
- 1995
|
|
415
|
The macroscopic behavior of the TCP congestion avoidance algorithm
– Mathis, Semke, et al.
- 1997
|
|
340
|
Dynamics of Random Early Detection
– Lin, Morris
- 1997
|
|
319
|
TCP Vegas: End to end congestion avoidance on a global internet
– BRAKMO, PETERSON
|
|
244
|
Resource pricing and the evolution of congestion control
– Gibbens, Kelly
- 1985
|
|
203
|
Modeling TCP Reno performance: a simple model and its empirical validation
– Padhye, Firoiu, et al.
- 2000
|
|
160
|
A Control Theoretic Analysis of RED
– Hollot, Mishra, et al.
- 2001
|
|
157
|
Analysis and design of an adaptive virtual queue (AVQ) algorithm for active queue management
– Kunniyur, Srikant
- 2001
|
|
143
|
Active Queue Management
– Athuraliya, Low, et al.
- 2001
|
|
132
|
A study of active queue management for congestion control
– Firoiu, Borden
|
|
107
|
End-to-end congestion control for the internet: delays and stability
– Johari, Tan
- 2001
|
|
61
|
Dynamics of TCP/RED and a scalable control
– Low, Paganini, et al.
- 2002
|
|
60
|
Period three implies chaos
– Li, Yorke
- 1975
|
|
55
|
Utility-based rate control in the internet for elastic traffic
– La, Anantharam
- 2002
|
|
31
|
Perspectives of Nonlinear Dynamics
– Jackson
- 1991
|
|
28
|
Limit behavior of ECN/RED gateways under a large number of TCP flows
– Tinnakornsrisuphap, Makowski
- 2003
|
|
27
|
A mean-field model for multiple TCP connections through a buffer implementing RED. Performance Evaluation
– Baccelli, McDonald, et al.
|
|
13
|
Hybrid modeling of tcp congestion control
– Hespanha, Bohacek, et al.
- 2001
|
|
13
|
Oscillations and Chaos in a Flow model of a Switching System
– Erramilli, Forys
- 1990
|
|
12
|
Bifurcations in two-dimensional piecewise smooth maps - Theory and applications in switching circuits
– Banerjee, Ranjan, et al.
- 2000
|
|
11
|
Border collision bifurcations including “period two to period three” for piecewise smooth maps
– Nusse, Yorke
- 1992
|
|
8
|
Stability of TCP-RED congestion control
– Kuusela, Lassila, et al.
- 2001
|
|
5
|
Characterization of general TCP traffic under a large number of flows regime
– Tinnakornsrisuphap, La, et al.
- 2003
|
|
4
|
designing improved controllers for AQM routers supporting TCP flows
– “On
- 2001
|
|
4
|
Nonlinear Analysis and Control of TCP-RED in a Simple Network Model,” Accepted for presentation at
– Ranjan, Abed
- 2002
|
|
4
|
Nonlinear instabilities
– Ranjan, Abed, et al.
- 2002
|
|
4
|
Hybrid Modeling
– Hespanha, Bohacek, et al.
- 2001
|
|
4
|
The Chaotic Nature
– Veres, Boda
- 2000
|
|
3
|
A Control Theoretic Analysis of RED,” CMPSCI
– Hollot, Misra, et al.
- 2001
|
|
3
|
On Catastrophic Behavior of Queueing Networks
– Grishechkin, Devetsikiotis, et al.
- 1998
|
|
3
|
Traffic Synchronization Effects
– Erramilli, Forys
- 1991
|
|
2
|
Chaos: an introduction to dynamcal systems
– Alligood, Sauer, et al.
- 1996
|
|
2
|
Local analysis of � -bifurcations in � -dimensional piecewise smooth dynamical systems
– Bernardo, Feigin, et al.
- 1999
|
|
2
|
Why is Flow Control Hard
– Korilis, Lazar
- 1992
|
|
2
|
A Study of Active Queue Management For Congestion Control
– Misra, Gong, et al.
- 2000
|
|
1
|
Nonlinearity of TCP and instability with RED,” presented at the SPIE ITCom
– La, Ranjan, et al.
- 2002
|
|
1
|
of Adaptive Random Early Detection (ARED),” presented at the 18th Int. Teletraffic Congr
– “Analysis
- 2003
|
|
1
|
Reasons not to deploy RED,” presented at
– May, Lyles, et al.
- 1997
|
|
1
|
Controlling RED using washout filter controller,” presented at the Automatic Control Conf
– Ranjan, La, et al.
- 2004
|
|
1
|
Available: http://nws.cs.ucsb.edu/ munication networking. Priya Ranjan received the B.Tech. degree from the Indian Institute of Technology
– Service
- 1997
|
|
1
|
Stability of TCPRED Congestion Control,” Sumitted for publication, available at http://www.tct.hut.fi/tutkimus/com2/publ
– Kuusela, Lassilaand, et al.
- 2000
|
