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Stability of RED Algorithm: Analysis Based on Nonlinear Control Theory

REN Feng-Yuan 1) LIN Chuang 1) WANG Fu-Bao 2) 1) (Department of Computer Science and Technology, Tsinghua University, Beijing 100084) 2) (Department of Computer, Northwestern Polytechnical University, Xi′an 710072)  
This paper analyzes the attributes of RED(Random Early Detection) and gentle-RED algorithms using the describing function approach, which is a classical analysis approach in nonlinear control theory. In fact, authors conclude that the essential reason that queue periodic motion is the self-oscillation caused by the nonlinear component in the packet dropping probability profile, this point is neglected by most of the existed schemes, and then deduce a more accurate criterion with which the stable operation region of RED scheme will be estimated, on the other hand, although gentle-RED is more powerful than RED to keep queues stable, this ability is very limited because it only extends the stable operation region with different nonlinear characteristic, but doesn't thoroughly eliminate it. The ideal solution should be to design more robust linear controller for AQM scheme.
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