  Since its inception, control of data congestion on the Internet has been
based on stochastic models. One of the first such models was Random Early
Detection. Later, this model was reformulated as a dynamical system, with the
average queue sizes at a router's buffer being the states. Recently, the
dynamical model has been generalized to improve global stability. In this paper
we review the original stochastic model and both nonlinear models of Random
Early Detection with a two-fold objective: (i) illustrate how a random model
can be "smoothed out" to a deterministic one through data aggregation, and (ii)
how this translation can shed light into complex processes such as the Internet
data traffic. Furthermore, this paper contains new materials concerning the
occurrence of chaos, bifurcation diagrams, Lyapunov exponents and global
stability robustness with respect to control parameters. The results reviewed
and reported here are expected to help design an active queue management
algorithm in real conditions, that is, when system parameters such as the
number of users and the round-trip time of the data packets change over time.
The topic also illustrates the much-needed synergy of a theoretical approach,
practical intuition and numerical simulations in engineering.
