Probability Theory and Internet

I will present results by Philippe Robert:
The Additive-Increase Multiplicative-Decrease (AIMD) schemes
designed to control congestion in communication networks are investigated
from a probalistic point of view. Functional limit theorem for a general
class of Markov Processes that describe these algorithms are described in
terms of the limiting Markov processes. For some special important cases,
including TCP congestion avoidance, an important autoregressive property
is proved. As a consequence, the explicit expression of the related invariant
probabilities is derived. The transient behavior of these algorithms is also analyzed.