In a general model (AIMD) of transmission control protocol (TCP)
used in internet traffic congestion management, the time dependent
data flow vector x(t) > 0 undergoes a biased random walk on
two distinct scales. The amount of data of each component xi(t)
goes up to xi(t)+a with probability 1-ζi(x) on
a unit scale or down to γxi(t), 0 < γ < 1 with
probability ζi(x) on a logarithmic scale, where ζi depends on the joint state of the system x. We
investigate the long time behavior, mean field limit, and the one
particle case. According to
c = lim inf|x|→∞ |x|ζi(x)
, the process drifts to ∞ in the
subcritical c < c+(n, γ) case and has an invariant
probability measure in the supercritical case c > c+(n, γ).
Additionally, a scaling limit is proved when ζi(x)
and a are of order N–1 and t → Nt, in the form of a
continuum model with jump rate α(x).