| Abstract
| - 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).
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