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 γx i(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|→∞ ζl(x)1 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).
Original language | English (US) |
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Pages (from-to) | 271-285 |
Number of pages | 15 |
Journal | ESAIM - Probability and Statistics |
Volume | 14 |
Issue number | 4 |
DOIs | |
State | Published - Oct 29 2010 |
Keywords
- AIMD
- Fluid limit
- Mean field interaction
- TCP
ASJC Scopus subject areas
- Statistics and Probability