The tech report about developing FAST TCP.

Standard AIMD: Window $$w(t)$$ of a source increase by 1 packet per RTT and decrease per unit time by $$x(t)q(t)\frac{1}{2}\frac{4}{3}w(t)$$ packets. The 4/3 is the peak window size before seeing loss and 1/2 is the MD factor. The rate is denoted by $$x(t)$$ (window size over RTT) and the loss probability is $$q(t)$$. Thus the flow-level model of AIMD can be expressed as the differential equation:

$\dot{w}(t)=\frac{1}{T(t)}-\frac{2}{3}x(t)q(t)w(t)$

From the D.E., the window size in equilibrium is $$q=\frac{3}{2w^2}$$ and this means on average we have $$qw=\frac{3}{2w}$$ packets lost per RTT. Moreover, the D.E. can be expressed as:

$\dot{w}(t)=\kappa(t)\big(1-\frac{q(t)}{u(t)}\big)$

which it is found that all TCP have such structure, different variants with different gain function $$\kappa(t)$$, utility function $$u(t)$$ and congestion measure (loss or delay) $$q(t)$$.

The dynamic of different TCP is illustrated in P.7: Reno oscillates about the point that is marginal to loss and with large queueing delay, while FAST and Vegas tries to stabilize at the knee of minimal queueing delay.

Loss-based TCP includes Reno, HSTCP and Scalable TCP. The HSTCP defines the equilibrium relation between e2e loss prob and window size as $$q = \frac{0.0789}{w^{1.1976}}$$, which then makes the AIMD of cwnd follows

\begin{aligned} w &:= w + a(w)/w, \textrm{ and} \\ w &:= w - b(w)w \end{aligned}

respectively with the values of functions $$a$$ and $$b$$ depend on window size. Scalable TCP is MIMD:

\begin{aligned} w &:= w + a, \textrm{ and} \\ w &:= w - bw \end{aligned}

with $$a$$ and $$b$$ equals to 0.01 and 0.125 respectively.

T.B.C.

## Bibliographic data

@techreport{
title = "FAST TCP: Motivation, Architecture, Algorithms, Performance",
author = "Cheng Jin and David X. Wei and Steven H. Low",
institution = "Caltech",
number = "CS Technical Report CaltechCSTR:2003.010",
howpublished = "Caltech CS TR",
year = "2003",
}