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",
}
```