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:

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:

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

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

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",
}