[e2e] [Fwd: RED-->ECN]

[Steven Low]

Alhussein

> The only work I know of that attempted to derive this marking function
> mathematically, though in an ATM environment, is "A random early
> discard framework for congestion control in ATM networks",
> AU: Mokhtar-A; Azizoglu-M, SO: IEEE ATM Workshop '99 Proceedings. Do you
> have any motivations behind choosing the shape of the marking/dropping
> function to be exponential, other than mathematical convenience.

The motivation came from the abstract algorithm in our ToN paper where
congestion is measured at each link by a number we call 'price' and each
source needs the aggregate price, summed over all links in the path of
the
source, to set its rate (window).   So the issue becomes how to feed
back
the *sum* of link prices over the path using a single bit.  The trick is
to 
make  the *link* marking probability exponential in the link price.  
Then 
since the *end to end* marking probability, which is observable
at the source, depends on the link marking probabilities in a
multiplicative
manner, the end2end prob becomes dependent on the *sum* of the prices
(which
appear in the exponent).   In order words, the exponential form exploits
the statistical independence of link marking to compute and feed back
the *aggregate* price.   Details in the paper.

Do you know a website where I can download the paper you mentioned?

 
> So my question in other words is: How would a different choice of the
> random drop/marking function affect the convergence properties of your
> algorithm.

Using a linearized model, one can show that the convergence property
depends on the marking function only through its derivative at
equilibrium.
This is true for any AQM, not just REM.

Another related point is that the choice of the phi parameter in REM 
seems to be the trickiest.  We do not
have theoretical characterization on how to set these parameters, though
we have good intuitions from extensive simulations.  

Steven


> 
> Regards,
> 
> Alhussein.

-- 
__________________________________________________________________
Steven Low, Assoc Prof of CS & EE 
slow at caltech.edu			netlab.caltech.edu
Tel: (626) 395-6767			Caltech MC256-80
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