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max-min fairness

Hi, there's something I didn't get about max-min fairness :

cc.pdf, p.9 third paragraph of Network Model :
... The name "max-min" comes from the idea that is is forbidden to decrease the share of sources that have small values, thus, in some sense, we give priority to flows with small values.

But by definition of max-min fairness, an increase of any rate is a the cost of a decrease of an already smaller one.

To me, theses two sentences seem contradictory and from the definition, I don't see why it would be forbidden to decrease a small rate. I agree that it would not be fair to further decrease an already small rate, but I don't see anything in the definition that would prevent it.
Posted by René Giller on Wednesday 31 January 2007 at 17:37
Comments
Hello,
look at definition 1.2.1: it defines when a feasible allocation is max-min fair. To me, both the affirmations you cited are in accordance with this definition. Where is the problem??
Posted by Gianluca Rizzo on Wednesday 31 January 2007 at 18:14
When an allocation is max-min fair, it's possible to increase a rate only if you decrease a smaller one. So in other words, it's possible to decrease a small rate in order to increase a greater one.
But the other sentence states that it's impossible to decrease small rates in a max-min fair allocation
Posted by René Giller on Thursday 1 February 2007 at 13:38
An allocation IS max-min fairness if an increase of any rate is a the cost of a decrease of an already smaller one. This is a condition for max-min fairness.

So assume you have a max-min fair allocation. if you increase any of the rates (and thus have to decrease one that is already smaller than the one you increased) it will not be max-min fair anymore (because if you reverse the process, you can increase the one you decreased before, and decrease the other one which is bigger)
Posted by Manuel Flury on Thursday 1 February 2007 at 18:22
Ok, I didn't understand it that way. So in short :

When an allocation is max-min fair, I don't change it unless there's a change in the network (new source, change of sending rates, ...).
When an allocation is not max-min fair, I increase the small rates until it becomes max-min fair. Decreasing small rates would not tend to max-min fairness, so that's why it's "forbidden" to do it.

Am I correct ?
Posted by René Giller on Thursday 1 February 2007 at 22:50
If your goal is to achieve max-min fairness: yes. Otherwise, nothing is "forbidden" ;-)
Posted by Manuel Flury on Friday 2 February 2007 at 8:41