Traffic Management for the Available Bit Rate (ABR) Service in ...

Observe that this de nition means that the optimal vector is such that its smallest
component is maximized over all feasible vectors, then, given the value of the smallest
component, the next smallest component is maximized, etc.
In other words, we know that the total number of feasible vectors is in nite.
For each allocation vector, the source that is getting the least allocation is in some
sense, the \unhappiest source." Given the set of all feasible vectors, nd the vector
that gives the maximum allocation to this unhappiest source. Actually, the number
of such vectors is also in nite although we have narrowed down the search region
considerably. Now we take this \unhappiest source" out and reduce the problem to
that of remaining n ; 1sourcesoperating on a network with reduced link capacities.
Again, we nd the unhappiest source among these n ; 1 sources, give that source
the maximum allocation and reduce the problem by one source. We keep repeating
this process until all sources have been given the maximum that they could get. In
summary,anetwork is considered to be in a state of max-min fairness if it is impossible
to increase the rate of any session without decreasing the rate of sessions whose rate
is equal or smaller.
Figure 3.3: Sample con guration for max-min fairness
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