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

Notice that max-min allocation is both fair and e cient. It is fair in the sense
that all sources get an equal share on every link provided that they can use it. It is
e cient in the sense that each link is utilized to the maximum load possible.
When we take the minimum cell rate (MCR) of sources into account, there are
several possible optimality criteria. Other criterion such as weighted fairness have
been proposed to determine optimal allocation of resources over and above MCR
[32].
Abraham and Kumar [1] develop a natural extension of the concept of max-min
fair rate allocation to the case of ABR sessions with non-zero MCRs. Speci cally,
the feasibility condition includes the fact that every VC's rate is at least its MCR�
the max-min criteria is the same: the network is considered to be in a state of max-
min fairness if it is impossible to increase the rate of any session, while maintaining
feasibility, without decreasing the rate of sessions whose rate is equal or smaller. The
characterization in terms of rate vectors is also the same, i.e., a rate vector is max-
min fair is it is lexicographically the largest among all feasible rate vectors. The
authors also develop centralized and distributed algorithms to achieve this max-min
allocation.
Finally, it should be pointed out that all de nitions of fairness assume that
the tra c sources always have data to send (i.e., are in nite sources). For tra c
which is \bursty" (i.e., contains active and idle periods), the concept of fairness is
ill-de ned. As a heuristic, the de nitions should be rephrased in terms of the through-
puts achieved by sources. Source throughput is measured over a long time interval
(covering many idle and active intervals) and not approximated as a series of instan-
taneous rate allocations. In other words, \fairness" is a long-term goal. While we
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