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

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A ow chart of <strong>the</strong> basic algorithm is presented <strong>in</strong> gure C.1 (see appendix C).<br />

The ow chart shows steps to be taken on three possible events: at <strong>the</strong> end of an<br />

averag<strong>in</strong>g <strong>in</strong>terval, on receiv<strong>in</strong>g a cell (data or RM), and on recev<strong>in</strong>g a backward RM<br />

cell. These steps have been numbered <strong>for</strong> reference <strong>in</strong> fur<strong>the</strong>r modi cations of <strong>the</strong><br />

basic scheme.<br />

6.2 Achiev<strong>in</strong>g Max-M<strong>in</strong> Fairness<br />

Assum<strong>in</strong>g that <strong>the</strong> measurements do not su er from high variance, <strong>the</strong> above<br />

algorithm is su cient to converge to e cient operation <strong>in</strong> all cases and to <strong>the</strong> max-<br />

m<strong>in</strong> fair allocations <strong>in</strong> most cases. The convergence from transient conditions to <strong>the</strong><br />

desired operat<strong>in</strong>g po<strong>in</strong>t israpid,oftentak<strong>in</strong>g less than a round trip time.<br />

However, we have discovered cases <strong>in</strong> which <strong>the</strong> basic algorithm does not converge<br />

to max-m<strong>in</strong> fair allocations. This happens if all of <strong>the</strong> follow<strong>in</strong>g three conditions are<br />

met:<br />

1. The load factor z becomes one<br />

2. There are some sources which are bottlenecked elsewhere upstream<br />

3. CCR <strong>for</strong> all rema<strong>in</strong><strong>in</strong>g sources is greater than <strong>the</strong> F airShare<br />

If this happens, <strong>the</strong>n <strong>the</strong> system rema<strong>in</strong>s <strong>in</strong> its current state, because <strong>the</strong> term CCR=z<br />

is greater than F airShare <strong>for</strong> <strong>the</strong> non-bottlenecked sources. This nal state may or<br />

may not be fair <strong>in</strong> <strong>the</strong> max-m<strong>in</strong> sense.<br />

To achieve max-m<strong>in</strong> fairness, <strong>the</strong> basic ERICA algorithm is extended by remem-<br />

ber<strong>in</strong>g <strong>the</strong> highest allocation made dur<strong>in</strong>g one averag<strong>in</strong>g <strong>in</strong>terval and ensur<strong>in</strong>g that<br />

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