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

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on a l<strong>in</strong>k, two cells are expected as <strong>in</strong>put to <strong>the</strong> l<strong>in</strong>k <strong>in</strong> <strong>the</strong> next RTT. This is<br />

true irrespective of <strong>the</strong> number of sources.<br />

This can be viewed <strong>in</strong> three ways:<br />

<strong>the</strong> number of cells <strong>in</strong> <strong>the</strong> network (<strong>in</strong> an RTT) doubles<br />

<strong>the</strong> overload measured over an RTT doubles<br />

<strong>the</strong> \active period" of <strong>the</strong> burst doubles every RTT<br />

2. Time to reach rate-limited operation: The m<strong>in</strong>imum number of RTTs re-<br />

quired to reach rate-limited operation decreases as <strong>the</strong> logarithm of <strong>the</strong> number<br />

of sources. In o<strong>the</strong>r words, <strong>the</strong> more <strong>the</strong> number of sources, <strong>the</strong> faster <strong>the</strong>y<br />

all reach rate-limited operation. <strong>Rate</strong>-limited operation occurs when <strong>the</strong> TCP<br />

sources are constra<strong>in</strong>ed by <strong>the</strong> network directed <strong>ABR</strong> rate ra<strong>the</strong>r than <strong>the</strong>ir<br />

congestion w<strong>in</strong>dow sizes. The m<strong>in</strong>imum numberofRTTs required is derived as<br />

follows:<br />

Suppose we nd that nd that TCP packets are available, but <strong>the</strong> source is not<br />

transmitt<strong>in</strong>g. There are two reasons <strong>for</strong> this: ei<strong>the</strong>r <strong>the</strong> source has exhausted<br />

its w<strong>in</strong>dow, or it is wait<strong>in</strong>g <strong>for</strong> <strong>the</strong> next transmission opportunity at <strong>the</strong> current<br />

ACR. In <strong>the</strong> rst case, we call <strong>the</strong> source w<strong>in</strong>dow-limited. In <strong>the</strong> second case,<br />

it is rate-limited.<br />

Initially, <strong>the</strong> w<strong>in</strong>dow is small (start<strong>in</strong>g from one). The sources are w<strong>in</strong>dow-<br />

limited (and not rate-limited). That is, each source exhausts its w<strong>in</strong>dow and<br />

may rema<strong>in</strong> idle <strong>for</strong> a while be<strong>for</strong>e it sends its next burst. As observed, <strong>the</strong><br />

number of cells <strong>in</strong> <strong>the</strong> network doubles every RTT. Stable closed loop rate-<br />

control can be established only after <strong>the</strong>re are enough cells to ll <strong>the</strong> pipe. The<br />

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