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

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number of cells <strong>in</strong> <strong>the</strong> rst RTT depends upon <strong>the</strong> number of sources start<strong>in</strong>g up<br />

toge<strong>the</strong>r (one MSS <strong>for</strong> each source). Hence<strong>for</strong>th, <strong>the</strong> number of cells only double<br />

irrespective of <strong>the</strong> number of sources. Hence, <strong>the</strong> number of RTTs required to<br />

ll <strong>the</strong> pipe depends upon <strong>the</strong> number of sources as follows:<br />

After KRTTs,<br />

w<strong>in</strong>dow W =2 K;1 MSS<br />

Note that MSS = 512 bytes + Overhead =12cells<br />

Or,<br />

E ective rate = MSS 2 K;1 N=RTT<br />

Here, N =number of sources<br />

The pipe is lled when <strong>the</strong> e ective <strong>in</strong>put rate rst exceeds capacity (or overload<br />

becomes greater than 1, <strong>for</strong> ERICA)<br />

MSS 2 K;1 N=RTT L<br />

Here, L is <strong>the</strong> l<strong>in</strong>k rate <strong>in</strong> cells per second.<br />

or<br />

L<strong>in</strong>k Bandwidth RT T<br />

K ; 1 = log2 ( )<br />

(MSS N)<br />

This shows that <strong>the</strong> number of RTTs decreases as <strong>the</strong> log of N. Note that<br />

once <strong>the</strong> l<strong>in</strong>k (or path/pipe) becomes fully loaded, <strong>the</strong> TCP w<strong>in</strong>dows <strong>in</strong>crease<br />

l<strong>in</strong>early and not exponentially (see section 8.3 earlier <strong>in</strong> this chapter). However,<br />

<strong>the</strong> sources may still not be rate-limited (<strong>the</strong> ACRs are still large, though <strong>the</strong><br />

bottleneck load is greater than unity). The sources reach rate-limited steady<br />

283

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