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<font face="Helvetica, Arial, sans-serif">Dave - This is variously
known as Little's Theorem or Little's Lemma. The general pattern is
true for many stochastic arrival processes into queues. It precedes
Kleinrock, and belongs to queueing theory.<br>
<br>
I continue to be shocked, and dismayed, at the number of practicing
protocol designers who have never learned (or even *studied* without
learning) basic queueing theory. In my opinion, one cannot be
qualified to speak about protocol engineering without working knowledge
of queueing theory, control theory, and information theory. Yet most
CS depts. fail their students by completely ignoring these disciplines
in favor of teaching network protocols as a course in bit-field layouts.<br>
<br>
One can actually get a Ph.D. in Computer Networking without ever
studying or using these important mathematical tools.<br>
<br>
</font><br>
On 06/20/2009 12:23 AM, Dave CROCKER wrote:
<blockquote cite="mid:4A3C6428.30002@dcrocker.net" type="cite"><br>
<br>
Paddy Ganti wrote:
<br>
<blockquote type="cite">The real reason for having buffers is the
fact that information about
<br>
congestions takes some time to propagate. (In TCP/IP congestion are
<br>
detected by seeing lost packets).
<br>
</blockquote>
<br>
<br>
In the late 70s and 80s, Kleinrock gave a rather simple explanation for
using queuing (buffering) that I think is compatible with Antonov's
point:
<br>
<br>
After a lengthy and detailed introduction, he put up a graph of
throughput (x) versus delay (y). It had a very shallow increase until
hitting a very sharp knee and then was almost vertical.
<br>
<br>
He observed that before the knee, you don't need queuing because
you don't have any congestion. And after the knee, queuing doesn't
help because you simply don't have enough capacity.
<br>
<br>
Queuing is for transient problems rather than an excessive average:
The knee of the curve.
<br>
<br>
d/
<br>
<br>
</blockquote>
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