[e2e] Why Buffering?

David P. Reed dpreed at reed.com
Sat Jun 20 17:41:20 PDT 2009

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.

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.

One can actually get a Ph.D. in Computer Networking without ever 
studying or using these important mathematical tools.

On 06/20/2009 12:23 AM, Dave CROCKER wrote:
> Paddy Ganti wrote:
>> The real reason for having buffers is the fact that information about
>> congestions takes some time to propagate. (In TCP/IP congestion are
>> detected by seeing lost packets).
> 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:
>      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.
>      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.
> Queuing is for transient problems rather than an excessive average:  
> The knee of the curve.
> d/
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