[e2e] Why Buffering?

David P. Reed dpreed at reed.com
Mon Jun 22 06:23:07 PDT 2009

As I noted, Little's theorem (at least its intuitive conclusion) applies 
to a wide variety of arrival processes and a wide variety of queues.  
Did I say that Little's theorem is the only knowledge one needs to get 
from studying queueing theory?  Of course not.

At least some of this discussion moved on to recognize that Little's 
theorem does NOT apply very well to arrival processes that involve 
closed-loop control of packet admission (such as TCP) do not follow 
Little's theorem, and arrival processes that involve even more complex 
control systems such as dynamic routing or packet scheduling involving 
propagation in WLANs or scheduled admission in WWANs.

So, as Detlef suggests, we should be careful in saying that Little's 
theorem should be gospel everywhere, without understanding how it 
derives from its assumptions.  That is why one needs to *learn* queueing 
theory, not as a cookbook, but as a way of thinking that one can adapt 
to complex problems.

I still remain shocked that the people who designed DOCSIS put many 
*seconds* of buffering into the downlink and uplink, which get filled 
(because the DOCSIS modem is the rate limiting device), and the result 
is that except for FTP, which cares little about latency, DOCSIS modems 
are *unusable* without implementing a "supervisory" layer on top of them 
that refuses to use the buffers inserted into the end-to-end path.  
Clearly this is due to bad decision making on the part of DOCSIS modem 
designers and deployers - assuming they wanted to support Internet 
service, rather than degrade it.

On 06/21/2009 05:33 AM, Detlef Bosau wrote:
> David P. Reed wrote:
>> 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.
> Little's Theorem can be easily applied in wired networks where a 
> link's capacity is easily expressed as "latency throghput product", 
> often referred to as "latency bandwidth product" which is in fact a 
> bit sloppy.
> The situation becomes a bit more complicated in wireless networks, 
> particularly WWAN, where the preconditions for Little's Theorem may 
> not hold, particularly the service time may not be stationary or stable.
> I sometimes wonder about papers who claim quite impressive "latency 
> bandwidth products" for wireless networks - and actually the authors 
> simply miss the fact that the transportation system is highly occupied 
> by local retransmissions and that we have a relationship between 
> average service, average throughput and the average amount of data  
> being in flight.
> I even remember a paper which claims latency bandwidth products for 
> GPRS in the range of MBytes IIRC.
> At a first glance, I wondered where this huge amount of data would fit 
> onto the air interface ;-)
> So, we should be extremely careful in applying Little's Theorem on 
> WWAN. As a consequence, we should even reconsider approaches like 
> packet pair, packet train and the like and whether they really hold in 
> WWAN or similar networks with highly volatile line conditions.
> Detlef
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