[e2e] Why do we need TCP flow control (rwnd)?

David P. Reed dpreed at reed.com
Fri Jul 11 10:41:44 PDT 2008

Ahem: phone networks are NOT demonstrably Poisson.  There is no such 
statement that is true, Craig.  At best, one can say that sometimes a 
Poisson arrival process has some statistics that match actual data.  
That's called "fitting a curve to data".

The evidence that a system *is* Poisson requires understanding of the 
structure of the system - one cannot prove by simple statistics that a 
*process* is Poisson, but instead must start by saying that a process is 
either Poisson or some other process, chosen over the entire space of 
non-Poisson processes, and do a reproducible scientific hypothesis test 
to discriminate between them.   And the most trivial observations of the 
humans that place phone calls will disprove that phone calls are 
generated by a Poisson process.  To think otherwise is to wear blinders.

All the modelers do is say, what if we *assume* a Poisson process that 
has been parameterized by statistics gathered from experiments.  They 
*hope* that this will characterize processes that are non-Poisson with 
similar statistics.

So all we know from the telephone network is that it has some statistics 
that we've measured about probability of a call arriving into the system.

Besides the epistemological issue above: We know, in fact, that a call 
arrival cannot occur for at least a few seconds on the same line after 
such a call.  That makes it non-Poisson at the line level, right there.  
We also know that when a call is in progress on a line, a new call 
cannot be originated on that line, so there is inter-line correlation 
between probabilities of arrival.

This suggests that the telephone system is very strongly non-Poisson, 
even if you assume humans are random actors, and they are not, because 
they walk to and from phones, they have physical needs, they plan their 
calls based on assumptions about the callees, etc.

So one should be very careful to distinguish an assumption from a fact.

Craig Partridge wrote:
> In message <4E44F683-8AAB-451F-BC39-0ECA9A6F688F at surrey.ac.uk>, Lloyd Wood writ
> es:
>> On 2 Jul 2008, at 00:56, Fred Baker wrote:
>>> The thing that I find a little hard to grasp is why folks might have  
>>> thought the network was Poisson in the first place.
>> I doubt they did; it was chosen because it made the arithmetic  
>> tractable.
>> "First, assume a spherical cow..."
> I think this is unfair to the legions of statisticians that got
> us to making Poisson models work in the first place.
> The reason folks thought that data networks would be Poisson was that
>     1. Phone networks were demonstrably Poisson
>     2. They had nothing else in the arsenal (that is, if you were going
>        to do anything non-trivial, you lacked an analytic alternative)
> I had long discussions with folks who did statistical modeling in the late
> 1980s, as it was increasingly clear Poisson was a mistake.  Up to that
> point, network traffic was in small enough networks that one could, and
> many did, imagine that as the Internet matured, it would start to behave
> like the existing big network -- the telephone network.  But the Internet
> growth took off and the disparities between what Poisson predicted and
> measurements showed became too large to shrug off.  Statistical folks
> were deeply puzzled and frustrated.
> Craig

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