[e2e] Why do we need TCP flow control (rwnd)?
David P. Reed
dpreed at reed.com
Fri Jul 11 23:42:18 PDT 2008
Actually, Ted, constructing a sequence of events that are Poisson
distributed in time *requires* a Poisson process.
Unless you mean the trivial statement that any sequence of events in
time is Poisson, because a Poisson process can produce any sequence of
The reason is that a sequence has NO PROBABILITY DISTRIBUTION
WHATSOEVER. It has a conditional probability of 1, given that it is the
sequence under consideration.
If you have a set of 5 such chosen sequences, they still have a
conditional probability of one in your sample set.
If you observe 5 such sequences in the world, you still cannot tell if
they are Poisson distributed without a *prior* that says they are (say)
either Poisson or Bernoulli distributed. Then you can evaluate the
conditional probability of them being generated, and this gives you some
evidence. But absent the prior that limits you to Poisson or Bernoulli,
you are unable to say anything of the sort.
And as I said, we have a prior. We know that telephone calls are
generated by people, who have constraints that *cannot* match the
Poisson process. So it would be arrogant and blind at the same time to
claim that "telephone calls are Poisson".
All one can say is that if we make the false assumption that telephone
calls are Poisson, then our simplified simulations and narrow modeling
fit the observed behavior of the system reasonably well, This is a
useful result. But it goes nowhere toward either
- proving that the process is Poisson,
- proving the distributions are Poisson, or
-proving that the assumption of Poisson behavior will always work
in new models that may amplify aspects of human behavior that are
definitely not Poisson.
This is not subtle. Teaching EE kids that behavior *is* Poisson
distributed is teaching them how NOT to think. Professors should be
Ted Faber wrote:
> On Fri, Jul 11, 2008 at 01:49:39PM -0400, Craig Partridge wrote:
>> Hi Dave:
>> My understanding of the literature (and I don't claim to be an expert)
>> is that between the late 1950s and the mid 1970s, the telephony system
>> fit Poisson very well (for arrivals and departures of phone calls and
>> the like) and that this was an essential driver to the introduction
>> of statistical muxing in the telephone system. As modems, faxes, changes in
>> charging models, etc. came along, that changed but that it was true
>> (a sort of golden moment for the statisticians) and drove advances.
>> But I wasn't there....
> I think David is drawing the distinction between a Poisson process,
> which is defined pretty precisely and something that produces events
> with a Poisson distribution.
> True Poisson processes are rare; the only one I can think of off the top
> of my head is radioactive decay. Series of events that are Poisson
> distributed are markedly easier to find. The pseudorandom number
> generator on my machine (which is certainly not a Poisson process) can
> be massaged to create a sequence of events that are Poisson distributed.
> I believe that the statements that the telephone interrarrivals were
> Poisson distributed and that they were not generated by a Poisson
> process are both true.
> This is like the fact that my students aren't Normal, but I still grade
> on a bell curve. :-) (Yes, yes, I know, I don't need to hear about the
> various laws of large numbers; that sentence was a joke...)
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