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

Ted Faber faber at ISI.EDU
Mon Jul 14 13:31:28 PDT 2008

On Sat, Jul 12, 2008 at 02:42:18AM -0400, David P. Reed wrote:
> Actually, Ted, constructing a sequence of events that are Poisson 
> distributed in time *requires* a Poisson process.

Given a random variable X that's uniformly distributed on (0,1), Y= -a
ln(1-X), for a > 0,  is exponentially distributed with parameter a.
Events with interarrivaltimes given by Y are Poisson distributed with
parameter a.

Poisson distributed events from a uniform random variable.

This isn't esoteric;  it's an example right out of my graduate
probability text.  I'm old enough that it's not online but if your
library has Kishor Trivedi's _Probability & Statistics With Reliability,
Queueing, And Computer Science Applications_,  you can find the proof in
the section on computing distributions of funtions of a random variable.
In my 1982 edition, the proof is on page 140.

Ted Faber
http://www.isi.edu/~faber           PGP: http://www.isi.edu/~faber/pubkeys.asc
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