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

[Joe Touch]

Lachlan Andrew wrote:
> Greetings Ted,
> 
> 2008/7/11 Ted Faber <faber at isi.edu>:
>> True Poisson processes are rare; the only one I can think of off the top
>> of my head is radioactive decay.
> 
> Just to be picky, that isn't Poisson either, although it is well
> approximated as Poisson on "short" time-scales (relative to the
> half-life).
> 
> In a Poisson process, events on disjoint intervals are independent.
> In radioactive decay, if there are a lot of decays in an early
> interval, there are fewer particles left to decay on later intervals,
> causing negative correlation.

There are two different effects to consider:

1. just saying "radioactive decay" isn't sufficient; as you note, decay
within any finite amount has negative correlations with the future (over
all timescales, not just far-term)

2. radioactive decay can cause cascades - so there is a positive
correlation with near-term decay (over the span of decay products)

It's not at all clear which of these dominates, or whether they balance. 
Both appear to be irrelevant for Geiger-counter mechanisms, though.

For U235, with a half-life of 700M years, you lose only 0.01% of a 
sample in a period of 100,000 years (longer than we think our species 
has existed); you lose 0.000001% over 10 years (longer than most 
simulations I know would care about such random number generators). When 
you have enough atoms for that to be statistically significant (i.e., 
that you don't get quantization impacts, as you would, e.g., with 100 
atoms), you're done. Even a miniscule amount, however, has more than 
enough atoms to suffice (e.g., 2.6 billion atoms in even 1 millionth of 
a gram).

#2 comes into play in significant ways only when specifically 
engineered; decay product neutrons are too fast to initiate a cascade 
naturally. They need to be slowed down, or other elements need to be 
present. In a small sample, it would be unlikely they'd even hit other 
nucleii.

I.e., a radioactive device would probably be sufficiently accurate to 
emulate a Possion process.

Joe


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