Indeed.
I'll give you another example of a serious misuse of a theorem outside its range of applicability:
Shannon proved a channel capacity theorem: C = W log(S / N). The proof is mathematical, and correct.
...and it is. But it needs to be applied correctly.But hiding in the assumptions are some very strong and rarely applicable conditions. It was a very useful result in founding information theory.
But... it is now called "Shannon's Law" and asserted to be true and applicable to ALL communications systems.
Ahem ... if it's proven, it's correct, even in practice ;-)
This turns out not to be correct. And it is hardly ever correct in practice.
Therein lies the problem. Correct theorem, incorrectly applied.An example of non-correct application turns out to be when multiple transmissions of electromagnetic waves occur at the same time. EE practice is to treat "all other signals" as Gaussian Noise. They are not - they never are
Note: N here isn't the noise power (just the number of signals)..
So, later information theorists discovered that where there are multiple signals received by a single receiving antenna, and only a little noise (usually from the RF Front End of the receiver, not the environment) the Slepian-Wolf capacity theorem applies C = W log(\sum(S[i]. i=1,N) /W).
Only if you lump in correlated signals with noise, which is an incorrect (or rather, over-simplified) application of the Shannon-Hartley theorem.That's a LOT more capacity than Shannon's Law predicts, especially in narrowband signalling.
And noise itself is actually "measurement error" at the receiver, which is rarely Gaussian, in fact it really is quite predictable and/or removable.
Noise in the Shannon sense is random and therefore not predictable or correlated. Interference can be both predictable and correlated, and therefore can sometimes be removed / to an extent. Modelling interference as noise means not exploiting its inherent properties, and yes that means ending lower capacity. But that doesn't mean that either theorem is inapplicable - Shannon's fundamental limit still holds, even in the multi-user case, as long as the noise you plug in is the "little noise" from the RF front end and leave the interference out.
The point I guess is that
models are just models, and the more you know about what it is
that you are dealing with, the better you can model.
Which, I suppose, applies to
managing queues also. The more you know what's in them and how
it'll respond when you manage it, the better.
-- **************************************************************** Dr. Ulrich Speidel School of Computer Science Room 303S.594 (City Campus) The University of Auckland u.speidel@auckland.ac.nz http://www.cs.auckland.ac.nz/~ulrich/ ****************************************************************