[e2e] Collaboration on Future Internet Architectures

[Vadim Antonov]

On Fri, 11 May 2007, Jon Crowcroft wrote:

> In missive <Pine.LNX.4.44.0705041458330.24385-100000 at gato.kotovnik.com>, Vadim Antonov typed:
> 
>  >>People who claim that increasing the density of raido nodes will increase 
>  >>the per-node bandwidth (or at least leave it unchanged) are simply not 
>  >>good with arithmetic.
>  
> conversely, at geometry
> 
> try a volume, not a plane. the number of alternate paths the the volume
> goes up faster, and one can use lots of disperity tricks (path, code etc)
> to make the alternates only have epsilon interference - if you then alternate
> dynamic power over a short haul hop to spread the signal to a neighbourhood, 
> with dynamic coding for longer haul to get the message to the next neighbourhood,
> you get capacity within epsilon*Nhops of N   - conjecture: a sequence of
> "knights moves" of 1 hop up, 2 hops forward can tile a volume in a systematic way and use the
> scheme above (due to Tse) in a very easy to self organised fashion...

You're talking about technology, not about scaling. The path and 
code dispersion tricks work just as well for nodes placed on some 2D 
surface.
 
Regarding scaling, with volume density of nodes in the network d the 
received signal power is proportional to d^(2/3) while noise power is 
proportional to d.

If transmitters emit any RF energy only during actual data transmission,
the transmitter duty cycle (given some constant S/N required by the
technology) goes down with increased density as 1/(d^(1/3)).

The average path length (in hops) increases with density as d^(1/3).

Thus the amount of bandwidth between fixed points in space depends on 
3D density of nodes as 1/(d^(2/3)).  Which is even worse than 2D case.

Note that this result does not depend on communication scheduling, 
antennae directionality, etc, etc, etc. Improvements in any of those
are merely constants, and do not affect scaling properties of the system.

> Imagine...

I don't need to imagine when I can calculate.

The saving grace of the smart dust is not in the density of motes, but
rather in ability to shift to higher frequencies (optical and above)
because reduced distances reduce high-frequency signal scattering in the
atmosphere.  (Actually, the same is true for macroscopic radio systems... 
with "atmosphere" being replaced with buildings, trees, fences, and such).

--vadim