[e2e] Collaboration on Future Internet Architectures

[Jon Crowcroft]

In missive <Pine.LNX.4.44.0705121512270.14800-100000 at gato.kotovnik.com>, Vadim Antonov typed:

 >>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.

it aint always quite as simple - 

some technology changines the path loss exponent, and some deployments
and technologies change the fading models that apply (wideband fading models for example
might not quite carry over from ricean or inakagami, which alter your equations below (i.e.
change the overal scaling) - but i agree that the dominant result in most cases is as you
say here (certainly noise scaing with d is pretty hard to beat:)

 >>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
 >>

 cheers

   jon