[e2e] Overly Overlay; Peer to peer is commonplace

[Bob Briscoe]

David,

At 17:49 02/01/02 -0500, David P. Reed wrote:
>At 04:10 PM 1/2/2002 -0600, Nitin H Vaidya wrote:
>>Does this result require some assumptions about the channel, or receivers?
>
>This is really not understood completely.  One set of approaches involves 
>taking advantage of diffusive media (multipath is your friend!) to make the 
>transmission matrix full-rank.  I am not aware that this is the only case 
>that applies.  

We are talking about whether the address of endpoint E_0 should be hierarchically related to m possible previous hops R_m in order for any of N other end-points E_n in the world (Solar System?) to send to E_0. This breaks down into two issues.

1/ do we need any previous hops at all? or can all N other end-points reach E_0 wirelessly?
2/ if a previous hop is needed, will most of the m possible previous hops tend to be more closely connected to each other than all the other impossible hops?

This is where a basic physical assumptions comes in, prompted by Nitin's question:

Assumption 1/
In free space, e-m energy propagates by an inverse square law with distance, depending on how directional it is, which depends on frequency. Whereas wireline/fibre networks confine the signal to a much better approximation to 'fully directional', whatever the frequency. 

So taking each issue above in turn:

1/ For E_0 to be globally reachable wirelessly, the other N senders have to pump up their power by the square of distance. Particularly in order get the signal to go round corners (assumption 2: the world has corners which get in the way between most pairs of points on its surface that want to communicate!) e.g. to bounce the signal off whatever layers of the atmosphere it will bounce off, if at all, or to drive it straight through the earth's core.

So we need to answer whether the cost of laying fibre to confine this e-m radiation to a single directional path is always going to be less than the cost of the energy required to pump data over global distances wirelessly.

Not to mention the cost in biological life terms of all this intense radiation from N high power transmitters!

It might sound as if I'm being sarcastic. But these Gedanken experiments are worth doing to see if someone else can point out an invalid assumption I'm making (I'm sure there are plenty, but I mean one that breaks the argument).

But for now, let's assume a global wireless network is infeasible compared to a fixed one. So all that (very interesting) discussion about why non-hierarchical addressing is relevant in a wireless world, is trumped by the inverse square law of energy propagation.

Therefore, as someone already said in this thread, let's assume there is a fixed network connecting over the wide area, with wireless at the extremities.

So we move on to issue 2/ (will all the m possible previous hops to E_0 be topologically closer to each other than to the impossible hops?)

Whether E_0 is wired or wireless, we can certainly say the previous hops are likely to be geographically close to each other (cost per km in the wired case, inverse square law and cost of transmission power again in the wireless case).

So the question boils down to whether 'geographically closer' implies a tendency to be 'topologically closer' on the fixed network side. Again, cost per km of glass/wire should tend to imply this (but this could be a bit of a non-sequiteur).

So even if the end station E_0 is rapidly switching between the m providers e.g. on some market-driven basis, it still seems to make sense to use some degree of hierarchy in the addressing.

QED

Can anyone point out an implicit assumption I've made that flaws this argument? Certainly its changes in assumptions that drive innovation. But if no-one can challenge the assumptions, we can't innovate (yet).

I suspect there might be some mileage in being more precise in the wording of the assumption about the inverse square law, directionality and frequency.

I think the assumption you were hanging on when discussing the multipath stuff was that you can get N to grow unlimited, but only by increasing the density of receivers within the range of the transmitters. Increasing the range wasn't part of the analysis.

Bob
____________________________________________________________________________
Bob Briscoe         http://www.btexact.com/people/briscorj/