[PLUG-TALK] Network routing is fractal, approaches N^2

Keith Lofstrom keithl at gate.kl-ic.com
Mon Jul 30 00:46:30 UTC 2012


Slowly reading and translating various documents from citynet.nl,
learning what they did in Amsterdam, and why they appear to be
stalled at 2% metro area deployment to the dense urban core.

The documents laud the capacity of fiber - 200 TBPS for a
single mode fiber - but neglect the switching fabric problem. 
If you want to generally connect N endpoints, you need up
to N^2 agile crosspoint switches.

Not quite - there are architectures (like Banyan tree) that
claim to be able to connect everyone with (on the order of)
N*ln(N) switches.  However, these tiered switches fail in
practice, because interconnectivity is fractal.  Right now,
everyone is watching the Olympics.  Then some nutball group
will blow up a stadium, and the news will move to the
nuclear immolation of Mudsylvania.  Then to the fallout
cloud spreading over China.  Then the radioactive consumer
electronics scare.  Slashdotting writ large.  That is how
the internet behaves.

A network that can handle real fractal network traffic is
more like N^1.5 connections, approaching to N^2 at the
lower tiers, assuming locals arrange for bittorent style
re-distribution combined with IPV6 multicast.  The real,
messy, changing world doesn't fit in a Banyan tree box.

If you are trying to connect, say, a million nodes in ten
thousand cities around the planet, you are going to need
on the order of 1E16 switch points.  If you plan to move
200TBPS through them, you will need on the order of 1E30
switching operations per second.  At 0.1 picojoule per
switch operation, that is 1E17 watts, about the amount of
sunlight power reaching the ground over the entire earth.
For comparison, global electric generation capacity is
about 3E12 W.

Obviously, we will not run the whole network at those speeds
all the time.  But projections based on continuous, rapid
exponential growth of fiber bandwidth (implying those switch
speeds, eventually) are quickly invalidated by limits set by
endpoints, switches, power consumption, and market demand. 
By all means, deploy high bandwidth fiber, but do so because
fiber is cheaper to maintain, and single mode needs fewer
repeaters, not because it offers "infinite" bandwidth.  

This isn't theoretical.  I designed some of the first switch
fabric used for the internet, for a now-defunct company I 
helped found called I-Cube Design Systems.  We were earning
75% profit on sales, and growing at 47% per quarter, selling
to companies like Cisco.  Then the V.C.s decided we ought to
be in the endpoint business rather than the switch business. 
That killed the company, because everyone else was hearing
the same thing from their V.C.s .  We owned the switch fabric
market, and we lost it because we did not stay focused on it.

Whatever percentage rate the net grows at, the switch business
grows at a higher percentage.  However, hyperoptimistic growth
projections remain hyperoptimistic, and doubling an unrealistic
growth extrapolation is going to get you into even more trouble.
The market explodes and plateaus, explodes and plateaus, as the
global economy cycles and new applications appear.  Anyone
extrapolating an exponential growth curve through a pair of
explosion-era data points is a fool or a con-man.

The switch fabric problem is why I am fond of spatial switching.
Whether it is 2Dx2D steered narrow-beam radio in the 3D sky, or
2Dx2D spatially steered lasers and receivers (which we do NOT 
know how to do yet!) through an open plenum in an optically
transparent 3D box.  Photons can pass through each other without
colliding.  We can't run enough electronic switches to connect N
to N endpoints at very high speed without melting down.  At very
high speeds, the signals must be routed as electronically steered,
point-to-point, modulated electromagnetic waves in free space.

Keith

-- 
Keith Lofstrom          keithl at keithl.com         Voice (503)-520-1993
KLIC --- Keith Lofstrom Integrated Circuits --- "Your Ideas in Silicon"
Design Contracting in Bipolar and CMOS - Analog, Digital, and Scan ICs



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