# RE: What is the limit? (was RE: multi-homing fixes)

From: Alex Bligh [mailto:alex@alex.org.uk]
Sent: Wednesday, August 29, 2001 11:20 AM

> To boost this point, exponential growth, approaching
infinity, becomes
> asymptotic.

The only asymptote of an exponential curve is it's asymptote towards
the X axis, for as X approaches negative infinity.

The point remains that it is nonsensical, given a finite universe. The curve
doesn't fit observable reality.

>> > To boost this point, exponential growth, approaching
>> infinity, becomes
>> > asymptotic.
>>
>> The only asymptote of an exponential curve is it's asymptote towards
>> the X axis, for as X approaches negative infinity.

The point remains that it is nonsensical, given a finite universe. The curve
doesn't fit observable reality.

This is math. Observable reality is irrelevant.

Alex

This reminds me of a great joke I heard from civil engineer roommate
of mine:

Engineers think that the equations are an approximation of reality.
Physicists think that reality is an approximation of the equations.
Mathematicians never make the connection.

--Jeff

...in that it is assumed (for instance) that network nodes will not
grow exponentially for ever. And recent prefix growth (the poster
less than exponential. See the slides at IETF/Ptomaine for example.

However, if you accept the analysis in that very same presentation,
you will believe that the a big chunk of growth comes in
'Traffic Engineered' /24s (interesting use of the term TE
here which includes some leaks and cluelessness, but I guess
that's just traffic misengineering, and we'll put that aside),
and another chunk comes from 'small' multihoming, especially
announcing more specifics. In general, these prefixes can be
dropped, without loss of reachability. And they cost to support.
So we are back to the 'who pays', and 'is this an appropriate
technology' questions.

Oh yes, there has two other conflations:

One is that for 'the internet' to support P prefixes in a
'full table' (terms in quotes lack good definition), the cost is
O(P), for an ISP with a fixed number of customers. In a single
ISIS autonomous system, this might be true. I suspect
even in terms of a single router, in practical terms
it's at least O(P log P), if not worse.

The second is that the expensive part of a router is the
main CPU running the routing process, and its RAM. This
is not true (I'm sure you could run Zebra on a palm pilot
and take a full table over IR these days). The expensive
part is the forwarding hardware, and the glue that gets
the forwarding decisions out the main processor onto
the line cards. [I'm sure router gurus will add
detail/corrections to this simplification]. This has to grow not
only with number of prefixes, but also with amount of
traffic (forwarding decisions per second). So comparing just
one of the growth items to Moore's law does not tell the full picture.
I believe most traffic forecasts still show growth ahead of Moore's
law. Therefore even linear prefix growth is going to increase
further an already increasing hardware bill.