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

made clear they were talking about histotic growth) has been far

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.