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

From: Leo Bicknell [mailto:bicknell@ufp.org]
Sent: Wednesday, August 29, 2001 8:35 AM

> The global routing table size HAS grown exponentially
> in the past. Rationalize it any way you want, blame whatever
> you like, but there is no known way to construct a router that
> can handle that kind of growth in anything but a short term,
> and the trend for the components in the router growth curve
> is simply not going to increase to a long term superlinear rate.

Ah, but exponential growth can't happen forever, and we can build
a system to handle the largest possible Internet (with v4, anyway).

Not to minimze the short term issue, but to hand wave and say
"it's exponential and we'll never get ahead of it" is crap. It
won't be forever, so let's get ahead of it.

To boost this point, exponential growth, approaching infinity, becomes
asymptotic. There is no way that is going to happen and there is no way we
can do anything about it if it does. For one thing, there is a finite number
of people on the planet. There is also a finite number of nodes we can build
in a year. Both factors create upper bounds for the problem under
discussion. What *can* happen is a classic "S" curve that has a rather steep
cliff at the front of it. But, that is like the six blind dudes and the
elephant. The cliff isn't the whole curve. Sooner or later, you run out of
atmosphere and you can't climb anymore.

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

Alex Bligh

It doesn't.

Sorry for nitpicking. Asympotic is 1/(x-a) when x -> a. e^x is never
asymptotic.