[address-policy-wg] 2007-05 New Policy Proposal (IPv6 ULA-Central)

On Fri, May 04, 2007 at 08:00:06PM +0800, Geoff Huston wrote:
> On 5/4/07, Gert Doering <gert at space.net> wrote:
> >
> >On Fri, May 04, 2007 at 11:54:22AM +0200, Shane Kerr wrote:
> >> The motivation for a version with a central registry however is
> >> not so obvious to me. The only justification I can think of is
> >> that you can be sure not to pick the same /48 as someone else has
> >> picked. But the chances of that are *billions* (that's "thousands
> >> of millions" to British folk) to one!
> >
> >Take the "birthday paradoxon" into account.  Chances for a clash
> >with "someone else in the room" are actually much higher than the
> >chance for a clash with "a *specific* number out of the ame pool".
> 
>   The general solution of the probability of a collision after d
>   draws from n possible values is given by:
> 
>      P = 1 - ((n!) / ((n**d)((n-d)!)))
> 
>   Given that the value for n is 2.199,023,255,552, then the
>   objective is to find the lowest value of d for which P is greater
>   than or equal to 0.5. In this case the value for d  is some 1.24
>   million.
> 
> http://draft-huston-ipv6-local-use-comments.potaroo.net

Since this address space is "local", the only time a collision matters
is when:

1. Two users have the same local space.
2. These users interoperate in some way.

The formula given only measures the first value.

To look at the degenerate case:

   If each local prefix is totally disconnected, then there is still
   no possibility for a collision that matters.

Another next case:

    For the case where each local prefix connects to a single other
    local prefix, then the if there are 1.24 million prefixes which
    result in a single collision, there is still only a 1 in 600000
    chance that this will affect any one of those 1.24 million
    prefixes at all.

I'm not feeling mathematical enough on this Friday afternoon to figure
out an exact formula for this (I'm not sure if you can use an average
value for the interconnectedness of the prefixes, for instance), but
intuitively I still claim this is not a problem.

--
Shane