You note two objections to my comments regarding the random self-selection method as described in the local use address draft.
Firstly: "That is, the P above needs to take into account the probability that two networks trying to use the same prefix are connected."
I would contend that this is an incomplete analysis of the uniqueness requirement.
The requirement for uniqueness is triggered when any two networks using
such self-selected global IDs as local address prefixes want to interact in such
a fashion that the expose their local use addresses to each other, now or at any
time in the future. This statement covers a broader range of potential scenarios
and underpins the entire argument for uniqueness in any form of addressing
architecture.
Your second issue is "with the formula itself". The underlying reasoning behind the
formula:
P = 1 - ((n!) / ((n**d)(n-d)!))
is that the probability of a clash within a pool of numbers where the pool is of size
d and the number space is of size n is 1 minus the probability that all the selected
numbers are unique. This is a simple exercise in probabilities:
for a pool of size 2 the probability of uniqueness is (n-1)/n for a pool of size 3 the probability of uniqueness is ((n-1)/n) x ((n-2)/n) with the general solution as indicated above.
I would observe that this is a correct analysis of the probability of a collision occurring within a pool of d selections from a total space of n possible values.
You appear to be asking a different question, namely: "the probability that two sources independently pick the same value", and this is a question relating to degree of entropy in the random selection algorithm. The formula provided above assumes 'perfect' entropy, where the selection algorithm is equally likely to pack any of the n possible values. In this case the changes of a collision occurring with a pool of size 2 is 1/n. My comment is that the factors you need to be mindful of are not only the true randomness of the random number generator, but also the total size of the pool and the size of the number space.
regards,
Geoff
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