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[Openstack] [Swift] Erasure code durability and overhead in small clusters

On 14/03/18 13:33, Mark Kirkwood wrote:
> Doing a bit more playing about leads me to think that for a *single 
> region* EC policy we can get a tighter lower bound on the number of 
> hosts: I'm calculating it as (k+m)/m.

I probably should have shared the reasoning rather than just plumping 
the formula out! So here it is:

Suppose we have n hosts. The k + m fragments get spread about these n 
hosts,. On average, therefore (k + m)/n will be on any one of them. We 
want to ensure that this number is <= m (so one losing 1 host does not 
take out too many fragments). i.e:

(k + m)/n <= m

Doing schoolboy algebra on this gets:

(k + m)/m <= n

Which is the stated conjecture for the minimum number of hosts.