There are three separate items in play here; the hardware limit, the User-level limit and the Role-level limit.
Your hardware limit will not change, if it can only handle 13 concurrent searches you will never be able to exceed this, regardless of what is applied to the user and role.
The User-level limit is the number of searches a single user with that role can run, If it is set to 8 any user with that role can run up to 8 searches before receiving limit warnings.
Now, there is also a Role-level limit. This is a shared limit between all users with that role. Lets say this is set to 10...
User A is running 5 concurrent searches, at the same time User B attempts to run 7 searches, both users have the permissions to do this, but User B will receive limit warnings because the total number of concurrent searches for the role has now exceeded 10, (5+7=12).
... View more