How does the atomic arrangement look like in a compound that has partial/mixed site occupancies

I am working on modelling of a material that has partial/mixed site occupancies. For example consider the tetragonal (P4mm) compound $$\ce{(Ba_{0.67}Sr_{0.33})TiO3}$$. Following is the atomic arrangement (visualised in VESTA) when looked along the Z axis.

One of the ways to model such structures is to create a supercell. In this specific case a 3x1x1 supercell is sufficient. There could be many 3x1x1 supercell configurations, here is one of them with periodic boundary conditions.

So my question is, does the atom arrangement in the real compound $$\ce{(Ba_{0.67}Sr_{0.33})TiO3}$$ look something like this. If it does; after the structural relaxations the $$\ce{Ba}$$ and $$\ce{Sr}$$ atoms (or $$\ce{Ti}$$ atoms) relax at slightly different x/y-coordinates. How do we merge such structures back to a single unit cell as shown in the first figure?

Or could there be vacancies at the A-site keeping the ratio $$\ce{Ba:Sr}$$ = $$\ce{2:1}$$. Or is it too complex to describe theoretically?

I would greatly appreciate relevant references as well.

When you get an experimental structure file that has partial occupations, as in your first figure, this implies that the occupations of the site do not have a periodic order (they are randomly occupied with probabilities determined by the occupation fractions of each ion). Otherwise, the ordering would be reflected in the symmetry of the unit cell, requiring it to be larger. Compare to something like the double perovskite $$\textrm{PrBaCo}_{2}\textrm{O}_{6}$$. The unit cell parameters in the partial occupations case reflect an average of the volume of material measured during the experiment.