I recommend to use the object Sorter. It is a buffer which sorts the part according to a certain sort criterion.
In the attached model the Source generates the sequence of part: E1, E2, E3, E1, E2, E3, E1, E2, ...
The MUs are equipped with a custom attribute customAttr of type integer.
The values of the MU-attribute are 1 for E2, 2 for E1 and 3 for E3.
Check the Sorter: Deactivate the check box Open Line. Run the simulation, activate the check box Open Line and start the simulation again. The object Line is filled. The first four MUs have the name "E2".