Assign Random Values in a Range

Start with queue names and % in A2:A5, so A2: q1, B2: 20%, etc. People's identifiers (names or IDs) in A11:A30.

C1: =COUNTA(A11:A30)
D1: =SUM(D2:D5)
F1: =C1-SUMPRODUCT(INT(C1*B2:B5))

C2: 0
D2: =INT(C$1*B2)+F2
E3: =MOD(C$1*B2,1)
F2: =(MATCH(MAX(E$2:E$5),$E$2:$E$5,0)=ROWS(F$2:F2))*F$1

Select D2:F2 and fill down into D3:D5.

C3: =C2+D2

Fill C3 down into C4:C5. This completes the setup for queues.

Select E11:E30. Type the formula =RAND(), hold down [Ctrl] and press [Enter]. This should fill that range with distinct random values.

B11: =LOOKUP(COUNTIF(E$11:E$30,">"&E11),C$2:C$5,A$2:A$5)

Fill B11 down into B12:B30. This gives random queue assignments in B11:B30 to each of the people in A11:A30.

FWIW, when and if you get the latest Excel with spilled formulas and dynamic arrays, you could use the following alternative formula for B11:B30 and dispense entirely with the E11:E30 formulas.

B11: =LOOKUP(SORTBY(SEQUENCE(C1,1,0),RANDARRAY(C1,1),1),C$2:C$5,A$2:A$4)