to all the control units of the elevator installation 10 in the method step 103 if the check in the method step 104 reveals that the portion of the traveling path required for serving the current destination call is free for the respective car 21 or 22 in the method step 106 the respective control unit 42 or 44 transmits via the direct data transmission line 50 to the other control unit of the cars 21 22 which can be made to travel along the common traveling path 16 17 a signal according to which the respectively required portion of the traveling path is provisionally assigned to the respective car 21 or 22 subsequently in the method step 107 it is checked by the control units 42 and 44 which of the two cars 21 and 22 has the better allocation assessment for this purpose the control units 42 and 44 transmit to one another the result of their allocation assessment via the data line 50 together with the provisional assignment of the portion of the traveling path and respectively compare the results the data transmission line 50 has for this purpose a data transmission rate which is higher than the data transmission rate of the data transmission system 73 as an alternative transmission via the normal data transmission system 73 may of course be chosen instead of the transmission via an additional data line 50 the control unit 42 or 44 that is associated with the car with the better allocation assessment then transmits in the method step 103 the result.