Abstract: In computers (Processor Unit 1, . . . , Processor Unit N) that handle the operation of an ATM switch, applications may communicate with each other by transmitting internal traffic cells to each other, which are transported among other subscriber traffic. By assigning service categories to the applications, which correspond as well as possible to their quality needs, it is possible to optimize the quality of the connection services of internal connections. By setting the traffic parameters of internal traffic individually changeable, internal traffic and subscriber traffic can be integrated in the best possible way. In the preferred embodiment, the service category can be selected connection-specifically. In such a case, each application selects the best possible service category. In the second embodiment, the connection-specific category is selected to be the same for all the applications. In such a case, all the applications use the same predetermined service category.