Abstract: In an ATM switching network, a limitation of traffic in an ATM switching apparatus is relaxed. In an ATM switching network capable of allocating a plurality of communication channels to a terminal unit of one subscriber, when the terminal of this subscriber requests setting of the plural communication channels, a traffic amount of the communication channels proposed to the ATM switching apparatus is declared as a total amount of the respective communication channels. The ATM switching apparatus measures a total traffic amount of the plural communication channels set in response to the request made by the terminal unit, and limits the traffic of the plural set communication channels in such a manner that the measured traffic amount becomes lower than, or equal to the traffic amount declared through the terminal unit.