The method establishes a number of permanent virtual circuits to be configured on a multiservice access device. At least one of the permanent virtual circuits is configured as an oversubscription (OS PVC). The OS PVC may be configured as a normal PVC with additional parameters. The additional parameters, such as a timer, allow the PVC to assume either an active state or an oversubscription state. It is put into the oversubscription state if the timer expires and there is no traffic during the timer interval. Once in the oversubscription state, the PVC can be activated upon the presence of traffic. The OS PVC may be configured by placing it into a service queue when it has cells to send. The service queue is processed in sequential order until it is empty.