A switching node (3) for providing admission control in a network comprises a number of separate priority queues (6) for receiving packets having different priority levels. Priority levels (1) to n provide guaranteed delay services, priority levels n+1 to m provide guaranteed loss services, and priority level Pm+1 provides best effort service. Measuring means 51 to 5m continually measure the average bit rate entering each priority level buffer P1 to Pm, except the lowest Pm+1. When a request arrives with a kth priority level, the network capacities for priority levels l=k..Pm are calculated. For all choices of l, the measurements of traffic loads of levels l and higher are taken into account. These capacity requirements are necessary to guarantee the quality of service for all flows already admitted to the lower priority queues. These capacities are compared to the network capacity, and if there is sufficient capacity, the request is accepted. Otherwise, the request is rejected.