Quality of service is assured for connections routed via a plurality of subregions of a packet-oriented network via connection paths having prescribed transmission system resources by a resource manager in the packet-oriented network which has access to associated information relating to address ranges of the subregions, routes from source subregions to destination subregions through other subregions, and prescribed transmission system resources between the subregions. When a connection is initialized, a requested scope of resources and source and destination addresses are signaled to the resource manager, and a route through the network is ascertained. Then, taking into account the requested scope of resources and the scope of resources between the subregions of the route, a check is carried out to determine whether the initialized connection is authorized. In addition, the transmission system resources may be reserved for the initialized connection in the subregions included in the ascertained route. The resource manager can be arranged centrally in the network in one of the subregions, and the connection controllers, e.g., the gatekeeper in H.323 networks, provided in the subregions involve the resource manager in the signaling that occurs when a connection is initialized.