1. A method of on-line admission control in an internet protocol network, where the needs of traffic flows belonging to different service types are either deterministic guarantees of delays or statistical guarantees of estimates of delays, where the packet-level differentiation is a fitting of the different service types to priority classes, with the packets of one priority class receiving absolute priority over the packets of lower priority classes, together with a partial isolation of packets of the different service types within any one priority class from each other, and where the network supports aggregate packet-level service differentiation and policing at the edge of the network of admitted traffic to make sure that it does not exceed its promised demand on network resources, the method comprising the step of coordinating the admission decisions for sessions with the needs of the sessions requesting admission, the needs of all sessions already in progress, and the packet-level behavior of handling the packets of different service types.