Providing quality of service (QoS) in large-scale networks like the Internet inherently needs to deal with heterogeneous network QoS systems. Therefore, the interworking between different network QoS systems is of high importance. In this paper, the interworking with respect to a basic characteristic of network QoS systems, the time scale of the system, is under investigation. The time scale of a network QoS system is its speed of reaction to individual requests for differentiated treatment of units of service. A slow time scale system will prefer requests to arrive with a low frequency and persist unaltered for a substantial period of time while a fast one is able to support much higher arrival rates of requests and is thus more amenable for short-lived units of service. Obviously, when overlaying a slow time scale QoS system over a faster one, there is no problem. However, and that is a more likely case, for the overlay of a fast time scale system on a slow one, there is a mismatch ...