This paper presents preliminary work on an abstract QoS model for analysing the observable performance characteristics of heterogeneous high-speed networks. We study the performance trade-offs resulting from protocol interactions between ATM and non-ATM networks. Generalised Stochastic Petri Nets (GSPNs) are used to model the network. We show how GSPNs can be used to study performance-related factors such as end-to-end delay, resource contention and synchronisation. This model represents initial work on the development of a reasoning tool which will allow us to understand and make decisions regarding the mappings of an ATM stream-based delivery into that of a shared media high-speed LAN/MAN.