A generalisation of Norton's theorem for multiclass queueing networks

Consider an arbitrary subset σ of service centres in a locally balanced multiclass queueing network for which a parametric analysis is to be undertaken. It is shown that the complete network only has to be solved once using the convolution algorithm, after which statistical measures for σ can be calculated repeatedly without re-evaluating the rest of the network. It has also been proved that the concept of replacing a subnetwork in a closed multiclass queueng network with a single composite service centre with a state dependent service rate (also called Norton's Theorem for queuing networks) is a very special case of the more general result mentioned above. An example is given in which the theoretical results are applied when σ is a subnetwork of a closed multiclass queueing network satisfying local balance.