Bottlenecks Identification in Multiclass Queueing Networks using Convex Polytopes

It is known that the resources that limit the overall performance of the system are the congested ones, referred to as bottlenecks. From the knowledge of the bottleneck stations with a limited computational effort it is possible to derive asymptotic values of several performance indices. While identifying the bottleneck stations under a single-class workload is a well-established practice, no simple methodology for multiclass models exist. In this paper we present new algorithms for identifying the bottlenecks in multiclass queueing networks with constant-rate servers. We show how the application of assessed techniques, such as the ones related to the convex polytopes, can provide insights on the performance of a queueing network. The application of our techniques to the asymptotic analysis of closed productform networks is also investigated.