Bottlenecks identification in multiclass queueing networks using convex polytopes

Abstract

It is known that the resources that limit the overall performance of a system are the congested ones, referred to as bottlenecks. From knowledge of bottleneck stations, it is possible, with limited computational effort, to derive asymptotic values of several performance indices. While identifying the bottleneck stations is a well-established practice under a single-class workload, no simple methodology for multiclass models exists. 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 convex polytopes, can provide insights on the performance of a queueing network. The application of our techniques to the asymptotic analysis of closed product-form networks is also investigated.