A Unified Framework for the Bottleneck Analysis of Multiclass Queueing

We introduce a new framework supporting the bottleneck analysis of closed, multiclass BCMP queueing networks in the limiting regime where the number of jobs proportionally grows to infinity while keeping fixed other input parameters. First, we provide a weak convergence result for the limiting behavior of closed queueing networks, which is exploited to derive a sufficient and necessary condition establishing the existence of a single bottleneck. Then, we derive the new framework proposing efficient algorithms for the identification of queueing networks bottlenecks by means of linear programming. Our analysis reduces the computational requirements of existing techniques and, under general assumptions, it is able to handle load-dependent stations. We also establish a primal-dual relationship between our approach and a recent technique. This connection lets us extend the dual to deal with load-dependent stations, which is non-intuitive, and provides a unified framework for the enumeration of bottlenecks. Theoretical and practical insights on the asymptotic behavior of multiclass networks are shown as application of the proposed framework