Asymptotic analysis of multiclass closed queueing networks: Multiple bottlenecks

Asymptotic expressions for the values of throughputs, utilizations, mean queue lengths, and mean cycle times are derived for multiclass product-form queueing networks with load independent servers, where different (sets of) stations may behave as bottlenecks when different population mixes load the network. The space of possible population mixes is shown to be partitioned into sectors within which several stations may saturate together. Analytic expressions for the computation of the edges of these sectors are provided. A synthesis of a large set of experiments is presented to numerically support a conjecture that is used to perform the asymptotic analysis of this class of networks.