An efficient algorithm for the exact analysis of multiclass queueing networks with large population sizes

We introduce an efficient algorithm for the exact analysis of closed multiclass product-form queueing network models with large population sizes. We adopt a novel approach, based on linear systems of equations, which significantly reduces the cost of computing normalizing constants. With the proposed algorithm, the analysis of a model with N circulating jobs of multiple classes requires essentially the solution of N linear systems with order independent of population sizes.A distinguishing feature of our approach is that we can immediately apply theorems, solution techniques, and decompositions for linear systems to queueing network analysis. Following this idea, we propose a block triangular form of the linear system that further reduces the requirements, in terms of both time and storage, of an exact analysis. An example illustrates the efficiency of the resulting algorithm in presence of large populations.

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