A New Method For Computing The Normalization Constant Of Multiple-Chain Queueing Networks

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Abstract
In a recent paper a new recursive expression was obtained for the normalization constant of product-form multiple chain closed queueing networks. This expression formed the basis of a new general purpose algorithm (named RECAL) for computing the mean performance measures. This paper is concerned with the computational aspects of obtaining the normalization constant using the new recursive expression. We present a computationally efficient formulation of the recursion and evaluate the computational complexity. This new algorithm, for computing the normalization constant, is substantially more efficient than the convolution algorithm when there are many routing chains in the network. The new algorithm therefore extends the range of queueing networks for which the normalization constant can be computed efficiently by exact means.