RECAL, a Recursion by Chain Algorithm for computing the mean performance measures of product-form multiple-chain closed queueing networks, is presented. It is based on a new recursive expression which relates the normalization constant of a network with r closed routing chains to those of a set of networks having (r-l) chains. It relies on the artifice of breaking down each chain into constituent sub-chains that each have a population of one. The time and space requirements of the algorithm are shown to be polynomial in the number of chains. When the network contains many routing chains the proposed algorithm is substantially more efficient than the convolution or mean value analysis algorithms. The algorithm therefore extends the range of queueing networks which can be analyzed efficiently by exact means. A numerical example is given.

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Three new decomposition methods are developed for the exact analysis of stochastic multi-facility blocking models of the product-form type. The first is a basic decomposition algorithm that reduces the analysis of blocking probabilities to that of two separate subsystems. The second is a generalized M-subsystem decomposition method. The third is a more elaborate and efficient incremental decomposition technique. All of the algorithms exploit the sparsity of locality that can be found in the demand matrix of a system. By reducing the analysis to that of a set of subsystems, the overall dimensionality of the problem is diminished and the computational requirements are reduced significantly. This enables the efficient computation of blocking probabilities in large systems. Several numerical examples are provided to illustrate the computational savings that can be realized.

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