Horner’s rule for the evaluation of general closed queueing networks

The solution of separable closed queueing networks requires the evaluation of homogeneous multinomial expressions. The number of terms in those expressions grows combinatorially with the size of the network such that a direct summation may become impractical. An algorithm is given which does not show a combinatorial operation count. The algorithm is based on a generalization of Horner's rule for polynomials. It is also shown how mean queue size and throughput can be obtained at negligible extra cost once the normalization constant is evaluated.

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