The art of computer programming, volume 2 (3rd ed.): seminumerical algorithms
The art of computer programming, volume 2 (3rd ed.): seminumerical algorithms
Open, Closed, and Mixed Networks of Queues with Different Classes of Customers
Journal of the ACM (JACM)
Computational algorithms for closed queueing networks with exponential servers
Communications of the ACM
Mean-Value Analysis of Closed Multichain Queuing Networks
Journal of the ACM (JACM)
On the convolution algorithm for separable queuing networks
SIGMETRICS '76 Proceedings of the 1976 ACM SIGMETRICS conference on Computer performance modeling measurement and evaluation
A critical overview of computer performance evaluation
ICSE '76 Proceedings of the 2nd international conference on Software engineering
Approximate techniques for modeling the performance of complex systems
Computer Languages
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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.