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Geometric Bounds: A Noniterative Analysis Technique for Closed Queueing Networks

Giuliano Casale, Richard Muntz, Giuseppe Serazzi

Journal Article
IEEE Transactions on Computers
Volume 57
Issue 6
May, 2008
IEEE Computer Society
ISSN 0018-9340
DOI 10.1109/TC.2008.37

We propose the Geometric Bounds (GB), a new family of fast and accurate non-iterative bounds on closed queueing network performance metrics that can be used in the on-line optimization of distributed applications. Compared to state-of-the-art techniques such as the Balanced Job Bounds (BJB), the GB achieve higher accuracy at similar computational costs, limiting the worst-case bounding error typically within 5%-13% when for the BJB it is usually in the range 15%-35%. Optimization problems that are solved with the GB bounds return solutions that are much closer to the global optimum than with existing bounds. We also show that the GB technique generalizes as an accurate approximation to closed fork-join networks commonly used in disk, parallel and database models, thus extending the applicability of the method beyond the optimization of basic product-form networks.

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