ACM Communications in Computer Algebra, Vol. 42, No. 4, December 2008 Formally Reviewed Article An Application of Exact Linear Algebra to Capacity Planning Models Giuliano Casale College of William and Mary Department of Computer Science 140 McGlothlin-Street Hall 23187-8795 Williamsburg, Virginia email: casale@cs.wm.edu Introduction This note illustrates a novel application of exact linear algebra to performance evaluation and stochastic modeling. We focus on queueing network models, which are high-level abstractions of Markov chains used in capacity planning of computer and communication systems [6, 7]. Until recently, it was prohibitively expensive to compute exact solutions for these models when they describe hundreds or thousands of users interacting with a network of servers, a case of large practical application when sizing web architectures. Here, we overview a new approach, which we have recently proposed [3, 4], that overcomes this limitation by means of a linear matrix difference equation that strictly requires exact linear algebra to be evaluated. Exact linear algebra is required in our method because of uncontrollable numerical instabilities that arise if round-off errors are introduced in the recursive evaluation of the matrix difference equation. This dif culty is also exasperated by the âastronomicalâ growth of the number of
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An application of exact linear algebra to capacity planning models
Casale, Giuliano
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, Volume 42 (4)
Association for Computing Machinery – Feb 6, 2009
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