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Accelerating Performance Inference over Closed Systems by Asymptotic Methods

Published:13 June 2017Publication History
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Abstract

Recent years have seen a rapid growth of interest in exploiting monitoring data collected from enterprise applications for automated management and performance analysis. In spite of this trend, even simple performance inference problems involving queueing theoretic formulas often incur computational bottlenecks, for example upon computing likelihoods in models of batch systems. Motivated by this issue, we revisit the solution of multiclass closed queueing networks, which are popular models used to describe batch and distributed applications with parallelism constraints. We first prove that the normalizing constant of the equilibrium state probabilities of a closed model can be reformulated exactly as a multidimensional integral over the unit simplex. This gives as a by-product novel explicit expressions for the multiclass normalizing constant. We then derive a method based on cubature rules to efficiently evaluate the proposed integral form in small and medium-sized models. For large models, we propose novel asymptotic expansions and Monte Carlo sampling methods to efficiently and accurately approximate normalizing constants and likelihoods. We illustrate the resulting accuracy gains in problems involving optimization-based inference.

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      cover image Proceedings of the ACM on Measurement and Analysis of Computing Systems
      Proceedings of the ACM on Measurement and Analysis of Computing Systems  Volume 1, Issue 1
      June 2017
      712 pages
      EISSN:2476-1249
      DOI:10.1145/3107080
      Issue’s Table of Contents

      Copyright © 2017 ACM

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      Association for Computing Machinery

      New York, NY, United States

      Publication History

      • Published: 13 June 2017
      Published in pomacs Volume 1, Issue 1

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