AI 中文总结
该研究针对封闭系统性能推断的计算瓶颈，通过将多类封闭排队网络的归一化常数转化为单位单纯形上的多维积分，结合求积规则、渐近展开及蒙特卡洛方法实现高效近似，提升了推断精度。
AI 中文摘要
近年来，人们对从企业应用收集的监控数据进行自动化管理和性能分析的兴趣迅速增长。尽管有这一趋势，即使是涉及排队论公式的简单性能推断问题也常常带来计算瓶颈，例如在计算批量系统模型中的似然时。受此问题驱动，我们重新研究了多类封闭排队网络的求解，这类网络是用于描述具有并行性约束的批量和分布式应用的流行模型。我们首先证明，封闭模型平衡状态概率的归一化常数可以精确地重新表述为单位单纯形上的多维积分，这作为副产品给出了多类归一化常数的新颖显式表达式。然后，我们提出一种基于求积规则的方法，用于在中小规模模型中高效评估所提出的积分形式。对于大规模模型，我们提出新颖的渐近展开和蒙特卡洛采样方法，以高效且准确地近似归一化常数和似然。我们在基于优化的推断问题中说明了由此带来的精度提升。
英文摘要
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.
CommentsRevised proof of Theorem 4.1. Fixed typos in (22) and (35). Main results unchanged
Journal refProc. ACM Meas. Anal. Comput. Syst. 1, 1, Article 7 (June 2017)
DOI：10.1145/3084445
