Global Attraction of ODE-based Mean Field Models with Hyperexponential Job Sizes
Global Attraction of ODE-based Mean Field Models with Hyperexponential Job Sizes
复制标题
具有超指数工作规模的基于 ODE 的平均场模型的全球吸引力
DOI：
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发表时间：
2018
期刊：
影响因子：
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通讯作者：
B. V. Houdt
中科院分区：
文献类型：
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作者：
B. V. Houdt
平均场模型是评估大规模计算机系统性能的一种常用方法。许多平均场模型的演化都是由一组具有唯一不动点的常微分方程来表征的。为了证明这个唯一不动点对应于有限系统的平稳测度的极限，这个唯一不动点必须是一个全局吸引子。虽然全球吸引力的情况下，指数的工作规模建立了各种系统，这往往是不清楚这些证明技术是否可以推广到非指数的工作规模。在本文中，我们将展示如何简单的单调性参数可以用来证明一个广泛的一类常微分方程，捕捉超指数工作规模的平均场模型的演变的全球吸引力。这个类包括现有的以及以前未研究的负载平衡计划，并可用于有限或无限缓冲区的系统。该方法的主要新奇存在于使用Coxian表示的超指数的工作大小和偏序，这是强于在指数的情况下使用的组件的偏序。
Mean field modeling is a popular approach to assess the performance of large scale computer systems. The evolution of many mean field models is characterized by a set of ordinary differential equations that have a unique fixed point. In order to prove that this unique fixed point corresponds to the limit of the stationary measures of the finite systems, the unique fixed point must be a global attractor. While global attraction was established for various systems in case of exponential job sizes, it is often unclear whether these proof techniques can be generalized to non-exponential job sizes. In this paper we show how simple monotonicity arguments can be used to prove global attraction for a broad class of ordinary differential equations that capture the evolution of mean field models with hyperexponential job sizes. This class includes both existing as well as previously unstudied load balancing schemes and can be used for systems with either finite or infinite buffers. The main novelty of the approach exists in using a Coxian representation for the hyperexponential job sizes and a partial order that is stronger than the componentwise partial order used in the exponential case.