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arXiv 1101.4306cs.NImath.AP
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具有阶段型服务时间的随机负载均衡模型的矩阵解析解

A Matrix-Analytic Solution for Randomized Load Balancing Models with Phase-Type Service Times

Quan-Lin Li, John C. S. Lui, Yang Wang

摘要:

在本文中,我们提供了一个矩阵分析解决方案的随机负载均衡模型(也称为\emph{supermarket models})与阶段型(PH)的服务时间。将服务时间推广到相型分布使得超市模型的分析比文献中广泛讨论的指数服务时间的情况更加困难和具有挑战性。我们首先将超市模型描述为一个微分向量方程组,并给出微分向量方程组不动点的双指数解。然后,我们分析了超市模型的当前位置的指数收敛到其不动点。最后,我们提出的数值例子来说明我们的方法,并显示其有效性在分析的随机负载均衡计划与非指数服务需求。

英文摘要:

In this paper, we provide a matrix-analytic solution for randomized load balancing models (also known as \emph{supermarket models}) with phase-type (PH) service times. Generalizing the service times to the phase-type distribution makes the analysis of the supermarket models more difficult and challenging than that of the exponential service time case which has been extensively discussed in the literature. We first describe the supermarket model as a system of differential vector equations, and provide a doubly exponential solution to the fixed point of the system of differential vector equations. Then we analyze the exponential convergence of the current location of the supermarket model to its fixed point. Finally, we present numerical examples to illustrate our approach and show its effectiveness in analyzing the randomized load balancing schemes with non-exponential service requirements.

机构、总结、中文摘要均由AI分析而来,可能存在错误,请以论文正文为准。

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