Transform Methods for Heavy-Traffic Analysis

Transform Methods for Heavy-Traffic Analysis
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高流量分析的转换方法

DOI:
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发表时间:
2019
期刊:
影响因子:
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通讯作者:
H. Milton
H. Milton
中科院分区:
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文献类型:
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作者:
Daniela Hurtado;S. T. Maguluri;H. Milton

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漂移法是近年来发展起来的一种研究稳态振荡系统的方法。它被成功地用于获得缩放队列长度的矩的界,这些矩在重传输中是渐近紧的,在各种各样的系统中,包括广义交换机[11],输入排队交换机[42,41],带宽共享网络[62]等。本文中,我们开发了使用变换技术进行重传输分析,特别关注矩生成函数的使用。该方法简化了漂移法的证明,为漂移法的研究提供了新的视角。本文给出了一个一般框架,然后利用MGF方法得到了满足完全资源池条件的重业务排队系统中队长的平稳分布。特别是,我们研究负载平衡系统和一般设置下的广义开关。
The drift method was recently developed to study queueing systems in steady-state. It was successfully used to obtain bounds on the moments of the scaled queue lengths, that are asymptotically tight in heavy-traffic, in a wide variety of systems including generalized switches [11], input-queued switches [42, 41], bandwidth sharing networks [62], etc. In this paper we develop the use of transform techniques for heavy-traffic analysis, with a special focus on the use of moment generating functions. This approach simplifies the proofs of the drift method, and provides a new perspective on the drift method. We present a general framework and then use the MGF method to obtain the stationary distribution of queue lengths in heavy-traffic in queueing systems that satisfy the Complete Resource Pooling condition. In particular, we study load balancing systems and generalized switches under general settings.
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