Steady-State Analysis of the Join-the-Shortest-Queue Model in the Halfin-Whitt Regime
Steady-State Analysis of the Join-the-Shortest-Queue Model in the Halfin-Whitt Regime
复制标题
Halfin-Whitt 机制中加入最短队列模型的稳态分析
DOI：
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发表时间：
2018
影响因子：
1.7
通讯作者：
Anton Braverman
中科院分区：
文献类型：
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作者：
Anton Braverman
本文研究了Halfin-Whitt区域下最短队列连接模型的稳态性质。我们将重点关注跟踪空闲服务器数量和具有非空缓冲区的服务器数量的进程。最近，Eschenfeldt和Gamarnik证明了这个过程的缩放版本，在有限的时间间隔内，当服务器的数量趋于无穷大时，收敛到二维扩散极限。在本文中，我们证明了扩散极限是指数遍历的，并且证明了空闲服务器和非空缓冲区的稳态数目的扩散比例序列是紧的。结合Eschenfeldt和Gamarnik证明的过程级收敛性，我们的结果暗示了稳态分布的收敛性。所使用的方法是基于Stein方法的生成器展开框架，在Stolyar中也称为基于漂移的流体极限Lyapunov函数方法。该框架的一个技术贡献是展示了如何将其用作建立指数遍历性的通用工具。
This paper studies the steady-state properties of the join-the-shortest-queue model in the Halfin–Whitt regime. We focus on the process tracking the number of idle servers and the number of servers with nonempty buffers. Recently, Eschenfeldt and Gamarnik proved that a scaled version of this process converges, over finite time intervals, to a two-dimensional diffusion limit as the number of servers goes to infinity. In this paper, we prove that the diffusion limit is exponentially ergodic and that the diffusion scaled sequence of the steady-state number of idle servers and nonempty buffers is tight. Combined with the process-level convergence proved by Eschenfeldt and Gamarnik, our results imply convergence of steady-state distributions. The methodology used is the generator expansion framework based on Stein’s method, also referred to as the drift-based fluid limit Lyapunov function approach in Stolyar. One technical contribution to the framework is to show how it can be used as a general tool to establish exponential ergodicity.
超越大流量制度：单服务器队列的通用边界和控制
影响因子：
2.7
作者：
Huang, Junfei;Gurvich, Itai
通讯作者：
Gurvich, Itai