论文标题
与考克斯的负载平衡的稳态分析 - $ 2 $分布式服务时间
Steady-State Analysis of Load Balancing with Coxian-$2$ Distributed Service Times
论文作者
论文摘要
本文研究了多服务器（$ n $服务器）系统的负载平衡。每个服务器都有一个尺寸$ b-1的缓冲区，$，并且最多可以在服务中拥有一项工作，而缓冲区的$ b-1 $作业。工作的服务时间遵循Coxian-2分布。我们专注于在严重的交通状态下负载平衡策略的稳态性能，以便系统的归一化负载为$λ= 1-n^{ - α} $，价格为$ 0 <α<0.5。$我们确定了一组实现渐近零等待的策略。一组政策包括几种古典政策，例如Join-the-theSt-Stere（JSQ），Join-the-Idle-Quesue（JIQ），Idle-One-First（I1F）和$ D $ -CHOICES（PO $ D $），带有$ d = O（n^α\ log n）$。主要结果的证明是基于Stein的方法和状态空间崩溃。本文的关键技术贡献是迭代状态太空崩溃方法，该方法在应用Stein方法时会导致简单的发生器近似。
This paper studies load balancing for many-server ($N$ servers) systems. Each server has a buffer of size $b-1,$ and can have at most one job in service and $b-1$ jobs in the buffer. The service time of a job follows the Coxian-2 distribution. We focus on steady-state performance of load balancing policies in the heavy traffic regime such that the normalized load of system is $λ= 1 - N^{-α}$ for $0<α<0.5.$ We identify a set of policies that achieve asymptotic zero waiting. The set of policies include several classical policies such as join-the-shortest-queue (JSQ), join-the-idle-queue (JIQ), idle-one-first (I1F) and power-of-$d$-choices (Po$d$) with $d=O(N^α\log N)$. The proof of the main result is based on Stein's method and state space collapse. A key technical contribution of this paper is the iterative state space collapse approach that leads to a simple generator approximation when applying Stein's method.
