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.

中文翻译：

---

Coxian-2分布式服务时间负载均衡的稳态分析

本文研究了多服务器（N台服务器）系统的负载平衡。每个服务器都有一个大小为b  - 1的缓冲区，并且缓冲区中最多可以有一个服务和b  - 1 个作业。作业的服务时间服从 Coxian-2 分布。我们专注于负载均衡策略在大流量情况下的稳态性能，使得系统的归一化负载为λ  = 1 −  N ^{− α}，0 <  α  < 0.5。我们确定了一组实现渐近零等待的策略。这组策略包括几个经典策略，例如加入最短队列 (JSQ)、加入空闲队列 (JIQ)、空闲一个优先 (I1F) 和 power-of- d-choices（宝 d）与d  =  Ö（Ñ ^α 登录 Ñ）。主要结果的证明基于 Stein 的方法和状态空间崩溃。本文的一个关键技术贡献是迭代状态空间崩溃方法，该方法在应用 Stein 方法时会产生简单的生成器近似。