Steady‐state analysis of load balancing with Coxian‐2 distributed service times
研究了多服务器系统中服务时间服从Coxian-2分布时的负载均衡策略，发现JSQ、JIQ等策略在重流量下可实现渐近零等待，证明基于Stein方法和状态空间塌缩。
Abstract 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.