Steady‐state analysis of load balancing with Coxian‐2 distributed service times

Abstract

AbstractThis 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(Nα 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.