Many-Server Asymptotics for Join-the-Shortest-Queue in the Super-Halfin-Whitt Scaling Window

• 成果类型: Article; Early Access
• 署名作者: Zhao, Zhisheng; Banerjee, Sayan; Mukherjee, Debankur
• 署名单位: University System of Georgia; Georgia Institute of Technology; University of North Carolina; University of North Carolina Chapel Hill; University of North Carolina School of Medicine
• 刊物名称: MATHEMATICS OF OPERATIONS RESEARCH
• ISSN/ISSBN: 0364-765X
• DOI: 10.1287/moor.2021.0133
• 发表日期: 2025
• 关键词: diffusion limit; regime; proofs

摘要

Join-the-shortest queue (JSQ) is a classical benchmark for the performance of parallel-server queueing systems because of its strong optimality properties. Recently, there has been significant progress in understanding its large-system asymptotic behavior. In this paper, we analyze the JSQ policy in the super-Halfin-Whitt scaling window when load per server scales with the system size N as lim(->infinity) (1 - ) = for is an element of (1/2, 1) and > 0. We establish that the centered and scaled total queue length process converges to a certain Bessel process with negative drift, and the associated (centered and scaled) steady-state total queue length, indexed by N, converges to a gamma(2, ) distribution. The limit laws are universal in the sense that they do not depend on the value of and exhibit fundamentally different behavior from both the Halfin-Whitt regime ( = 1/2) and the nondegenerate slowdown (NDS) regime ( = 1).