Many-Server Asymptotics for Join-the-Shortest-Queue in the Super-Halfin-Whitt Scaling Window
研究了超Halfin-Whitt缩放窗口下最短队列加入策略的渐近行为，发现中心化与缩放后的总队长过程收敛到带负漂移的贝塞尔过程，稳态分布收敛到χ²分布，且该极限定律具有普适性。
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 [Formula: see text] scales with the system size N as [Formula: see text] for [Formula: see text] and [Formula: see text]. 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 [Formula: see text] distribution. The limit laws are universal in the sense that they do not depend on the value of [Formula: see text] and exhibit fundamentally different behavior from both the Halfin–Whitt regime ([Formula: see text]) and the nondegenerate slowdown (NDS) regime ([Formula: see text]). Funding: This work was supported by the National Science Foundation to S. Banerjee [Grants CAREER DMS-2141621 and RTG DMS-2134107] and D. Mukherjee and Z. Zhao [Grants CIF-2113027 and CPS-2240982].