Diffusion-level universality of many-server systems with concurrent service

We present diffusion limits for a queuing system with n parallel servers with concurrent service capabilities. The diffusion limits are established in the many-server heavy-traffic regime where (1 - pn)n alpha -> /3 as n -> infinity, for alpha is an element of (0, infinity) \ {1/2} and pn a notion of normalized system load. This encompasses the so-called sub-Halfin-Whitt, super-Halfin-Whitt, non-degenerate slowdown, and super-slowdown regimes. The diffusion limits are universal in that they depend only on whether alpha < 1/2 or alpha > 1/2 and do not depend on specific values of alpha and /3 in both cases. (c) 2023 The Authors. Published by Elsevier B.V. This is an open access article under the CC BY license (http://creativecommons .org /licenses /by /4 .0/).