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

Abstract

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−ρn)nα→β as n→∞, for α∈(0,∞)∖{1/2} and ρn 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 α<1/2 or α>1/2 and do not depend on specific values of α and β in both cases.