The Join-the-Shortest-Queue System in the Halfin-Whitt Regime: Rates of Convergence to the Diffusion Limit

Abstract

We bound the rate at which the steady-state distribution of the join-the-shortest-queue (JSQ) system converges, in the Halfin-Whitt regime, to its diffusion limit. Our proof uses Stein’s method and, specifically, the recently proposed prelimit generator comparison approach. The JSQ system is nontrivial and high-dimensional and has a state-space col-lapse component; our analysis may serve as a helpful example to readers wishing to apply the approach to their own setting.