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We show that the steady-state distribution of the join-the-shortest-queue(JSQ) system converges, in the Halfin-Whitt regime, to its diffusion limit at arate of at least $1/\sqrt{n}$, where $n$ is the number of servers. Our proofuses Stein's method and, specifically, the recently proposed prelimit generatorcomparison approach. The JSQ system is non-trivial, high-dimensional, and has astate-space collapse component, and our analysis may serve as a helpful exampleto readers wishing to apply the approach to their own setting.

The join-the-shortest-queue system in the Halfin-Whitt regime: rates of convergence to the diffusion limit