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 collapse component; our analysis may serve as a helpful example to readers wishing to apply the approach to their own setting.

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