2022/02/06 by Anton Braverman, Braverman, Anton
Business, Management and Accounting · Mathematics · Decision Sciences · #Advanced Queuing Theory Analysis #Random Matrices and Applications #Probability and Risk Models
paper · pdf · doi:10.48550/arxiv.2202.02889
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 a rate of at least 1/√(n), where n is the number of servers. Our proof uses Stein's method and, specifically, the recently proposed prelimit generator comparison approach. The JSQ system is non-trivial, high-dimensional, and has a state-space collapse component, and our analysis may serve as a helpful example to readers wishing to apply the approach to their own setting.