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

Anton Braverman

doi:10.1287/stsy.2022.0102

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

Anton Braverman^*

^*Corresponding author for this work

Managerial Economics, Decision Sciences and Operations

Research output: Contribution to journal › Article › peer-review

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.

Original language	English (US)
Pages (from-to)	1-39
Number of pages	39
Journal	Stochastic Systems
Volume	13
Issue number	1
DOIs	https://doi.org/10.1287/stsy.2022.0102
State	Published - Mar 2023

Keywords

Stein’s method
diffusion approximation
generator comparison
join the shortest queue
load balancing

ASJC Scopus subject areas

Statistics and Probability
Modeling and Simulation
Statistics, Probability and Uncertainty
Management Science and Operations Research

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title = "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{\textquoteright}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.",

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N2 - 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.

AB - 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.

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KW - load balancing

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

Abstract

Keywords

ASJC Scopus subject areas

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