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

Abstract

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.Being the first application of the prelimit approach to a non-trivial and high-dimensional model, this paper may be helpful to readers wishing to apply the approach to their own setting. For example, the approach has the potential to be applied to other heavy-traffic regimes or load-balancing policies.

Large-System Insensitivity of Zero-Waiting Load Balancing Algorithms

“…Significant processes have been made over the past few years on understanding achieving asymptotic zero-waiting (as the system size approaches infinity) in a large-scale data center with distributed queues, including the classic supermarket model [14,8,32,17,3,4,30,24,25,23,22,45,9], models with data locality [40,31] and models where each job consists of parallel tasks [39,37,19], etc.…”

“…However, almost all these results assume exponential service time distributions. While each of these results [14,8,32,17,29,30,24,25,23,22,40,31,39,37,19,45,9] provided important insights of achieving zero-waiting in a practical system, theoretically, it is not clear whether these principles hold for general service times. This is a very important question to answer because it is well-known that service time distributions in real-world systems are not exponential.…”