Heavy Traffic Limits for Join-the-Shortest-Estimated-Queue Policy Using Delayed Information

• 成果类型: Article
• 署名作者: Atar, Rami; Lipshutz, David
• 署名单位: Technion Israel Institute of Technology
• 刊物名称: MATHEMATICS OF OPERATIONS RESEARCH
• ISSN/ISSBN: 0364-765X
• DOI: 10.1287/moor.2020.1056
• 发表日期: 2021
• 页码: 268-300
• 关键词: Differential equations; uniqueness; EXISTENCE

摘要

We consider a load-balancing problem for a network of parallel queues in which information on the state of the queues is subject to a delay. In this setting, adopting a routing policy that performs well when applied to the current state of the queues can perform quite poorly when applied to the delayed state of the queues. Viewing this as a problem of control under partial observations, we propose using an estimate of the current queue lengths as the input to the join-the-shortest-queue policy. For a general class of estimation schemes, under heavy traffic conditions, we prove convergence of the diffusion-scaled process to a solution of a so-called diffusion model, in which an important step toward this goal establishes that the estimated queue lengths undergo state-space collapse. In some cases, our diffusion model is given by a novel stochastic delay equation with reflection, in which the Skorokhod boundary term appears with delay. We illustrate our results with examples of natural estimation schemes, discuss their implementability, and compare their relative performance using simulations.