Asymptotic Product-Form Steady State for Generalized Jackson Networks in Multiscale Heavy Traffic

• 成果类型: Article
• 署名作者: Dai, J. G.; Glynn, Peter W.; Xu, Yaosheng
• 署名单位: Cornell University; Stanford University; University of Chicago
• 刊物名称: OPERATIONS RESEARCH
• ISSN/ISSBN: 0030-364X
• DOI: 10.1287/opre.2023.0184
• 发表日期: 2026
• 关键词: single-class queueing networks; product-form stationary distributions; reflected Brownian motions; Interchange of limits; heavy traffic approximation; performance analysis; multiclass queuing-networks; diffusion-approximation

摘要

We prove that under a multiscale heavy traffic condition, the stationary distribution of the scaled queue length vector process in any generalized Jackson network has a product-form limit. Each component in the product form follows an exponential distribution, corresponding to the Brownian approximation of a single station queue. The single station can be constructed precisely, and its parameters have a good intuitive interpretation.