High-Order Steady-State Diffusion Approximations

• 成果类型: Article
• 署名作者: Braverman, Anton; Dai, J. G.; Fang, Xiao
• 署名单位: Northwestern University; Cornell University; Shenzhen Research Institute of Big Data; The Chinese University of Hong Kong, Shenzhen; Chinese University of Hong Kong
• 刊物名称: OPERATIONS RESEARCH
• ISSN/ISSBN: 0030-364X
• DOI: 10.1287/opre.2022.2362
• 发表日期: 2024
• 关键词: queuing-networks; queues; stationarity

摘要

We derive and analyze new diffusion approximations of stationary distributions of Markov chains that are based on second- and higher-order terms in the expansion of the Markov chain generator. Our approximations achieve a higher degree of accuracy compared with diffusion approximations widely used for the last 50 years while retaining a similar computational complexity. To support our approximations, we present a combination of theoretical and numerical results across three different models. Our approximations are derived recursively through Stein/Poisson equations, and the theoretical results are proved using Stein's method.