An Approximation to the Invariant Measure of the Limiting Diffusion of G/Ph/n plus GI Queues in the Halfin-Whitt Regime and Related Asymptotics

• 成果类型: Article
• 署名作者: Jin, Xinghu; Pang, Guodong; Xu, Lihu; Xu, Xin
• 署名单位: Hefei University of Technology; University of Macau; Rice University; South China Normal University
• 刊物名称: MATHEMATICS OF OPERATIONS RESEARCH
• ISSN/ISSBN: 0364-765X
• DOI: 10.1287/moor.2021.0241
• 发表日期: 2025
• 关键词: multivariate normal approximation; steady-state approximations; levy-driven sde; steins method; recursive computation; subgeometric rates; CONVERGENCE; ergodicity; stationarity; THEOREMS

摘要

In this paper, we develop a stochastic algorithm based on the Euler-Maruyama scheme to approximate the invariant measure of the limiting multidimensional diffusion of G/Ph/n + GI queues in the Halfin-Whitt regime. Specifically, we prove a nonasymptotic error bound between the invariant measures of the approximate model from the algorithm and the limiting diffusion. To establish the error bound, we employ the recently developed Stein's method for multidimensional diffusions, in which the regularity of Stein's equation obtained by the partial differential equation (PDE) theory plays a crucial role. We further prove the central limit theorem (CLT) and the moderate deviation principle (MDP) for the occupation measures of the limiting diffusion of G/Ph/n + GI queues and its Euler-Maruyama scheme. In particular, the variances in the CLT and MDP associated with the limiting diffusion are determined by Stein's equation and Malliavin calculus, in which properties of a mollified diffusion and an associated weighted occupation time play a crucial role.