An Approximation to The Invariant Measure of The Limiting Diffusion of G/PH/N+GI queues in The Halfin-Whitt Regime and Related Asymptotics

作     者：Jin, Xinghu Pang, Guodong Xu, Lihu Xu, Xin 

作者机构：Department of Computational Applied Mathematics and Operations Research George R. Brown College of Engineering Rice University HoustonTX77005 United States Department of Mathematics Faculty of Science and Technology University of Macau Av. Padre Tomás Pereira Taipa China UM Zhuhai Research Institute Zhuhai China 

出 版 物：《arXiv》 (arXiv)

年 卷 期：2022年

核心收录：

主　　题：Diffusion 

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/P h/n + GI queues in the Halfin-Whitt regime. Specifically, we prove a non-asymptotic 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 multi-dimensional diffusions, in which the regularity of Stein’s equation developed by Gurvich (2014, 2022) 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/P h/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. Copyright © 2022, The Authors. All rights reserved.