论文标题
与g/pH/n+gi队列在半温泰特（Halfin-Whitt）态度和相关渐近性的限制扩散的限制度量的近似值
An approximation to the invariant measure of the limiting diffusion of G/Ph/n+GI queues in the Halfin-Whitt regime and related asymptotics
论文作者
论文摘要
在本文中，我们基于欧拉山（Maruyama）方案开发了一种随机算法，以近似限制的限制性量度的限制性多维扩散，以$ g/pH/n+gi $排队在Halfin-Whitt制度中。具体而言，我们证明了算法的近似模型的不变度度量与限制扩散之间的非质子误差。为了建立界限，我们采用了最近开发的Stein方法来进行多维扩散，其中Gurvich（2014，2022）开发的Stein方程的规律性起着至关重要的作用。 我们进一步证明了中央限制定理（CLT）和中等偏差原理（MDP），用于$ g/pH/n+gi $ queues及其Euler-Maruyama方案的限制扩散量。特别是，与限制扩散相关的CLT和MDP中的方差由Stein的方程和Malliavin conculus确定，在该方程式中，在该方程式中，散布扩散的特性和相关的加权职业时间起着至关重要的作用。
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 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 $G/Ph/n+GI$ 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.
