An approximation to steady-state of M/Ph/n+ M queue

：徐礼虎（澳门大学）
：2021-12-09 10:30
：腾讯会议ID：590100085（无密码）

报告人：徐礼虎（澳门大学）

时  间：12月9日上午10:30

地  点：腾讯会议ID：590100085（无密码）

内容摘要:

In this paper, we develop a stochastic algorithm based on Euler-Maruyama scheme to approximate the invariant measure of the limiting multidimensional diffusion of the queue. Specifically, we prove a non-asymptotic error bound between the invariant measures of the approximate model from the algorithm and the limiting diffusion of the queueing model. Our result also provides an approximation to the steady-state of the prelimit diffusion-scaled queueing processes in the Halfin-Whitt regime given the well established interchange of limits property. To establish the error bound, we employ the recently developed Stein's equation and Malliavian calculus for multi-dimensional diffusions. The main difficulty lies in the non--differentiability of the drift in the limiting diffusion, so that the standard approaches in Euler type of schemes for diffusions and Stein's method do not work. We first propose a mollified diffusion which has a sufficiently smooth drift to circumvent the nondifferentiability difficulty. We then provide some insights on the limiting diffusion and approximate diffusion from the algorithm by investigating some useful occupation times, as well as the associated Harnack inequalities, the support of the invariant measures and ergodicity properties. These results are used in analyzing the Stein's equation, which provide useful estimates to bound the differences between the corresponding invariant measures. This talk is based on https://arxiv.org/abs/2109.03623.

个人简介：

徐礼虎教授，2001年本科毕业于山东大学; 2004年研究生毕业于北京大学， 2008年博士研究生毕业于帝国理工大学(Imperial College London, UK),现为澳门大学教授，主要从事随机偏微分方程和概率极限理论方面的研究。徐礼虎教授在Proab. Theory Related Fields, Ann. Statist.，Ann. Appl. Probab., J.Funct. Anal.等期刊上发表40余篇论文。

 

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