报告题目：An approximation to steady state of M/Ph/M+n queue

报告人： 徐礼虎 副教授  (澳门大学)

报告时间： 2022年5月5日（星期四）15:00-16:00

报告地点： 腾讯会议（ID：582-863-420）

校内联系人：鲁大伟 教授             联系电话：84708351-8040

报告摘要:

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 M/Ph/n+M 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.

报告人简介：

徐礼虎，澳门大学副教授，博士生导师。2001年毕业于山东大学，获学士学位；2004年毕业于北京大学，获硕士学位；2008年毕业于英国帝国理工学院，获博士学位。主要研究方向：随机分析、极限理论。在国内外学术刊物Annals of Statistics, Probability Theory and Related Fields, Bernoulli等上发表学术论文多篇。