报告时间：2026年9月28日（星期一）08:30-9:30

报告地点：科教楼B座1710会议室

报  告  人：徐礼虎 教授

工作单位：澳大大学

举办单位：数学学院

报告简介：

We study a sequence of Markovian many-server queues with customer abandonment and power-law batch arrivals. Batches arrive at Poisson times, and the probability of a batch of size \(\ell\) is proportional to \(\ell^{-(1+\alpha)}\), up to a cutoff of order \(n^\gamma\), where \(\alpha\in(0,2)\). Service and patience times are exponentially distributed. The asymptotic behavior differs sharply across three regimes. When \(\alpha\in(0,1)\), the mean batch size grows as \(n^{(1-\alpha)/\alpha}\), the number of servers is of order \(n^{1/\alpha}\), and the uncentered arrival noise converges to a truncated \(\alpha\)-stable subordinator. When \(\alpha=1\), the mean batch size is of order \(\log n\), the number of servers is of order \(n\log n\), and the centered arrival noise converges to a compensated Lévy process with jumps bounded by one. When \(\alpha\in(1,2)\), the mean batch size remains bounded and the number of servers is of order \(n\); the centered arrival noise converges to a truncated stable-type Lévy process when \(\gamma=1/\alpha\), and to an \(\alpha\)-stable Lévy process when \(\gamma>1/\alpha\). In all three regimes, the centered queue-length process, scaled by \(n^{1/\alpha}\), converges to a Lévy-driven stochastic differential equation with a piecewise linear drift determined by service and abandonment. We further prove that the stationary distribution of the scaled queue converges to the stationary distribution of the limiting process and establish explicit Wasserstein-\(1\) convergence rates. The steady-state estimates are obtained through the Duhamel principle, generator comparison, and semigroup gradient bounds.

报告人简介：

徐礼虎，2008年博士毕业于Imperial College London，2007-2011在Bonn University做博士后；2026年至今，澳门大学理学院教授。主持两项国自然科学面上基金，研究方向主要包括：（1）Applied Probability (analysis of stochastic algorithms in machine learning, heavy tailed distribution, rare events analysis)；（2）Statistics and Data Science (high dimensional robust estimation, high dimensional distribution estimation via DNN, Stein’s method in data science)；（3）Stochastic Dynamical Systems (ergodic theory of SPDEs, numerical methods for SDEs, Malliavin calculus)；在Annals of Statistics, Journal of Machine Learning Research, Annals of Applied Probability, Bernoulli,Mathematics of Operations Research, Probability Theory and Related Fields, Transactions in American Mathematical Society, Stochastic Processes and Their Applications, Electronic Journal of Statistics, Electronic Journal of Probability等期刊共计发表50余篇论文。