报告题目: Several Topics on Queueing System

报告人: 杨建奎 教授 北京邮电大学

报告日期：6月27日 星期六

报告时间：9：40-10：20

报告地点：逸夫楼1537

报告摘要：This survey provides a compact review of queueing theory, organized around seven interconnected themes: transient analysis, stationary distribution, ergodicity, fluid approximation, diffusion approximation, tail analysis, and optimization. Historically rooted in A. K. Erlang’s early telephone models, the field has been profoundly developed. A number of theoretical results in queueing theory, such as Little’s law, Lindley’s recursion, fluid approximation models, and hydrodynamic (or diffusion) approximations, provide quantitative relationships describing queue length and waiting time, the recursive relation between waiting time and the inter-arrival and service times, the connection between stability of deterministic system and stochastic ergodicity, and delicate time characterizations under diffusion scaling. These tools offer highly convenient and efficient methods for evaluating system performance. Queueing theory research has also given rise to many research areas and directions, including the theory of birth-death processes, ergodic theory of Markov processes, and semi-martingale reflected Brownian motion in stochastic analysis. The theoretical results of queueing theory are widely applied across various fields, not only in communication networks, but also in transportation management, healthcare operations, customer service in commerce, scheduling of large‑scale production lines, inventory management, reliability analysis, computer networks, and many other industries.