报告题目：Dynamics in Internet Congestion Control Models
摘要：We consider two Internet congestion control systems which are presented as a group of differential equations with time delay, modeling the random early detection (RED) algorithm and implement the TCP/RED algorithm by a new frame of dynamic routing, based on the measurement of occupation ratio of router buffer for different links, which only requires the information of the queue size at the buffer of the router, to stabilize the system. For the simple network topology, we show that the Filippov solution exists under some restrictions on parameters. For the case with a single user group and two alternative links, we prove that the discontinuous boundary, or equivalently the sliding region, always exists and is locally attractive. We also classify several types of equilibrium in the designed dynamic routing and employ the numerical method to study the stability of the steady state.
报告人简介：袁沅，纽芬兰纪念大学数学与统计系教授。本科毕业于武汉大学，后于中南大学、西安大略大学获得硕士和博士学位，之后在滑铁卢大学从事博士后研究。袁教授主要研究领域为数学生物学、数学生态学、非线性动力系统、时滞微分方程等；已在J. Differential Equations, SIAM J. Appl. Math., SIAM J. Appl. Dyn. Syst., J. Math. BIol.等国际著名学术期刊上发表高水平学术论文50余篇，并兼任多个国际期刊编委、特邀编辑等。