加州理工学院Steven H. Low教授在我院开设一门研究生短期课程《电力和无线网络中的控制和优化》（课程编号32040010），本期主题为：Analytical Methods for Internet Congestion Control，具体课程信息如下。

课程时间：4月18日至4月22日每天上午9点45至11点45
课程地点：工控新楼501
学分：1分
报名方式：本周日（4月10日）前将姓名+学号发送至邮箱pcyou@zju.edu.cn

—————————————  SHORT COURSE  ——————
 
Analytical Methods for Internet Congestion Control
Steven Low, Caltech
 
This short course introduces mathematical methods for designing and analyzing congestion control algorithms for the Internet.    We will model Internet traffic as fluids that flow from sources to destinations and model congestion control algorithms using ordinary differential equations.   We will discuss the existence and uniqueness of solutions to these equations, characterize their equilibrium points, and prove their stability properties.   We will use several real protocols for illustration but the emphasis will be on various mathematical techniques for the analysis of congestion control algorithms.  We will rigorously prove several main results.
 
A tentative schedule is as follows:
 
1: Congestion control models
2: Equilibrium structure
a) Basic convex optimization 
b) Network utility maximization  
3: Global stability
a) Lyapunov stability method 
b) Passivity method 
c) Gradient projection method 
4: Local stability with delay
a) Nyquist stability theory 
b) Stability of primal and of dual algorithms