Course No.：S070105ZJ005
Course Category：Professional Basic Course
Period/Credits：40/2
Prerequisites：Probability.
Aims & Requirements：
This course is intended for graduate students of mathematical sciences, while can also serve as an elective for students from areas like management sciences. Stochastic Queuing Networks has wide applications and rich content. Its applications can mainly be found in areas like computer sciences, engineering management, transportation, communication, production, public management. This course mainly focuses on methodology in Queuing Theory. Particularly, given a realistic problem in this area, we would talk about how to model and analyze it in order to solve it. By addressing that, this course can help students lay foundation for further research and solving realistic problems.
Primary Coverage：
Chapter 1 Introduction
Introducing and categorizing various stochastic network models, characterizing quantitative indices of stochastic queuing networks: length of queues, waiting time, idle time.
Chapter 2 M/M/1 & M/M/c
Transient states of systems, stationary solutions, Little’s Formula.
Chapter 3 M/G/1
Embedding Markov Process, stationary solutions, Little’s Formula, Diffusion approximation.
Chapter 4 G/M/1
Embedding Markov Process, stationary solutions, Khintchine’s Formula, Diffusion approximation.
Chapter 5 G/G/1
Principle of Lindley, Diffusion approximation.
Chapter 6 Ph Method
Definition and properties of Ph distribution, queuing of Ph/G/1 and G/Ph/1,Ph/Ph/1.
Chapter 7 Queuing Network
Open queuing network, closed queuing network, product-form solutions.
References：
[1] Cohen J.W. the Single Server Queue, North-Holland Publishing Company, 1982.
Author：Hanqin Zhang (Academy of Mathematics and Systems Science)
Date：March, 2010
