Course Name: Queuing Theory and Traffic Systems

Course Code: S2293173

Semester: 5

Credit: 4

Program: Electronics

Course Module: Optional Courses (Communications)

Responsible: Shuo Li

E-mail: shuo.li@tju.edu.cn

Department:Tianjin International Engineering Institute, Tianjin University

TimeAllocation(1 credit hour = 45 minutes)

Course Description

This class deals with the modelling and analysis of queuing systems, with applications in communications, manufacturing, computers, call centres, service industries and transportation. Topics include birth-death processes and simple Markovian queues, networks of queues and product form networks, single and multi-server queues, multi-class queuing networks, fluid models, adversarial queuing networks, heavy-traffic theory and diffusion approximations. The course will also cover state of the art results which lead to research opportunities.

Prerequisite

Graph Theory, Statistics, Probability.

Course Objectives

The course is designed to familiarize students with the ways that queuing systems are modelled and analyzed. Queuing systems are used by any industry or company that needs to manage a large number of units over time, such as in the manufacturing, transportation, communications, computers, services and call centre industries. The course introduces students to queue networks, multi-server queues, fluid models, traffic limits, multiclass networks, distribution laws and PASTA.

Course Syllabus

1. Fundamental Insights: The M/M/s Type Systems

2. Little's Law and Generalizations

   1. Distributional Laws

   2. Conservation Laws

3. PASTA

4. Systems with No Overtaking: Exact Solutions

5. Systems with No Overtaking: Asymptotic Solutions

6. Priority, Polling Systems

   1. Multiserver Queues

   2. Queues in Halfin-Whitt Regime

   3. Applications to Call Centers

7. Open Jackson Networks

8. Closed Jackson Networks

9. Multiclass Networks

   1. Adversarial Queuing Networks I

   2. Adversarial Queuing Networks II

   3. Transient Behavior of Queuing Systems

   4. Fluid Models of Queueing Systems I

   5. Fluid Models of Queueing Systems II

10. Stability of Queuing Networks

11. Optimization of Queuing Systems

12. Optimization of Multiclass Networks and Fluid Models

13. Queues in Heavy Traffic

14. Multiclass Networks in Heavy Traffic

    1. Long Range Dependence

    2. Large Deviations and Queues

15. Take-Home Final Exam Period

Textbooks & References

• Chen, Hong, and David Yao.Fundamentals of Queueing Networks: Performance, Asymptotics, and Optimization. New York, NY: Springer-Verlag, 2001. ISBN: 0387951660.(Required)

• Additional References:

• Kleinrock, Leonard.Queueing Systems. New York, NY: John Wiley & Sons, 1975-1976. ISBN: 0471491101.

• Kelly, Frank P.Reversibility and Stochastic Networks. New York, NY: John Wiley & Sons, 1979. ISBN: 0471276014.

• Halfin, Shlomo, and Ward Whitt. "Heavy-Traffic Limits for Queues with Many Exponential Servers."Operations Research29, no. 3 (1981): 567-588.

Grade Distribution

Attendance: 10% Homework: 10% Midterm text:20% Final Exam:60%

Capability Tasks

CT1: To understand basic science, and to have analytical ability and the ability to integrate related knowledge.

CT2: To apply relevant professional knowledge to the field of science and technology: understanding of the basic concepts and its connotation, application of different methods and concepts which have been learned, capability of judging the scope and limitations of such applications.

CT3: To grasp methodologies and engineering tools: identifying, utilizing and solving problems. Even if the students are not familiar with the content, they can turn to computer tools for systematic analysis.

CT4: To carry out experiments in research environment with the abilities to utilize tools, especially for data collection and processing.

CT10: To have the capacity to work in international environment; the capability to master one or more foreign languages and be open to foreign cultures; be able to acclimatize themselves to the international language environment.

Achievements

• To be able to apply queuing theory in networks. - Level: A

• To design and analyze a queuing model for a practical network. - Level: M

• To know the ways that queuing systems are modeled and analyzed. - Level: M

Students: Electronics, Year 3