课程名称 (Course Name) ： Stochastic Processes and Queueing Theory

课程代码 (Course Code）： X034501

学分/学时 (Credits/Credit Hours)：32

开课时间 (Course Term )：Autumn

开课学院（School Providing the Course）:  SEIEE

任课教师（Teacher）:  Jianhong Shi

课程讨论时数（Course Discussion Hours）:  0

课程实验数（Lab Hours）:   0

课程内容简介(Course Introduction):

This course will introduce the student to a basic set of mathematical tools which are appropriate for dealing with the randomness / stochasticity that underlies the operation of many technological, economic and social systems.

教学大纲(Course Teaching Outline):

Introduction

  1. Overview
     – Definition of Probability, Random Variable, Stochastic Process
     – Classification of Stochastic Processes

     – Overview of Queueing Theory

Part I:Stochastic Processes Theory

  2. Conditional Probability and Conditional Expections
     -- Math Definition
     -- Applications
  3. Markov Processes and Poisson Process
     -- Definition
     -- Chapman-Kolmogorov Equations
     -- Limiting Probability
     -- Time Reversibility
     -- Markov Decision Process
     -- Kolmogorov Forward and Backward Equation
     -- Definition of Exponential Distribution
     -- Properties of Exponential Random Variable
     -- Convolutions of Exponential Random Variable
     -- Defintiation of Counting Process, Poisson
     -- Properties of Poisson Process
     -- Variations of Poisson Process (nonhomogenous, Compound, Conditional)
  4. Renew Processes, Random Walk, Brownian Motion
     -- Definition of Renewal Process
     -- Distribution of N(t)
     -- Wald's Equatioin
     -- Insights of Renewal
     -- Variations on Brownina Motion
     -- Absorbed Brownian Motion
     -- Reflected Brownian Motion
     -- Geometric Brownian Motion
     -- Integrated Brownian Motion
     -- Brownian Motion with drift
     -- Analyze Brownian Motion through Martingale
     -- Kolmogrov Differential Equations for Brownian Motion
 5. Martingale Processes, Stationary Processes
     -- Supper Martiginale, Sub Martingale
     -- Fundamental Martingale Inequalities
     -- Doob's Martingale Convergence Theorem
     -- Definition of Stationary Process
     -- Limiting Theorems and Ergodic Theory

Part II:Queueing Theory

6. M/M/1, M/M/C, etc
7. M/Er/1, Er/M/1, etc
8. M/G/1
9. G/M/1

10. Priority Queue
11. G/G/1

12. Queueing Networks (Jackson Networks, Wittle Networks)

课程进度计划(Course Schedule):

1st week：Overview

2nd week：Conditional Probability and Conditional Expections

3rd Week：Poisson Process

4th Week：Markov Processes

5Th Week：Renew Processes

6th Week：Random Walk

7th Week：Brownian Motion

8th Week：Martingale Processes

9th Week：Stationary Processes

10th Week：Queueing Theory

11th Week：Review

 

课程考核要求(Course Assessment Requirements)：

  1.Class performance  20%

  2.Home work        30%

  3.Final project       50%

参考文献(Course References)：

Introduction to Probability Models, 10th Edition", by Sheldon Ross

预修课程（Prerequisite Course）

Understanding of elementary probability