TIM 207
Spring 2012
Random Process Models in
Engineering
Course
Description:
TIM 207 is a first
graduate course
in stochastic process modeling and analysis for applications in
technology
management, information systems design, and engineering. Many problems
in
technology management, information systems, and as well as engineering
in
general, involve decision making in an uncertain and dynamically
changing
environment. Stochastic process modeling is thus an essential topic for
students in these fields. In TIM 207, students will learn both the
fundamental
techniques of analyzing stochastic processes, as well as acquire a
sense of how
to identify the best techniques to study problems that arise in
technology
management, information systems, and engineering.
Instructor:
John Musacchio (johnm@soe.ucsc.edu)
Office: E2 Room 557
Office hours: 12 Thursdays
Email: johnm@soe.ucsc.edu
Textbook
‘Essentials of Stochastic Processes’ by Rick Durrett, 1^{st} ed., Springer (1999).
Other reading materials may be distributed from the website in the “reading” column of the lecture plan chart.
Grading:
Midterm
30%
Homework
40%
Final Exam
30%
Homework will be assigned approximately once per week throughout the quarter.
Tentative
Lecture Plan
Class # 
Date 
Topics 
Reading 
Assignments 
1 
4/3 
Linear
Algebra and Probability Review Probability Space Independence Cond Probability, Bayes
Rule Expectation and Cond. Expectation 
Durrett Chapter 1, pp 125 (Required) Probability Notes Sections 26 (Reference) 

2 
4/5 
Linear
Algebra and Probability Review Range, rank, etc. Matrix Inverse Matrix Diagonalization,
Jordan Form Singular Value Decomposition 
Assignment 1 Out 

3 
4/10 
Gaussian
Random Vectors CLT background Normal Distribution and Density Covariance Matrix Jointly Gaussian Concept LLSE 
Gallager Notes on Gaussian Random Vectors Probability Notes
Section 7 Gallager Estimation Notes (Reference) Gallager Detection Notes (Reference) 

4 
4/12 
Random
Processes and Linear Systems Random Process definition White Noise Linear Time Invariant systems 
Gallager Notes on Stochastic Processes
 (Section 1 and 2) Probability Notes Section
13, pp 212215 
Assignment 2 out 
5 
4/17 
Random Processes
and Linear Systems Discrete Fourier Transform Wide Sense
Stationarity 
Gallager Notes on Stochastic Processes 
(Section 2 and 5) Probability Notes
Section 13 pp 215219 
Assignment 1 Due 
6 
4/19 
Random Processes
and Linear Systems Power Spectrum LTI systems driven by random processes Wiener Filter
Preview 
Gallager Notes on Stochastic Processes  (White
Gaussian Noise Section) Probability Notes
Section 13 pp 219223 
Assignment 3 out 
7 
4/24 
Discrete
Time Markov Chains Definition and Examples Transition Probabilities Classification of States 
Durrett Chapter 1, pp 2848 
Assignment 2 Due 
8 
4/26 
Discrete
Time Markov Chains Limit Behavior Convergence Theorems Invariant Distribution Random Walk First Passage times 
Durrett Chapter 1, pp 4865 
Assignment 4 out 
9 
5/1 
Discrete
Time Markov Chains Queuing Applications Strong Law for Markov Chains One step calculations Examples 
Durrett Chapter 1, pp 6688 
Assignment 3 due 
10 
5/3 
Discrete
Time Markov Chains Limit Theorems 
Durrett Chapter1, pp 100120 
Assignment 5 out 
11 
5/8 
Martingales
Conditional Expectation Examples Optional Stopping Theorem Applications in Investing 

Assignment 4 due 
12 
5/10 
MIDTERM Study Questions 


13 
5/15 
Martingales
Conditional Expectation Examples Optional Stopping Theorem 
Durrett Chapter 2 
Assignment 5 due Assignment 6 out 
14 
5/17 
Poisson
Processes Exponential Distribution Poisson process definition Conditioning Applications in Traffic Modeling 
Durrett Chapter 3 

15 
5/22 
Continuous
Time Markov Chains Definitions and Examples Transition Probabilities Limit Behavior 
Durrett Chapter 4 

16 
5/24 
Continuous
Time Markov Chains Reversibility Queuing Networks Call Center Models 
Durrett Chapter 4 

17 
5/29 
Renewal
Processes Definitions Laws of Large Numbers 
Durrett Chapter 5, pp 209221 
Assignment 6 due Assignment 7 out 
18 
5/31 
Renewal
Processes Queuing Applications M/G/1 queue 
Durrett Chapter 5, pp 221234 

19 
6/5 
Brownian
Motion Definitions Markov Property; Reflection Principle 
Durrett Chapter 6 
Assignment 7 Due 
20 
6/7 
Brownian
Motion Hitting Times BlackScholes 




FINAL EXAM June 11 4  7pm 
