CEN 601: Engineering Stochastic Processes and its applications.

Description:

Random variables. Moments. Conditional distributions and moments. Functions of random variables. Joint distributions and moments. Random process models: basic concepts, properties. Stationary random processes: covariance and spectrum. Response of linear systems to random inputs: discrete-time and continuous-time models. Time averages and Ergodic principle. Sampling principle and interpolation. Selected applications in Control, Networks and Communication Systems.

Objectives:

The main objective of this course is to allow our graduate students to understand the concepts of probability and facilitate the use of probability tools to solve problems that arise in engineering practice. The students will also develop problem-solving skills and learn the transition from a real problem to a probability model for that problem. There is no any pre-requisite for this course.

Topics:

Name	sessions
Review of Probability	1
Random Variables	3
Stochastic Processes and autocorrelation function	2
Poisson process	1
Markov chains and Markov processes	2
Applications	2
Review and evaluation	2

Text and References:

• Probability and Random Processes for Electrical Engineers, by Alberto Leon-Garcia, Addison Wesley, 1994.
• Probability, Random Variables, and Stochastic Processes, by Papoulis and Pillai, McGraw-Hill, 2002.
• Data Networks, by Bertsekas and Gallager, Prentice Hall, 1992.
• Simulation a Statistical Perspective, Jack Kleijnen and Willem Van Groenendaal, John & Wiley, 1994.
• Queueing Systems - vol. 1-2: computer applications, by Kleinrock.
• Telecommunication Networks - protocols, modeling and analysis, by Mischa Schwartz, Addison Wesley, 1988.
• Stochastic Processes, by Ross, John & Wiley, 1983.
• Stochastic Methods of Operations Research, by Kohlas, Cambridge University Press, 1982.

Grading:

Category	Percent
Homework	20
Project	20
Exam	20
Final	40

Project Policies:

At least two projects will be assigned. The projects will be of two types:

• Model Study: a recent paper describing a stochastic model will be studied.
• Stochastic Modeling: a simple real system will be studied and modeled.
• One project should be presented by each student.