E2 204, Spring 2016

Stochastic Processes & Queueuing Theory

Lectures

• 12 Jan 2016: Lecture-01 Introduction
• 14 Jan 2016: Lecture-02 Poisson Process
• 19 Jan 2016: Lecture-03 Properties of Poisson Process
• 21 Jan 2016: Lecture-04 Compound and Non-Stationary Poisson Processes
• 28 Jan 2016: Lecture-05 Introduction to Renewal Theory
• 02 Feb 2016: Lecture-06 Limit Theorems in Renewal Theory
• 04 Feb 2016: Lecture-07 Inspection Paradox and Limiting Mean Excess Time
• 09 Feb 2016: Lecture-08 Renwal Process Examples and Delayed Renewal Process
• 11 Feb 2016: Lecture-09 Equilibrium Renewal Processes and Renewal Reward Processes
• 18 Feb 2016: Lecture-10 Discrete Time Markov Chains
• 23 Feb 2016: Lecture-11 Stationary Distribution and Ergodic Theorems
• 25 Feb 2016: Lecture-12 The Coupling Methods
• 01 Mar 2016: Lecture-13 Foster Lyapunov Theorem and Examples
• 03 Mar 2016: Lecture-14 Continuous Time Markov Chains
• 08 Mar 2016: Lecture-15 Limiting Probabilities and Uniformization
• 10 Mar 2016: Lecture-16 Reversibility
• 13 Mar 2016: Lecture-17 Reversed Processes
• 17 Mar 2016: Lecture-18 Queueing Networks
• 22 Mar 2016: Lecture-19 Martingales
• 24 Mar 2016: Lecture-20 Polya’s Urn Scheme
• 29 Mar 2016: Lecture-21 Exchangeability
• 31 Mar 2016: Lecture-22 Random Walks
• 05 Apr 2016: Lecture-23 Martingale Concentration Inequalities
• 07 Apr 2016: Lecture-24 Brownian Motion

Course Syllabus

Poisson process, Renewal theory, Markov chains, Reversibility, Queueing networks, Martingales, Random walk.

Course Description

Basic mathematical modeling is at the heart of engineering. In both electrical and computer engineering, many systems must be modeled using stochastic processes. This course will introduce students to basic stochastic processes tools that can be utilized for performance analysis of stochastic dynamic systems and networks.

GitHub Information

All the students in the class have access to Stochastic-Processes course public repository on GitHub.
Please follow the guidelines in the sample lecture.
The source file for the sample lecture is in the repository.
It is recommended you save it with another name in your local repository for creating a new lecture.
A good book for Git is here and a simple tutorial here.

Instructors

– Aditya Gopalan
Office: ECE 2.09
Hours: M/W 11:00 am - 12:00 noon.

Parimal Parag
Office: ECE 2.17
Hours: M/W 11:00 am - 12:00 noon.

Time and Location

Classroom: ECE 1.07, Main ECE Building
Hours: Tu/Th 04:00 pm - 05:30 pm.

Teaching Assistants

TBD

Textbooks

Stochastic Processes, Sheldon M. Ross, 2nd edition, 1996.

Introduction to Stochastic Processes, Erhan Cinlar, 2013.

Markov Chains: Gibbs Fields, Monte Carlo Simulation, and Queues, Pierre Bremaud, 1999.

Markov Chains, James R. Norris, 1998.

Reversibility and Stochastic Networks, Frank P. Kelly, 2011.

Probability: Theory and Examples, Rick Durett, 4th edition, 2010.