E2 204, Spring 2017

Stochastic Processes & Queueuing Theory

Lectures

• 03 Jan 2017: Lecture-01 Introduction
• 05 Jan 2017: Lecture-02 Bernoulli Processes
• 10 Jan 2017: Lecture-03 Poisson Process
• 12 Jan 2017: Lecture-04 Properties of Poisson Process
• 17 Jan 2017: Lecture-05 Compound and Non-Stationary Poisson Processes
• 19 Jan 2017: Lecture-06 Introduction to Renewal Theory
• 24 Jan 2017: Lecture-07 Regenerative Processes
• 26 Jan 2017: Lecture-08 Key Renewal Theorem and Applications
• 31 Jan 2017: Lecture-09 Applications: Age-dependent Branching and Delayed Renewal
• 02 Feb 2017: Lecture-10 Applications: Equilibrium Renewal and Renewal Reward
• 07 Feb 2017: Lecture-11 Markov Chains
• 09 Feb 2017: Lecture-12 Markov Chains: Ergodicity
• 14 Feb 2017: Lecture-13 Markov Chains: Convergence
• 16 Feb 2017: Lecture-14 Markov Chains: Stability
• 21 Feb 2017: Lecture-15 Markov Processes
• 23 Feb 2017: Lecture-16 Markov Processes: Evolution
• 27 Feb 2017: Lecture-17 Markov Processes: Uniformization
• 28 Feb 2017: Lecture-18 Reversibility
• 02 Mar 2017: Lecture-19 Reversed Processes
• 07 Mar 2017: Lecture-20 Reversible Processes
• 09 Mar 2017: Lecture-21 Tandem Queues
• 13 Mar 2017: Lecture-22 Jackson Network
• 14 Mar 2017: Lecture-23 Martingales
• 16 Mar 2017: Lecture-24 Martingale Convergence Theorem
• 28 Mar 2017: Lecture-24 Exchangeability
• 30 Mar 2017: Lecture-26 Martingale Concentration Inequalities
• 04 Apr 2017: Lecture-27 Random Walks
• 06 Apr 2017: Lecture-28 Random Walks: GI/G/1 Queue

Homework

• 10 Jan 2017: Homework 1
• 24 Jan 2017: Homework 2
• 07 Feb 2017: Homework 3
• 21 Feb 2017: Homework 4
• 07 Mar 2017: Homework 5
• 21 Mar 2017: Homework 6
• 04 Apr 2017: Homework 7

Tests

• 20 Jan 2017: Quiz 1
• 10 Feb 2017: Quiz 2
• 17 Feb 2017: Mid Term
• 20 Mar 2017: Quiz 3
• 31 Mar 2017: Quiz 4
• 07 Apr 2017: Quiz 5
• 14 Apr 2017: Final
• 17 Apr 2017: Take-home
• 29 Apr 2017: Project

Grading Policy

Mid Term: 20
Homework: 20
Project : 20
Final : 40

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 complex systems are modeled using stochastic processes. This course will introduce students to basic stochastic processes tools that can be utilized for performance analysis and stochastic modeling.

Slack/GitHub Information

Slack

Students can signup for slack using their ece.iisc.ernet.in email at Slack signup.

GitHub

All the students in the class have read access to Stochastic-Processes public repository on GitHub.

Instructors

Aditya Gopalan
Office: ECE 2.09

Parimal Parag Office: ECE 2.17

Time and Location

Classroom: ECE 1.07, Main ECE Building
Hours: Tu/Th 05:00 pm - 06:30 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.