E2 204, Spring 2025
Stochastic Processes & Queueuing Theory
Lectures
- 02 Jan 2025: Lecture-01 Introduction
- 07 Jan 2025: Lecture-02 Probability Review
- 09 Jan 2025: Lecture-03 Conditional Expectation
- 14 Jan 2025: Lecture-04 Progressive Measurability
- 16 Jan 2025: Lecture-05 Stopped Event Spaces
- 21 Jan 2025: Lecture-06 Strong Markov Property
- 23 Jan 2025: Lecture-07 Renewal Processes
- 28 Jan 2025: Lecture-08 Renewal Processes: Distribution Functions
- 30 Jan 2025: Lecture-09 Renewal Processes: Limit Theorems
- 01 Feb 2025: Lecture-10 Regenerative Processes
- 04 Feb 2025: Lecture-11 Blackwell’s Theorem
- 06 Feb 2025: Lecture-12 Key Renewal Theorem
- 11 Feb 2025: Lecture-13 Key Renewal Theorem: Applications
- 13 Feb 2025: Lecture-14 Discrete Time Markov Chains
- 18 Feb 2025: Lecture-15 DTMC: Class Properties
- 20 Feb 2025: Lecture-16 DTMC: Invariant Distribution
- 25 Feb 2025: Lecture-17 Continuous Time Markov Chains
- 27 Feb 2025: Lecture-18 CTMC: Embedded Markov Chain and Jump Times
- 04 Mar 2025: Lecture-19 CTMC: Uniformization
- 06 Mar 2025: Lecture-20 CTMC: Invariant Distribution
- 11 Mar 2025: Lecture-21 Reversibility
- 13 Mar 2025: Lecture-22 Queues
- 18 Mar 2025: Lecture-23 Reversed Processes
- 20 Mar 2025: Lecture-24 Stochastic Networks
- 25 Mar 2025: Lecture-25 Martingales
- 27 Mar 2025: Lecture-26 Martingale Convergence Theorem
- 01 Apr 2025: Lecture-27 Martingale Concentration Inequalities
- 03 Apr 2025: Lecture-28 Exchangeability
- 08 Apr 2025: Lecture-29 Random Walks
- 10 Apr 2025: Lecture-30 GI/G/1 Queues
Homework
- 04 Jan 2025: Homework-01
- 18 Jan 2025: Homework-02
- 01 Feb 2025: Homework-03
- 15 Feb 2025: Homework-04
- 29 Feb 2025: Homework-05
- 14 Mar 2025: Homework-06
- 28 Mar 2025: Homework-07
- 11 Apr 2025: Homework-08
Tests
Test Hours: 10:00am-01:00pm
Venue: EC 1.07, ECE main building
- 10 Feb 2025: Mid Term 1
- 23 Mar 2025: Mid Term 2
- 26 Apr 2025: Final (09:00am-01:00pm)
Grading Policy
Mid Terms: 50
Final: 50
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 of dynamic systems and networks.
Teams/GitHub Information
Teams
We will use Microsoft Teams for all the course related communication.
Please do not send any email regarding the course.
You can signup for the course team Stochastic-Processes-2025 using the following code fzg5i06.
Instructor
Parimal Parag
Office: EC 2.17
Hours: By appointment.
Time and Location
Classroom: EC 1.07, ECE main building
Hours: Tue/Thu 08:30am-10:00am.
Teaching Assistants
Srinivas Nomula
Email: sivasrinivas@iisc.ac.in
Hours: By appointment.
Textbooks
Stochastic Processes, P. Parag and Vinod Sharma.
Stochastic Processes, Sheldon M. Ross, 2nd edition, 1996. You can get a copy of the textbook from the campus book store.
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.