E2 204, Spring 2026
Stochastic Processes & Queueuing Theory
Lectures
- 01 Jan 2026: Lecture-01 Introduction
- 06 Jan 2026: Lecture-02 Probability Review
- 08 Jan 2026: Lecture-03 Conditional Expectation
- 13 Jan 2026: Lecture-04 Progressive Measurability
- 15 Jan 2026: Lecture-05 Stopped Event Spaces
- 20 Jan 2026: Lecture-06 Strong Markov Property
- 22 Jan 2026: Lecture-06 Strong Markov Property
- 27 Jan 2026: Lecture-07 Renewal Processes: Definitions
- 29 Jan 2026: Lecture-08 Renewal Processes: Distribution Functions
- 03 Feb 2026: Lecture-09 Renewal Processes: Limit Theorems
- 05 Feb 2026: Lecture-10 Regenerative Processes: Renewal Equation
- 10 Feb 2026: Lecture-11 Regenerative Processes: Limit Theorems
- 12 Feb 2026: Lecture-12 Regenerative Processes: Renewal Reward
- 14 Feb 2026: Lecture-13 Regenerative Processes: Limiting Distribution
- 17 Feb 2026: Lecture-14 Regenerative Processes: Ergodicity
- 19 Feb 2026: Lecture-15 Discrete Time Markov Chains
- 24 Feb 2026: Lecture-16 DTMC: Class Properties
- 26 Feb 2026: Lecture-17 DTMC: Invariant Distribution
- 03 Mar 2026: Lecture-18 Continuous Time Markov Chains
- 05 Mar 2026: Lecture-19 CTMC: Embedded Markov Chain and Jump Times
- 10 Mar 2026: Lecture-20 CTMC: Uniformization
- 12 Mar 2026: Lecture-21 CTMC: Invariant Distribution
- 17 Mar 2026: Lecture-22 Reversibility
- 19 Mar 2026: Lecture-23 Queues
- 24 Mar 2026: Lecture-24 Reversed Processes
- 26 Mar 2026: Lecture-25 Stochastic Networks
- 21 Mar 2026: Lecture-26 Martingales
- 02 Apr 2026: Lecture-27 Martingale: convergence and concentration
- 07 Apr 2026: Lecture-28 Exchangeability
- 09 Apr 2026: Lecture-29 Random walks
Homework
- 04 Jan 2026: Homework-01
- 18 Jan 2026: Homework-02
- 01 Feb 2026: Homework-03
- 15 Feb 2026: Homework-04
- 01 Mar 2026: Homework-05
- 15 Mar 2026: Homework-06
- 29 Mar 2026: Homework-07
- 12 Apr 2026: Homework-08
Tests
Test Hours: 10:00am-01:00pm
Venue: EC 1.07, ECE main building
- 21 Feb 2026: Mid Term 1
- 21 Mar 2026: Mid Term 2
- xx Apr 2026: Final (09:00am-12:00noon)
Grading Policy
Mid Term 1: 20
Mid Term 2: 20
Attendance: 10
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 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-2026 using the following code 58kp2tf.
Instructor
Parimal Parag
Office: EC 2.17
Hours: By appointment.
Time and Location
Classroom: EC 1.07, ECE main building
Hours: TTh 05:00pm-06:30pm.
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.
