Instructor

Jayakrishnan Nair

Semester

Autumn ‘21

Course Difficulty

With a strong background of first-year math and probability, the course shouldn’t be too challenging. Rigor is, however, a constant feature, so if you’re not a fan of long proofs and theorems, this may not be the course for you.

Time Commitment Required

Recorded videos were uploaded to YouTube and the lecture slot was used for discussion of the lecture content. This meant that a little bit of preparation was needed to follow the stuff taught in class.

Grading Policy and Statistics

Quite generous.
15 AAs, 23 ABs and 19 BBs in a class of 83

Attendance Policy

None as such, however class participation counted for 5% of the grade.

Pre-requisites

EE325 is a semi-official prerequisite, but any other probability course from SC, IE or your own department should work alongside instructor’s consent

Evaluation Scheme

Homework assignments – 25%
Quizzes (2) — 20%
Mid-term – 20%
End-term – 30%
Class participation – 5%
Quizzes + assignments for audit grade

Topics Covered in the Course

As the name suggests, the first half is about Markov chains while the latter half looks at the modelling of queuing systems.
Discrete-time Markov chains
Introduction to Renewal Reward Theory
Continuous-time Markov chains
Markovian queueing models — M/M/1, Erlang B & C
Phase-type distributions and Matrix Analytic Methods
M/G/1 mean value analysis via Renewal Reward
M/G/1 transform analysis
Scheduling policies in M/G/1: FCFS, LCFS, PLCFS, SRPT
Burke’s Theorem & Queueing Networks

Teaching Style

The professor would upload at least two videos every weekend and students were expected to have watched the content by the lectures on Monday and Thursday (one apiece). The professor was extremely patient and explained the concepts very well using a digital whiteboard. The pace was reasonably slow and the professor ensured that everyone in the class was awake with his enthusiasm. The use of real-word examples throughout makes going through the course content extremely interesting.

Tutorials/Assignments/Projects

Homework Assignments - quite easy, avoid plagiarism at all costs

Feedback on Exams

Exams - rarely heavy on proofs or theory, unlike the lectures, easy to score well in if one does the homework diligently
All exams were conducted using SAFE + web proctoring, with sporadic experiments with Code Tantra

Motivation for taking this course

Given my interest in Mathematical Finance, and how ubiquitous Markov Chains and other advanced probabilistic models are in financial market modelling, taking this course was a no-brainer

Course Highlights

The examples of queuing systems discussed in class, super-interesting

Course Importance

Great as an advanced probability course - once this is done you can branch out into Derivative Pricing, Stochastic Optimization, Stochastic Control or Statistical Machine Learning, for which there are a multitude of courses within EE as well as outside

How strongly would I recommend this course?

Great, if not for the amazing content but for the professor’s teaching

When to take this course?

6th semester, ideally take it after you’ve done a proper probability course

References Used

The textbook for the course is Performance Modeling and Design of Computer Systems by Mor Harchol-Balter. Other useful references are:

Markov chains:
Anurag Kumar’s lecture notes on discrete event stochastic processes [link]
R. G. Gallager, Stochastic Processes: Theory for applications
J. R. Norris, Markov chains
Queueing systems:
R. Wolff, Stochastic Modeling and the Theory of Queues
Lecture notes on queueing theory by Ivo Adan and Jacques Resing [link]
L. Kleinrock, Queueing Systems, Vol. 1 & 2

Review By: Aditya Iyengar