E2 204, Spring 2015

Stochastic Processes & Queueuing Theory

Lectures

  • Poisson Process
  • Characterizations/Properties of Poisson Process
  • Compound Poisson Process
  • Introduction to Renewal Theory
  • Limit Theorems in Renewal Theory
  • Key Renewal Theorem and Applications
  • Limiting Mean Excess Time, Branching Processes, Delayed Renewal Process
  • Equilibrium Renewal Processes and Renewal Reward Processes
  • Discrete Time Markov Chains
  • Examples of Discrete Time Markov Chains
  • Time Reversibility of Discrete Time Markov Chains
  • Continuous Time Markov Chains
  • Limiting Probabilities and Reversibility
  • Applications of Reversibility to Queueing Networks
  • Examples of Queueing Networks
  • Martingales
  • Martingales Examples
  • Martingales Convergence Theorems
  • Random Walks
  • Queues as Random Walks
  • Martingales as Random Walks

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.

Instructor

Office: ECE 2.17
Hours: M/W 4:00-5:00pm.

Time and Location

Classroom: ECE 1.07, Main ECE Building
Hours: M/W 10:00 am - 12:00 noon.

Teaching Assistants

Konchady Gautam Shenoy
Email: konchady@iisc.ac.in
Office Hours: Wednesdays, 3:00-5:00pm, EC 2.15

Deekshith P K
Email: deekshithp@iisc.ac.in
Office Hours: Fridays, 1:30-3:30pm, EC 2.19

Textbook

Stochastic Processes, Sheldon M. Ross, 2nd edition, 1996. You can get a copy of the textbook from the campus book store.

Stochastic Processes