Program Overview

Department of Industrial Engineering & Operations Research, IIT Bombay

About the Department

The Department of Industrial Engineering & Operations Research at IIT Bombay is a leading institution for education and research in the field of industrial engineering and operations research.

Academics

The department offers various academic programs, including:

• Ph.D.
• M.Sc.
• M.Sc-Ph.D.
• M.Tech
• B.Tech
• B.Tech Minor
• IDDDP
• CEP

Courses

The department offers a range of courses, including:

• IEOR Courses
• Time Table

Research

The department is involved in various research areas, including:

• Research Topics
• Publications
• Student Projects
• Computing
• FedEx ALFA
• TCAAI

Opportunities

The department provides various opportunities, including:

• Faculty Positions
• Corporate Visitors
• Placements

News

The department publishes news and announcements, including:

• Past News
• Past Announcements
• Departmental convocation

IE3xx: Stochastic Processes & Queueing Systems

Prerequisites

The prerequisites for this course include:

• IE1xx Probability & Statistics

Contents

The course covers models and techniques to deal with randomness that underlie many industrial and social systems, with an emphasis on models, their properties, and their applications. The topics include:

• Elementary stochastic processes: random walks
• Markov chains: first step analysis, state classifications, invariant distributions, Finite state Markov chains, Chapman-Kolmogorov equations, Recurrent Markov Chains, positive & null recurrence, limiting state probabilities, Stationary distributions
• Gambler's ruin, Random walk, Birth death chain
• Memory-less property of exponential random variables and related models & examples, Poisson processes
• Queueing systems, Little law, PASTA
• Introduction to renewal processes, Machine repair problems, replacement problems

References

The course references include:

• Sheldon Ross, Probability Models, 10th Edition, Academic Press, 2010
• S. M. Ross, Stochastic processes, 2nd Edition, 1996, John Wiley, New York
• D.P. Bertsekas and John N. Tsitsiklis, Introduction to Probability, 2002
• R. W. Wolff, Stochastic modeling and the theory of queues, 1989, Prentice Hall Inc., Engle-woodCliffs
• Hoel, Port, Stone, Introduction to Stochastic Processes
• Jean Jacod and Philip Protter, Probability Essentials, Springer, 2004
• James Norris, Markov Chains, CUP, 1998