**Prerequisite:** Instructor's permission

**Prerequisite:**Instructor's permission

**Contents**

Models and techniques to deal with randomness that underlie many industrial and social systems. It includes discussions on models, their properties and their applications.

Review of basic probability concepts: conditional probability and random variables. Stochastic processes, sample paths, finite dimensional distribution functions. Time averages and Laws of large numbers. Finite state Markov chains, Chapman-Kolmogorov equations, limiting state probabilities, Stationary distributions. Memory-less property of exponential random variables and related models & examples. Poisson process and its applications. Renewal processes with examples.

Elementary Queueing theory: steady state probabilities, Little's Law. Exponential models with examples. Applications of open and closed queueing systems. Applications in reliability theory, systems with parallel and series of components, component life vs. system life, expected system life. Applications in inventory, random demand and stockouts, notions of service levels.

Performance measures of above models in terms of relevant transient and steady state distributions.

**References**

- Sheldon M. Ross (2006) Introduction to Probability Models, 9th edition, Academic Press.
- Wayne L. Winston (2003) Introduction to Probability Models: Operations Research, Volume II, 4th edition, Duxbury Resource Center.
- Hamdy. A. Taha (2002) Operations Research: An Introduction, 8th edition, Prentice Hall of India.
- Wayne L. Winston (2004) Operations Research: Applications and Algorithms, 4th edition, Thomson Learning.
- Dimitri P. Bertsekas and John N. Tsitsiklis (2008) Introduction to Probability, 2nd edition, Athena Scientific.