M.Venkateswrarao.K

Syllabus:
1. Basic Queueing Theory: Fundamentals of analysing single queues
- Markov Processes and Markov Chains
- Birth Death Process
- Kendall's Notation for Queues
- Little's Law
- Equilibrium Solution for M/M/-/- Queues
- Delay Analysis for FCFS M/M/1 Queues
- Departure process from M/M/1 Queue
- Time Reversibility Property of Irreducible, Aperiodic Markov Chain
- The Method of Stages for Solving a M/-/1 FCFS Queue
2. Analysis of M/G/1 queue in equilibrium
- The Residual Life Approach for Analysing the M/G/1 Queue.
- The Imbedded Markov Chain Approach for Analysing M/G/1 Queue.
- Distribution of Time Spent in System and The Waiting Time Prior
to Service in a FCFS M/G/1 queue.
- Busy Period Analysis of M/G/1 queue.

Reference books:
1. Sanjay K. Bose (2002), An Introduction to Queueing Systems, Kluwer
Academic/Plenum Publishers, New York.
2. Robert B. Cooper, Introduction to Queueing Theory.

Syllabus:
- Construction of Probability Measure.
- Conditional Probability and Independence.
- Random Variables on a countable Space.
- Integration with respect to a Probability Measure.
- Independent Random variables.
- Probability Distributions on R.
- Sum of independent random variables.
- Convergence of random variables.
- Conditional expectation
- Martingales
- Super and sub Martingales.
- Martingale Inequalities.
- Martingale Convergence Theorems.

Reference books:
Probability Essentials by Jean Jacod, Philip Protter.
Probability and Measure by Patrick Billingsley.