Roll Number
11i190012
Category
TA
Topics for PhD Qualifiers
Optimisation Techniques
Stochastic Models
Stochastic Models
Elective1
Queueing Theory
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:
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.
Elective2
Probability 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.
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.
PhD. Supervisor (if decided)
Prof. Veeraruna Kavitha
Proposed Research Plan (if decided)
We are working on stability and average waiting time in zero-service time continuous polling models. We want to study the Pseudo conservation laws for Continuous polling models.