Learn · Stochastic Modeling and the Theory of Queues
Lecture 58 of 81week-09
mod09lec58 - Stationary Distribution of a Countable State Space DTMC and Renewal Theory
Prof. Krishna Jagannathan · IIT Madras
Credits and licence
- From
- Stochastic Modeling and the Theory of Queues, IIT Madras (at NPTEL)
- Licence
- CC BY-NC-SA, as NPTEL states it. Non-commercial use only.
- Attribution
- NPTEL states: "Distributed under Creative Commons Attribution-ShareAlike / CC BY - NC - SA", beside a BY-NC-SA badge.
- Who can watch
- Teens profiles and older. How courses are placed
All the lectures
- mod01lec01 - Review of Probability Theory: Random Variable
- mod01lec02 - Sequence of Random Variables
- mod01lec03 - Laws of Large Numbers and Central Limit Theorem
- mod01lec04 - What is a stochastic process?
- mod01lec05 - Counting Process
- mod01lec06 - Poisson Process-Introduction
- mod01lec07 - Poisson Process-Memorylessness
- mod01lec08 - Poisson Process-Increment properties
- mod02lec09 - Distribution of arrival epoch Sn and N(t) for a Poisson Process
- mod02lec10 - Alternate definitions of a Poisson Process
- mod02lec11 - Merging of Poisson Processes - I
- mod02lec12 - Merging of Poisson Processes - Part 2
- mod02lec13 - Splitting of Poisson Process - Part 1
- mod02lec14 - Splitting of Poisson Process - Part 2
- mod02lec15 - Example: Poisson Splitting
- mod03lec16 - Conditional arrival density and order statistics - Part 1
- mod03lec17 - Conditional arrival density and order statistics - Part 2
- mod03lec18 - Non Homogeneous Poisson Process
- mod03lec19 - Introduction to Queueing (with examples)
- mod03lec20 - Examples: Non homogeneous Poisson process
- mod03lec21 - Examples: Competing Poisson processes
- mod03lec22 - Introduction to Renewal Processes
- mod03lec23 - Strong law for renewal processes
- mod03lec24 - Strong law for renewal processes - Proof
- mod04lec25 - Residual life, age and duration (Time average) - Part 1
- mod04lec26 - Residual life, age and duration (Time average) - Part 2
- mod04lec27 - Renewal Reward Theorem (Time average) - Part 1
- mod04lec28- Renewal Reward Theorem (Time average) - Part 2
- mod04lec29 - Stopping time
- mod04lec30 - Wald's Equality
- mod04lec31 - Wald's Equality (Contd.)
- mod05lec32 - Elementary Renewal Theorem
- mod05lec33 - The Renewal Equation
- mod05lec34 - The Renewal Equation (Contd.)
- mod05lec35 - G/G/1 Queue and Little's theorem
- mod05lec36 - Little's theorem
- mod06lec37 - M/G/1 Queue
- mod06lec38 - M/G/1 Queue & PK Formula
- mod06lec39 - M/G/1 Queue & PK Formula (Contd.)
- mod06lec40 - Ensemble rewards - Age and Duration
- mod06lec41 - Ensemble rewards - Age and Duration (Contd.)
- mod06lec42 - Key Renewal Theorem & Ensemble rewards
- mod07lec43 - Introduction to finite state Discrete Time Markov Chains
- mod07lec44 - Class and Types of Classes in a DTMC
- mod07lec45 - Periodicity in a DTMC
- mod07lec46 - Matrix Representation of a DTMC
- mod07lec47 - The long term behaviour of a DTMC
- mod07lec48 - Stationary Distribution and Long term behaviour of a DTMC - Part 1
- mod07lec49 - Stationary Distribution and Long term behaviour of a DTMC - Part 2
- mod07lec50 - Stationary Distribution and Long term behaviour of a DTMC - Part 3
- mod08lec51 - Spectral Properties of Stochastic Matrices - Part 1
- mod08lec52 - Spectral Properties of Stochastic Matrices - Part 2
- mod08lec53 - The Short-term Behaviour of a DTMC
- mod08lec54 - Introduction to Countable-state DTMC
- mod08lec55 - Introduction to Countable-state DTMC (Contd)
- mod08lec56 - The Strong Markov Property
- mod09lec57 - Renewal Theory applied to DTMC's
- mod09lec58 - Stationary Distribution of a Countable State Space DTMC and Renewal Theory
- mod09lec59 - Stationary Distribution of a Countable State Space DTMC and Renewal Theory (Contd)
- mod09lec60 - Stationary Distribution and The Steady State Behaviour of a Countable-state DTMC - P1
- mod09lec61 Stationary Distribution and The Steady State Behaviour of a Countable-state DTMC - Part 2
- mod09lec62 Convergence to Steady State of a Coutable-state DTMC (Stochastic Coupling)
- mod10lec63 - The Birth-Death Markov Chains
- mod10lec64 - The Reversibility Markov Chains
- mod10lec65 - The Reversibility Markov Chains Contd...
- mod10lec66 - Time Sampled M/M/1 Queue and The Burke's Theorem
- mod10lec67 - Introduction to Continuous Time Markov Chains
- mod10lec68 - Introduction to CTMC (Contd.)
- mod11lec69 - The Steady State Behaviour of CTMC - Part 1
- mod11lec70 - The Steady State Behaviour of CTMC - Part 2
- mod11lec71 - The Steady State Behaviour of CTMC - Part 3
- mod11lec72 - The Steady State Behaviour of CTMC - Part 4
- mod11lec73 - The chapman-kolmogrov equations for CTMC's
- mod11lec74 - The Birth-Death Continuous time Markov Chains
- mod11lec75 - The Reversibility of Continuous time Markov Chains
- mod12lec76 - Burke's Theorem and the Tandem Queues - Part 1
- mod12lec77 - Burke's Theorem and the Tandem Queues - Part 2
- mod12lec78 - The Jackson Networks - Part 1
- mod12lec79 - The Jackson Networks - Part 2
- mod12lec80 - Semi Markov Processes - Part 1
- mod12lec81 - Semi Markov Processes - Part 2