NPTEL : NOC:Stochastic Modeling and the Theory of Queues (Electrical Engineering)

Co-ordinators : Prof. Krishna Jagannathan


Lecture 1 - Review of Probability Theory: Random Variable

Lecture 2 - Sequence of Random Variables

Lecture 3 - Laws of Large Numbers and Central Limit Theorem

Lecture 4 - What is a stochastic process?

Lecture 5 - Counting Process

Lecture 6 - Poisson Process - Introduction

Lecture 7 - Poisson Process - Memorylessness

Lecture 8 - Poisson Process - Increment properties

Lecture 9 - Distribution of arrival epoch Sn and N(t) for a Poisson Process

Lecture 10 - Alternate definitions of a Poisson Process

Lecture 11 - Merging of Poisson Processes - Part 1

Lecture 12 - Merging of Poisson Processes - Part 2

Lecture 13 - Splitting of Poisson Process - Part 1

Lecture 14 - Splitting of Poisson Process - Part 2

Lecture 15 - Example: Poisson Splitting

Lecture 16 - Conditional arrival density and order statistics - Part 1

Lecture 17 - Conditional arrival density and order statistics - Part 2

Lecture 18 - Non Homogeneous Poisson Process

Lecture 19 - Introduction to Queueing (with examples)

Lecture 20 - Examples: Non homogeneous Poisson process

Lecture 21 - Examples: Competing Poisson processes

Lecture 22 - Introduction to Renewal Processes

Lecture 23 - Strong law for renewal processes

Lecture 24 - Strong law for renewal processes - Proof

Lecture 25 - Residual life, age and duration (Time average) - Part 1

Lecture 26 - Residual life, age and duration (Time average) - Part 2

Lecture 27 - Renewal Reward Theorem (Time average) - Part 1

Lecture 28 - Renewal Reward Theorem (Time average) - Part 2

Lecture 29 - Stopping time

Lecture 30 - Wald's Equality

Lecture 31 - Wald's Equality (Continued...)

Lecture 32 - Elementary Renewal Theorem

Lecture 33 - The Renewal Equation

Lecture 34 - The Renewal Equation (Continued...)

Lecture 35 - G/G/1 Queue and Little's theorem

Lecture 36 - Little's theorem

Lecture 37 - M/G/1 Queue

Lecture 38 - M/G/1 Queue and PK Formula

Lecture 39 - M/G/1 Queue and PK Formula (Continued...)

Lecture 40 - Ensemble rewards - Age and Duration

Lecture 41 - Ensemble rewards - Age and Duration (Continued...)

Lecture 42 - Key Renewal Theorem and Ensemble rewards

Lecture 43 - Introduction to finite state Discrete Time Markov Chains

Lecture 44 - Class and Types of Classes in a DTMC

Lecture 45 - Periodicity in a DTMC

Lecture 46 - Matrix Representation of a DTMC

Lecture 47 - The long term behaviour of a DTMC

Lecture 48 - Stationary Distribution and Long term behaviour of a DTMC - Part 1

Lecture 49 - Stationary Distribution and Long term behaviour of a DTMC - Part 2

Lecture 50 - Stationary Distribution and Long term behaviour of a DTMC - Part 3

Lecture 51 - Spectral Properties of Stochastic Matrices - Part 1

Lecture 52 - Spectral Properties of Stochastic Matrices - Part 2

Lecture 53 - The Short-term Behaviour of a DTMC

Lecture 54 - Introduction to Countable-state DTMC

Lecture 55 - Introduction to Countable-state DTMC (Continued...)

Lecture 56 - The Strong Markov Property

Lecture 57 - Renewal Theory applied to DTMC's

Lecture 58 - Stationary Distribution of a Countable State Space DTMC and Renewal Theory

Lecture 59 - Stationary Distribution of a Countable State Space DTMC and Renewal Theory (Continued...)

Lecture 60 - Stationary Distribution and The Steady State Behaviour of a Countable-state DTMC - Part 1

Lecture 61 - Stationary Distribution and The Steady State Behaviour of a Countable-state DTMC - Part 2

Lecture 62 - Convergence to Steady State of a Coutable-state DTMC (Stochastic Coupling)

Lecture 63 - The Birth-Death Markov Chains

Lecture 64 - The Reversibility Markov Chains

Lecture 65 - The Reversibility Markov Chains (Continued...)

Lecture 66 - Time Sampled M/M/1 Queue and The Burke's Theorem

Lecture 67 - Introduction to Continuous Time Markov Chains

Lecture 68 - Introduction to CTMC (Continued...)

Lecture 69 - The Steady State Behaviour of CTMC - Part 1

Lecture 70 - The Steady State Behaviour of CTMC - Part 2

Lecture 71 - The Steady State Behaviour of CTMC - Part 3

Lecture 72 - The Steady State Behaviour of CTMC - Part 4

Lecture 73 - The chapman-kolmogrov equations for CTMC's

Lecture 74 - The Birth-Death Continuous time Markov Chains

Lecture 75 - The Reversibility of Continuous time Markov Chains

Lecture 76 - Burke's Theorem and the Tandem Queues - Part 1

Lecture 77 - Burke's Theorem and the Tandem Queues - Part 2

Lecture 78 - The Jackson Networks - Part 1

Lecture 79 - The Jackson Networks - Part 2

Lecture 80 - Semi Markov Processes - Part 1

Lecture 81 - Semi Markov Processes - Part 2