NOC:Stochastic Modeling and the Theory of Queues

Media Storage Type : 32 GB USB Stick

NPTEL Subject Matter Expert : Prof. Krishna Jagannathan

NPTEL Co-ordinating Institute : IIT Madras

NPTEL Lecture Count : 81

NPTEL Course Size : 5.8 GB

NPTEL PDF Text Transcription : Available and Included

NPTEL Subtitle Transcription : Available and Included (SRT)

Lecture Titles:

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