# Stochastic Modeling and the Theory of Queues

- Institution: IIT Madras
- Department: Electrical Engineering
- Teacher: Prof. Krishna Jagannathan
- Level: Undergraduate
- Language: English
- Subjects: Engineering
- Source: [NPTEL](https://nptel.ac.in/courses/108106179)
- Licence: [CC BY-NC-SA](https://nptel.ac.in/faq) (Non-commercial use only.)
- Syllabus: [at the source](https://nptel.ac.in/courses/108106179)
- Who can watch: Teens profiles and older (sources give no ratings; placed by Invisible Network from the source's own words)

## Lectures

1. [mod01lec01 - Review of Probability Theory: Random Variable](https://invisiblenetwork.ai/learn/nptel/108106179/31df012aeac9) (Video)
2. [mod01lec02 - Sequence of Random Variables](https://invisiblenetwork.ai/learn/nptel/108106179/c3b23a1ed6ef) (Video)
3. [mod01lec03 - Laws of Large Numbers and Central Limit Theorem](https://invisiblenetwork.ai/learn/nptel/108106179/2ce63f449138) (Video)
4. [mod01lec04 - What is a stochastic process?](https://invisiblenetwork.ai/learn/nptel/108106179/07adc228e1a7) (Video)
5. [mod01lec05 - Counting Process](https://invisiblenetwork.ai/learn/nptel/108106179/b816d5b83084) (Video)
6. [mod01lec06 - Poisson Process-Introduction](https://invisiblenetwork.ai/learn/nptel/108106179/05ffd5105829) (Video)
7. [mod01lec07 - Poisson Process-Memorylessness](https://invisiblenetwork.ai/learn/nptel/108106179/2c8df7c6dbeb) (Video)
8. [mod01lec08 - Poisson Process-Increment properties](https://invisiblenetwork.ai/learn/nptel/108106179/4d4a41d80b47) (Video)
9. [mod02lec09 - Distribution of arrival epoch Sn and N(t) for a Poisson Process](https://invisiblenetwork.ai/learn/nptel/108106179/a61cdee455fb) (Video)
10. [mod02lec10 - Alternate definitions of a Poisson Process](https://invisiblenetwork.ai/learn/nptel/108106179/d9aca87cdbcc) (Video)
11. [mod02lec11 - Merging of Poisson Processes - I](https://invisiblenetwork.ai/learn/nptel/108106179/db322517234a) (Video)
12. [mod02lec12 - Merging of Poisson Processes - Part 2](https://invisiblenetwork.ai/learn/nptel/108106179/ec53eae09451) (Video)
13. [mod02lec13 - Splitting of Poisson Process - Part 1](https://invisiblenetwork.ai/learn/nptel/108106179/9fcb2efe539e) (Video)
14. [mod02lec14 - Splitting of Poisson Process - Part 2](https://invisiblenetwork.ai/learn/nptel/108106179/5a1b756d70c2) (Video)
15. [mod02lec15 - Example: Poisson Splitting](https://invisiblenetwork.ai/learn/nptel/108106179/6cb70ba47802) (Video)
16. [mod03lec16 - Conditional arrival density and order statistics - Part 1](https://invisiblenetwork.ai/learn/nptel/108106179/5525f1ecfb6d) (Video)
17. [mod03lec17 - Conditional arrival density and order statistics - Part 2](https://invisiblenetwork.ai/learn/nptel/108106179/70287925e4e8) (Video)
18. [mod03lec18 - Non Homogeneous Poisson Process](https://invisiblenetwork.ai/learn/nptel/108106179/27da674d7413) (Video)
19. [mod03lec19 - Introduction to Queueing (with examples)](https://invisiblenetwork.ai/learn/nptel/108106179/5e3c0bdd5420) (Video)
20. [mod03lec20 - Examples: Non homogeneous Poisson process](https://invisiblenetwork.ai/learn/nptel/108106179/71dc108e0c3b) (Video)
21. [mod03lec21 - Examples: Competing Poisson processes](https://invisiblenetwork.ai/learn/nptel/108106179/658b7b7b3e55) (Video)
22. [mod03lec22 - Introduction to Renewal Processes](https://invisiblenetwork.ai/learn/nptel/108106179/eb3940d75c3d) (Video)
23. [mod03lec23 - Strong law for renewal processes](https://invisiblenetwork.ai/learn/nptel/108106179/ba4ede44b8d1) (Video)
24. [mod03lec24 - Strong law for renewal processes - Proof](https://invisiblenetwork.ai/learn/nptel/108106179/b4d660f5af5d) (Video)
25. [mod04lec25 - Residual life, age and duration (Time average) - Part 1](https://invisiblenetwork.ai/learn/nptel/108106179/fb8b8bcc389d) (Video)
26. [mod04lec26 - Residual life, age and duration (Time average) - Part 2](https://invisiblenetwork.ai/learn/nptel/108106179/da1516a06c9c) (Video)
27. [mod04lec27 - Renewal Reward Theorem (Time average) - Part 1](https://invisiblenetwork.ai/learn/nptel/108106179/93f57d02b516) (Video)
28. [mod04lec28- Renewal Reward Theorem (Time average) - Part 2](https://invisiblenetwork.ai/learn/nptel/108106179/969bc9fabe0d) (Video)
29. [mod04lec29 - Stopping time](https://invisiblenetwork.ai/learn/nptel/108106179/bf1ca9bc4f5f) (Video)
30. [mod04lec30 - Wald's Equality](https://invisiblenetwork.ai/learn/nptel/108106179/122c6b9d388b) (Video)
31. [mod04lec31 - Wald's Equality (Contd.)](https://invisiblenetwork.ai/learn/nptel/108106179/c50e8606e5b0) (Video)
32. [mod05lec32 - Elementary Renewal Theorem](https://invisiblenetwork.ai/learn/nptel/108106179/32e51725fe81) (Video)
33. [mod05lec33 - The Renewal Equation](https://invisiblenetwork.ai/learn/nptel/108106179/8ff7ba7e6aa2) (Video)
34. [mod05lec34 - The Renewal Equation (Contd.)](https://invisiblenetwork.ai/learn/nptel/108106179/1dedb840a42e) (Video)
35. [mod05lec35 - G/G/1 Queue and Little's theorem](https://invisiblenetwork.ai/learn/nptel/108106179/2644e6809754) (Video)
36. [mod05lec36 - Little's theorem](https://invisiblenetwork.ai/learn/nptel/108106179/ad82777383e1) (Video)
37. [mod06lec37 - M/G/1 Queue](https://invisiblenetwork.ai/learn/nptel/108106179/5b6f87429a34) (Video)
38. [mod06lec38 - M/G/1 Queue & PK Formula](https://invisiblenetwork.ai/learn/nptel/108106179/e7c6000b4684) (Video)
39. [mod06lec39 - M/G/1 Queue & PK Formula (Contd.)](https://invisiblenetwork.ai/learn/nptel/108106179/788bb16b6539) (Video)
40. [mod06lec40 - Ensemble rewards - Age and Duration](https://invisiblenetwork.ai/learn/nptel/108106179/513c2262008f) (Video)
41. [mod06lec41 - Ensemble rewards - Age and Duration (Contd.)](https://invisiblenetwork.ai/learn/nptel/108106179/18ca42f26118) (Video)
42. [mod06lec42 - Key Renewal Theorem & Ensemble rewards](https://invisiblenetwork.ai/learn/nptel/108106179/a7a1b58e7366) (Video)
43. [mod07lec43 - Introduction to finite state Discrete Time Markov Chains](https://invisiblenetwork.ai/learn/nptel/108106179/6fbca6e46199) (Video)
44. [mod07lec44 - Class and Types of Classes in a DTMC](https://invisiblenetwork.ai/learn/nptel/108106179/55adf17e75df) (Video)
45. [mod07lec45 - Periodicity in a DTMC](https://invisiblenetwork.ai/learn/nptel/108106179/855a3f969603) (Video)
46. [mod07lec46 - Matrix Representation of a DTMC](https://invisiblenetwork.ai/learn/nptel/108106179/98fd9ba36e52) (Video)
47. [mod07lec47 - The long term behaviour of a DTMC](https://invisiblenetwork.ai/learn/nptel/108106179/83903e71dfd6) (Video)
48. [mod07lec48 - Stationary Distribution and Long term behaviour of a DTMC - Part 1](https://invisiblenetwork.ai/learn/nptel/108106179/4600c9416080) (Video)
49. [mod07lec49 - Stationary Distribution and Long term behaviour of a DTMC - Part 2](https://invisiblenetwork.ai/learn/nptel/108106179/d692f812b9b1) (Video)
50. [mod07lec50 - Stationary Distribution and Long term behaviour of a DTMC - Part 3](https://invisiblenetwork.ai/learn/nptel/108106179/2baab1af1ca7) (Video)
51. [mod08lec51 - Spectral Properties of Stochastic Matrices - Part 1](https://invisiblenetwork.ai/learn/nptel/108106179/956259ea6b0a) (Video)
52. [mod08lec52 - Spectral Properties of Stochastic Matrices - Part 2](https://invisiblenetwork.ai/learn/nptel/108106179/4eb24c9e2207) (Video)
53. [mod08lec53 - The Short-term Behaviour of a DTMC](https://invisiblenetwork.ai/learn/nptel/108106179/60ec63c9c2b7) (Video)
54. [mod08lec54 - Introduction to Countable-state DTMC](https://invisiblenetwork.ai/learn/nptel/108106179/e033c8f9636a) (Video)
55. [mod08lec55 - Introduction to Countable-state DTMC (Contd)](https://invisiblenetwork.ai/learn/nptel/108106179/bba5d8d9b1b2) (Video)
56. [mod08lec56 - The Strong Markov Property](https://invisiblenetwork.ai/learn/nptel/108106179/a4dff14ad5dc) (Video)
57. [mod09lec57 - Renewal Theory applied to DTMC's](https://invisiblenetwork.ai/learn/nptel/108106179/568356506468) (Video)
58. [mod09lec58 - Stationary Distribution of a Countable State Space DTMC and Renewal Theory](https://invisiblenetwork.ai/learn/nptel/108106179/1cd30405271f) (Video)
59. [mod09lec59 - Stationary Distribution of a Countable State Space DTMC and Renewal Theory (Contd)](https://invisiblenetwork.ai/learn/nptel/108106179/277ac5b0faad) (Video)
60. [mod09lec60 - Stationary Distribution and The Steady State Behaviour of a Countable-state DTMC - P1](https://invisiblenetwork.ai/learn/nptel/108106179/5d76a50877ca) (Video)
61. [mod09lec61 Stationary Distribution and The Steady State Behaviour of a Countable-state DTMC - Part 2](https://invisiblenetwork.ai/learn/nptel/108106179/57f551566ee1) (Video)
62. [mod09lec62 Convergence to Steady State of a Coutable-state DTMC (Stochastic Coupling)](https://invisiblenetwork.ai/learn/nptel/108106179/812d5edd8cfa) (Video)
63. [mod10lec63 - The Birth-Death Markov Chains](https://invisiblenetwork.ai/learn/nptel/108106179/f545a41f6c68) (Video)
64. [mod10lec64 - The Reversibility Markov Chains](https://invisiblenetwork.ai/learn/nptel/108106179/2b49937a09fc) (Video)
65. [mod10lec65 - The Reversibility Markov Chains Contd...](https://invisiblenetwork.ai/learn/nptel/108106179/cc9d5eb938cb) (Video)
66. [mod10lec66 - Time Sampled M/M/1 Queue and The Burke's Theorem](https://invisiblenetwork.ai/learn/nptel/108106179/cdffb9806784) (Video)
67. [mod10lec67 - Introduction to Continuous Time Markov Chains](https://invisiblenetwork.ai/learn/nptel/108106179/e84efdf9608e) (Video)
68. [mod10lec68 - Introduction to CTMC (Contd.)](https://invisiblenetwork.ai/learn/nptel/108106179/b6e8e0c9d164) (Video)
69. [mod11lec69 - The Steady State Behaviour of CTMC - Part 1](https://invisiblenetwork.ai/learn/nptel/108106179/c1d6630b4fa3) (Video)
70. [mod11lec70 - The Steady State Behaviour of CTMC - Part 2](https://invisiblenetwork.ai/learn/nptel/108106179/3479599720ad) (Video)
71. [mod11lec71 - The Steady State Behaviour of CTMC - Part 3](https://invisiblenetwork.ai/learn/nptel/108106179/524b07714bdd) (Video)
72. [mod11lec72 - The Steady State Behaviour of CTMC - Part 4](https://invisiblenetwork.ai/learn/nptel/108106179/3b3ab0f9b15f) (Video)
73. [mod11lec73 - The chapman-kolmogrov equations for CTMC's](https://invisiblenetwork.ai/learn/nptel/108106179/eb9ed2a14595) (Video)
74. [mod11lec74 - The Birth-Death Continuous time Markov Chains](https://invisiblenetwork.ai/learn/nptel/108106179/9151d48d8409) (Video)
75. [mod11lec75 - The Reversibility of Continuous time Markov Chains](https://invisiblenetwork.ai/learn/nptel/108106179/29a522853e45) (Video)
76. [mod12lec76 - Burke's Theorem and the Tandem Queues - Part 1](https://invisiblenetwork.ai/learn/nptel/108106179/10926a4313ff) (Video)
77. [mod12lec77 - Burke's Theorem and the Tandem Queues - Part 2](https://invisiblenetwork.ai/learn/nptel/108106179/24613c680f32) (Video)
78. [mod12lec78 - The Jackson Networks - Part 1](https://invisiblenetwork.ai/learn/nptel/108106179/40e01f321a8a) (Video)
79. [mod12lec79 - The Jackson Networks - Part 2](https://invisiblenetwork.ai/learn/nptel/108106179/fd0c1a209967) (Video)
80. [mod12lec80 - Semi Markov Processes - Part 1](https://invisiblenetwork.ai/learn/nptel/108106179/fab10a2a8017) (Video)
81. [mod12lec81 - Semi Markov Processes - Part 2](https://invisiblenetwork.ai/learn/nptel/108106179/abbbecb48ea5) (Video)