Learn · Introduction To Queueing Theory

Lecture 6 of 50Week-02: Discrete-Time Markov Chains

Lec 5: An Overview of Stochastic Processes

Prof. N. Selvaraju · IIT Guwahati

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From
Introduction To Queueing Theory, IIT Guwahati (at NPTEL)
Licence
CC BY-NC-SA, as NPTEL states it. Non-commercial use only.
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NPTEL states: "Distributed under Creative Commons Attribution-ShareAlike / CC BY - NC - SA", beside a BY-NC-SA badge.
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All the lectures

  1. Prerequisite: Review of Probability Video
  2. Lec 1: Queueing Systems, System Performance Measures Video
  3. Lec 2: Characteristics of Queueing Systems, Kendall's Notation Video
  4. Lec 3: Little's Law, General Relationships Video
  5. Lec 4: Laplace and Laplace-Stieltjes Transforms, Probability Generating Functions Video
  6. Lec 5: An Overview of Stochastic Processes Video
  7. Lec 6: Markov Chains: Definition, Transition Probabilities Video
  8. Lec 7: Classification Properties of Markov Chains Video
  9. Lec 8: Long-Term Behaviour of Markov Chains Video
  10. Lec 9: Exponential Distribution and its Properties, Poisson Process Video
  11. Lec 10: Poisson Process and its Properties, Generalizations Video
  12. Lec 11: Continuous-Time Markov Chains, Generator Matrix, Kolmogorov Equations Video
  13. Lec 12: Stationary and Limiting Distributions of CTMC, Balance Equations, Birth-Death Processes Video
  14. Lec 13: Birth-Death Queues: General Theory, M/M/1 Queues and their Steady State Solution Video
  15. Lec 14: M/M/1 Queues: Performance Measures, PASTA Property, Waiting Time Distributions Video
  16. Lec 15: M/M/c Queues, Erlang Delay Formula Video
  17. Lec 16: M/M/c/K Queues Video
  18. Lec 17: Erlang's Loss System, Erlang Loss Formula, Infinite-Server Queues Video
  19. Lec 18: Finite-Source Queues, Engset Loss System, State-Dependent Queues, Queues with Impatience Video
  20. Lec 19: Transient Solutions: M/M/1/1, Infinite-Server and M/M/1 Queues, Busy Period Analysis Video
  21. Lec 20: Queues with Bulk Arrivals Video
  22. Lec 21: Queues with Bulk Service Video
  23. Lec 22: Erlang and Phase-Type Distributions Video
  24. Lec 23: Erlangian Queues: Erlangian Arrivals, Erlangian Service Times Video
  25. Lec 24: Nonpreemptive Priority Queues Video
  26. Lec 25: Nonpreemptive and Preemptive Priority Queues Video
  27. Lec 26: M/M/1 Retrial Queues Video
  28. Lec 27: Discrete-Time Queues: Geo/Geo/1 (EAS), Geo/Geo/1 (LAS) Video
  29. Lec 28: Introduction to Queueing Networks, Two-Node Network Video
  30. Lec 29: Burke's Theorem, General Setup, Tandem Networks Video
  31. Lec 30: Queueing Networks with Blocking, Open Jackson Networks Video
  32. Lec 31: Waiting Times and Multiple Classes in Open Jackson Networks Video
  33. Lec 32: Closed Jackson Networks Video
  34. Lec 33: Closed Jackson Networks, Convolution Algorithm Video
  35. Lec 34: Mean-Value Analysis Algorithm Video
  36. Lec 35: Cyclic Queueing Networks, Extensions of Jackson Networks Video
  37. Lec 36: Renewal Processes Video
  38. Lec 37: Regenerative Processes, Semi-Markov Processes Video
  39. Lec 38: M/G/1 Queues, The Pollaczek-Khinchin Mean Formula Video
  40. Lec 39: M/G/1 Queues, The Pollaczek-Khinchin Transform Formula Video
  41. Lec 40: M/G/1 Queues: Waiting Times and Busy Period Video
  42. Lec 41: M/G/1/K Queues, Additional Insights on M/G/1 Queues Video
  43. Lec 42: M/G/c, M/G/∞ and M/G/c/c Queues Video
  44. Lec 43: G/M/1 Queues Video
  45. Lec 44: G/G/1 Queues: Lindley's Integral Equation Video
  46. Lec 45: G/G/1 Queues: Bounds Video
  47. Lec 46: Vacation Queues: Introduction, M/M/1 Queues with Vacations Video
  48. Lec 47: M/G/1 Queues with Vacations Video
  49. Live Session 21-02-2022 Video
  50. Live Session 17-03-2022 Video