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Course11110315950 lectures

Introduction To Queueing Theory

Prof. N. Selvaraju · IIT Guwahati

Start with lecture 1 At NPTEL

Lectures

week-00

  1. Prerequisite: Review of Probability Video

Week-01: Introduction to Queues

  1. Lec 1: Queueing Systems, System Performance Measures Video
  2. Lec 2: Characteristics of Queueing Systems, Kendall's Notation Video
  3. Lec 3: Little's Law, General Relationships Video
  4. Lec 4: Laplace and Laplace-Stieltjes Transforms, Probability Generating Functions Video

Week-02: Discrete-Time Markov Chains

  1. Lec 5: An Overview of Stochastic Processes Video
  2. Lec 6: Markov Chains: Definition, Transition Probabilities Video
  3. Lec 7: Classification Properties of Markov Chains Video
  4. Lec 8: Long-Term Behaviour of Markov Chains Video

Week-03: Continuous-Time Markov Chains

  1. Lec 9: Exponential Distribution and its Properties, Poisson Process Video
  2. Lec 10: Poisson Process and its Properties, Generalizations Video
  3. Lec 11: Continuous-Time Markov Chains, Generator Matrix, Kolmogorov Equations Video
  4. Lec 12: Stationary and Limiting Distributions of CTMC, Balance Equations, Birth-Death Processes Video

Week-04: Birth-Death Queueing Systems

  1. Lec 13: Birth-Death Queues: General Theory, M/M/1 Queues and their Steady State Solution Video
  2. Lec 14: M/M/1 Queues: Performance Measures, PASTA Property, Waiting Time Distributions Video
  3. Lec 15: M/M/c Queues, Erlang Delay Formula Video
  4. Lec 16: M/M/c/K Queues Video

Week-05: Birth-Death Queueing Systems (contd...)

  1. Lec 17: Erlang's Loss System, Erlang Loss Formula, Infinite-Server Queues Video
  2. Lec 18: Finite-Source Queues, Engset Loss System, State-Dependent Queues, Queues with Impatience Video
  3. Lec 19: Transient Solutions: M/M/1/1, Infinite-Server and M/M/1 Queues, Busy Period Analysis Video

Week-06: General Markovian Queueing Systems

  1. Lec 20: Queues with Bulk Arrivals Video
  2. Lec 21: Queues with Bulk Service Video
  3. Lec 22: Erlang and Phase-Type Distributions Video
  4. Lec 23: Erlangian Queues: Erlangian Arrivals, Erlangian Service Times Video

Week-07: General Markovian Queueing Systems (contd...)

  1. Lec 24: Nonpreemptive Priority Queues Video
  2. Lec 25: Nonpreemptive and Preemptive Priority Queues Video
  3. Lec 26: M/M/1 Retrial Queues Video
  4. Lec 27: Discrete-Time Queues: Geo/Geo/1 (EAS), Geo/Geo/1 (LAS) Video

Week-08: Queueing Networks

  1. Lec 28: Introduction to Queueing Networks, Two-Node Network Video
  2. Lec 29: Burke's Theorem, General Setup, Tandem Networks Video
  3. Lec 30: Queueing Networks with Blocking, Open Jackson Networks Video
  4. Lec 31: Waiting Times and Multiple Classes in Open Jackson Networks Video

Week-09: Queueing Networks (contd...)

  1. Lec 32: Closed Jackson Networks Video
  2. Lec 33: Closed Jackson Networks, Convolution Algorithm Video
  3. Lec 34: Mean-Value Analysis Algorithm Video
  4. Lec 35: Cyclic Queueing Networks, Extensions of Jackson Networks Video

Week-10: Semi-Markovian Queueing Systems

  1. Lec 36: Renewal Processes Video
  2. Lec 37: Regenerative Processes, Semi-Markov Processes Video
  3. Lec 38: M/G/1 Queues, The Pollaczek-Khinchin Mean Formula Video
  4. Lec 39: M/G/1 Queues, The Pollaczek-Khinchin Transform Formula Video

Week-11: Semi-Markovian Queueing Systems (contd...)

  1. Lec 40: M/G/1 Queues: Waiting Times and Busy Period Video
  2. Lec 41: M/G/1/K Queues, Additional Insights on M/G/1 Queues Video
  3. Lec 42: M/G/c, M/G/∞ and M/G/c/c Queues Video
  4. Lec 43: G/M/1 Queues Video

Week-12: General Queueing Systems

  1. Lec 44: G/G/1 Queues: Lindley's Integral Equation Video
  2. Lec 45: G/G/1 Queues: Bounds Video
  3. Lec 46: Vacation Queues: Introduction, M/M/1 Queues with Vacations Video
  4. Lec 47: M/G/1 Queues with Vacations Video

Live Session

  1. Live Session 21-02-2022 Video
  2. Live Session 17-03-2022 Video

Syllabus and materials

At NPTEL, as the course publishes them.

Credits and licence

Institution
IIT Guwahati
Department
Mathematics
Teacher
Prof. N. Selvaraju
Level
Undergraduate
Language
English
Subjects
Mathematics
Source
NPTEL
Licence
CC BY-NC-SA, as NPTEL states it. Non-commercial use only. NPTEL's terms
Attribution
NPTEL states: "Distributed under Creative Commons Attribution-ShareAlike / CC BY - NC - SA", beside a BY-NC-SA badge.
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