Introduction to Queueing Theory (English)

   Saturday, April 06, 2024   

Starting a new Lecture Notes Series on Introduction to Queueing Theory

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Introduction to Queueing Theory By Lecture Notes together!

Lecture 1: Introduction to Queueing Theory

Lecture 2: Prerequisite: Review of Probability

Lecture 3: Lec 1: Queueing Systems, System Performance Measures

Lecture 4: Lec 2: Characteristics of Queueing Systems, Kendall's Notation

Lecture 5: Lec 3: Little's Law, General Relationships

Lecture 6: Lec 4: Laplace and Laplace-Stieltjes Transforms, Probability Generating Functions

Lecture 7: Lec 5: An Overview of Stochastic Processes

Lecture 8: Lec 6: Markov Chains: Definition, Transition Probabilities

Lecture 9: Lec 7: Classification Properties of Markov Chains

Lecture 10: Lec 8: Long-Term Behaviour of Markov Chains

Lecture 11: Lec 9: Exponential Distribution and its Properties, Poisson Process

Lecture 12: Lec 10: Poisson Process and its Properties, Generalizations

Lecture 13: Lec 11: Continuous-Time Markov Chains, Generator Matrix, Kolmogorov Equations

Lecture 14: Lec 12: Stationary and Limiting Distributions of CTMC, Balance Equations, Birth-Death Processes

Lecture 15: Lec 13: Birth-Death Queues: General Theory, M/M/1 Queues and their Steady State Solution

Lecture 16: Lec 14: M/M/1 Queues: Performance Measures, PASTA Property, Waiting Time Distributions

Lecture 17: Lec 15: M/M/c Queues, Erlang Delay Formula

Lecture 18: Lec 16: M/M/c/K Queues

Lecture 19: Lec 17: Erlang's Loss System, Erlang Loss Formula, Infinite-Server Queues

Lecture 20: Lec 18: Finite-Source Queues, Engset Loss System, State-Dependent Queues, Queues with Impatience

Lecture 21: Lec 19: Transient Solutions: M/M/1/1, Infinite-Server and M/M/1 Queues, Busy Period Analysis

Lecture 22: Lec 20: Queues with Bulk Arrivals

Lecture 23: Lec 21: Queues with Bulk Service

Lecture 24: Lec 22: Erlang and Phase-Type Distributions

Lecture 25: Lec 23: Erlangian Queues: Erlangian Arrivals, Erlangian Service Times

Lecture 26: Lec 24: Nonpreemptive Priority Queues

Lecture 27: Lec 25: Nonpreemptive and Preemptive Priority Queues

Lecture 28: Lec 26: M/M/1 Retrial Queues

Lecture 29: Lec 27: Discrete-Time Queues: Geo/Geo/1 (EAS), Geo/Geo/1 (LAS)s

Lecture 30: Lec 28: Introduction to Queueing Networks, Two-Node Network

Lecture 31: Lec 29: Burke's Theorem, General Setup, Tandem Networks

Lecture 32: Lec 30: Queueing Networks with Blocking, Open Jackson Networks

Lecture 33: Lec 31: Waiting Times and Multiple Classes in Open Jackson Networks

Lecture 34: Lec 32: Closed Jackson Networks

Lecture 35: Lec 33: Closed Jackson Networks, Convolution Algorithm

Lecture 36: Lec 34: Mean-Value Analysis Algorithm

Lecture 37: Lec 35: Cyclic Queueing Networks, Extensions of Jackson Networks

Lecture 38: Lec 36: Renewal Processes

Lecture 39: Lec 37: Regenerative Processes, Semi-Markov Processes

Lecture 40: Lec 38: M/G/1 Queues, The Pollaczek-Khinchin Mean Formula

Lecture 41: Lec 39: M/G/1 Queues, The Pollaczek-Khinchin Transform Formula

Lecture 42: Lec 40: M/G/1 Queues: Waiting Times and Busy Period

Lecture 43: Lec 41: M/G/1/K Queues, Additional Insights on M/G/1 Queues

Lecture 44: Lec 42: M/G/c, M/G/∞ and M/G/c/c Queues

Lecture 45: Lec 43: G/M/1 Queues

Lecture 46: Lec 44: G/G/1 Queues: Lindley's Integral Equation

Lecture 47: Lec 45: G/G/1 Queues: Bounds

Lecture 48: Lec 46: Vacation Queues: Introduction, M/M/1 Queues with Vacations

Lecture 49: Lec 47: M/G/1 Queues with Vacations