NPTEL : NOC:Introduction to Queueing Theory (Mathematics)

Co-ordinators : Prof. N. Selvaraju


Lecture 0 - Prerequisite: Review of Probability

Lecture 1 - Queueing Systems, System Performance Measures

Lecture 2 - Characteristics of Queueing Systems, Kendall's Notation

Lecture 3 - Little's Law, General Relationships

Lecture 4 - Laplace and Laplace-Stieltjes Transforms, Probability Generating Functions

Lecture 5 - An Overview of Stochastic Processes

Lecture 6 - Markov Chains: Definition, Transition Probabilities

Lecture 7 - Classification Properties of Markov Chains

Lecture 8 - Long-Term Behaviour of Markov Chains

Lecture 9 - Exponential Distribution and its Properties, Poisson Process

Lecture 10 - Poisson Process and its Properties, Generalizations

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

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

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

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

Lecture 15 - M/M/c Queues, Erlang Delay Formula

Lecture 16 - M/M/c/K Queues

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

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

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

Lecture 20 - Queues with Bulk Arrivals

Lecture 21 - Queues with Bulk Service

Lecture 22 - Erlang and Phase-Type Distributions

Lecture 23 - Erlangian Queues: Erlangian Arrivals, Erlangian Service Times

Lecture 24 - Nonpreemptive Priority Queues

Lecture 25 - Nonpreemptive and Preemptive Priority Queues

Lecture 26 - M/M/1 Retrial Queues

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

Lecture 28 - Introduction to Queueing Networks, Two-Node Network

Lecture 29 - Burke's Theorem, General Setup, Tandem Networks

Lecture 30 - Queueing Networks with Blocking, Open Jackson Networks

Lecture 31 - Waiting Times and Multiple Classes in Open Jackson Networks

Lecture 32 - Closed Jackson Networks

Lecture 33 - Closed Jackson Networks, Convolution Algorithm

Lecture 34 - Mean-Value Analysis Algorithm

Lecture 35 - Cyclic Queueing Networks, Extensions of Jackson Networks

Lecture 36 - Renewal Processes

Lecture 37 - Regenerative Processes, Semi-Markov Processes

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

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

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

Lecture 41 - M/G/1/K Queues, Additional Insights on M/G/1 Queues

Lecture 42 - M/G/c, M/G/∞ and M/G/c/c Queues

Lecture 43 - G/M/1 Queues

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

Lecture 45 - G/G/1 Queues: Bounds

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

Lecture 47 - M/G/1 Queues with Vacations