While most texts address only the classical methods of queuing theory, "A Course on Queuing Theory" also covers fundamentals, such as Markovian and regenerative non-Markovian models, as well as computational methods, statistical inference, and simulation. The authors integrate different models to emphasize the Markovian structure and present detailed descriptions of network queues, discrete time queues, and optimization as well as advanced topics, including combinatorial treatments in transient analysis, general queues, duality in queues, and new computational methods. Each self-contained chapter features a discussion section that summarizes material and makes connections within the text.
QUEUES: BASIC CONCEPTS
Introduction
Queues: Features and Characteristics
Graphical Methods
Modelling
Scope and Organization
MARKOVIAN QUEUES
Introduction
A Simple Model: Steady-State Behaviour
Birth-Death Models: Steady-State Behaviour
Erlangian Models: Steady-State Behaviour
Transient Behaviour
Waiting Time and Little's Formula
Busy Periods and Idle Periods 3
Networks of Queues - I
Optimization
Discussion
REGENERATIVE NON-MARKOVIAN QUEUES - I
Introduction
Markovian Input Models
Markovian Service-Time Models
Bulk Queues
Functional Relations: A Heuristic Approach
Busy Periods
Discrete-Time Queues
Discussion
COMPUTATIONAL METHODS - I
Introduction
Root Finding Methods
The State Reduction Method
Transient Behaviour: Numerical Approaches
Discussion
STATISTICAL INFERENCE AND SIMULATION
Introduction
Statistical Inference
Solving Queueing Problems by Simulation
A Practical Application
Discussion
REGENERATIVE NON-MARKOVIAN QUEUES - II
Introduction
Non-Markovian Queues: Transient Solution
Combinatorial Methods
Functional Relations
Discussion
GENERAL QUEUES
Introduction
Waiting Time and Idle Time: An Analytic Method
Bounds for the Average Waiting Time
A Heavy Traffic Approximation
Diffusion Approximation
Waiting Time and Idle Time: A Probabilistic Method
Duality
Discussion
COMPUTATIONAL METHODS - II
Introduction
The Matrix-Geometric Solution
The Block Elimination Method
The Fourier Series Method for Inverting Transforms
Discussion
DISCRETE-TIME QUEUES: TRANSIENT SOLUTIONS
Introduction
Combinatorial Methods: Lattice Path Approach
Recurrence Relations
Algebraic Methods
Discussion
MISCELLANEOUS TOPICS
Introduction
Priority Queues
Queues with Infinite Servers
Design and Control of Queues
Networks of Queues II
Discussion
APPENDICES
INDEX
Each chapter includes exercises and references.
