The application of engineering principles in divergent fields such as management science and communications as well as the advancement of several approaches in theory and computation have led to growing interest in queueing models, creating the need for a comprehensive text. Emphasizing Markovian structures and the techniques that occur in different models, A Course on Queueing Models discusses recent developments in the field, different methodological tools - some of which are not available elsewhere - and computational techniques.
While most books essentially address the classical methods of queueing theory, this text covers a broad range of methods both in theory and in computation. The first part of the textbook exposes you to many fundamental concepts at an introductory level and provides tools for practitioners. It discusses the basics in queueing theory for Markovian and regenerative non-Markovian models, statistical inference, simulation and some computational procedures, network and discrete-time queues, algebraic and combinatorial methods, and optimization. The second part delves deeper into the topics examined in the first part by presenting more advanced methods. This part also includes general queues, duality in queues, and recent advancements on computational methods and discrete-time queues. Each chapter contains a discussion section that summarizes material and highlights special features.
Incorporating different queueing models, A Course on Queueing Models achieves an ideal balance between theory and practice, making it compatible for advanced undergraduate and graduate students, applied statisticians, and engineers.
Table of Contents
QUEUES: BASIC CONCEPTS
Queues: Features and Characteristics
Scope and Organization
A Simple Model: Steady-State Behaviour
Birth-Death Models: Steady-State Behaviour
Erlangian Models: Steady-State Behaviour
Waiting Time and Little's Formula
Busy Periods and Idle Periods 3
Networks of Queues - I
REGENERATIVE NON-MARKOVIAN QUEUES - I
Markovian Input Models
Markovian Service-Time Models
Functional Relations: A Heuristic Approach
COMPUTATIONAL METHODS - I
Root Finding Methods
The State Reduction Method
Transient Behaviour: Numerical Approaches
STATISTICAL INFERENCE AND SIMULATION
Solving Queueing Problems by Simulation
A Practical Application
REGENERATIVE NON-MARKOVIAN QUEUES - II
Non-Markovian Queues: Transient Solution
Waiting Time and Idle Time: An Analytic Method
Bounds for the Average Waiting Time
A Heavy Traffic Approximation
Waiting Time and Idle Time: A Probabilistic Method
COMPUTATIONAL METHODS - II
The Matrix-Geometric Solution
The Block Elimination Method
The Fourier Series Method for Inverting Transforms
DISCRETE-TIME QUEUES: TRANSIENT SOLUTIONS
Combinatorial Methods: Lattice Path Approach
Queues with Infinite Servers
Design and Control of Queues
Networks of Queues II
Each chapter includes exercises and references.
"…This text is evidence of the inroads engineering is making, covering a broad range of theory and applications and emphasizing Markovian structures and the techniques of different models. The bank of international authors cover the basics of queues … . Each chapter includes exercises and the authors provide appendices with basic information on such topics as random variables, stochastic processes, and statistical processes."
-SciTech Book News, June 2007
". .. those whose job it is to solve practical queuing problems will find this an excellent and well-documented source of general solution methods. The chapters on exact computational approaches are particularly useful . . . Given the clarity of exposition and the careful organization of the book, I would certainly recommend it for student use. It would also be a useful reference source for researchers."
– B. Atkinson, University of North London, in Journal of the Operational Research Society, 2008, Vol. 59