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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.
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.
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