Fundamentals of queueing theory

Table of Content

Introduction.

• Description of the Queueing Problem.

• Characteristics of Queueing Processes.

• Notation.

• Measuring System Performance.

• Some General Results.

• Simple Data Bookkeeping for Queues.

• Poisson Process and the Exponential Distribution.

• Markovian Property of the Exponential Distribution.

• Stochastic Processes and Markov Chains.

Problems.



Simple Markovian Queueing Models.

• Birth Death Processes.

• Single-Server Queues (M/M/1).

• Multi-Server Queues (M/M/c).

• Choosing the Number of Servers.

• Queues with Truncation (M/M/c/K).

• Erlang?s Loss Formula (M/M/c/c).

• Queues with Unlimited Service (M/M/1).

• Finite Source Queues.

• State-Dependent Service.

• Queues with Impatience.

• Transient Behavior.

• Busy-Period Analysis.

Problems.



Advanced Markovian Queueing Models.

• Bulk Input (M[X]/M/1).

• Bulk Service (M/M[Y ]/1).

• Erlangian Models.

• Priority Queue Disciplines.

• Retrial Queues.



Networks, Series, and Cyclic Queues.

• Series Queues.

• Open Jackson Networks.

• Closed Jackson Networks.

• Cyclic Queues.

• Extensions of Jackson Networks.

• Non-Jackson Networks.



General Arrival or Service Patterns.

• General Service, Single Server (M/G/1).

• General Service, Multi-Server (M/G/c/ú, M/G/1).

• General Input (G/M/1, G/M/c).



More General Models and Theoretical Topics.

• G/Ek/1, G[k]/M/1, and G/PHk/1.

• General Input, General Service (G/G/1) .

• Multichannel Queues with Poisson Input and Constant Service (M/D/c).

• Semi-Markov and Markov Renewal Processes in Queueing.

• Other Queue Disciplines.

• Design and Control of Queues.

• Statistical Inference in Queueing.



Bounds and Approximations.

• Bounds.

• Approximations.

• Network Approximations.

Problems.



Numerical Techniques and Simulation.

• Numerical Techniques.

• Numerical Inversion of Transforms.

• Discrete-Event Stochastic Simulation.

Problems.



Bibliography.

Appendix 1. Symbols and Abbreviations.

Appendix 2. Tables.

Appendix 3. Transforms and Generating Functions.

Appendix 4. Differential and Difference Equations.

Appendix 5. QTSPlus Software.

This revised and expanded edition of Fundamentals of Queueing Theory presents the analytic modeling of queues using up-to-date examples. Though the detailed coverage of the fundamentals of analytic modeling remains virtually the same, this new edition contains additional material (call centers and simulation), discussions (Transform Approximation Method and Level Crossing Analysis), and exercises. A fresh emphasis on the telecommunications boom enlivens the text, and spreadsheet programs for Excel and Quattro on the book's related Web site aids in understanding the sensitivity of waiting-line systems to parameter and environmental changes. Software programs for additional systems are spread throughout the text. In the treatment of the advanced material, the authors have commingled mathematical details with numerical results and intuitive arguments.