Analysis of Queues : Methods and Applications book cover
1st Edition

Analysis of Queues
Methods and Applications

ISBN 9781138073067
Published March 29, 2017 by CRC Press
802 Pages 141 B/W Illustrations

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Book Description

Written with students and professors in mind, Analysis of Queues: Methods and Applications combines coverage of classical queueing theory with recent advances in studying stochastic networks. Exploring a broad range of applications, the book contains plenty of solved problems, exercises, case studies, paradoxes, and numerical examples.

In addition to the standard single-station and single class discrete queues, the book discusses models for multi-class queues and queueing networks as well as methods based on fluid scaling, stochastic fluid flows, continuous parameter Markov processes, and quasi-birth-and-death processes, to name a few. It describes a variety of applications including computer-communication networks, information systems, production operations, transportation, and service systems such as healthcare, call centers and restaurants.

Table of Contents

Analysis of Queues: Where, What, and How?
Systems Analysis: Key Results
Queueing Fundamentals and Notations
Psychology in Queueing
Reference Notes

Exponential Interarrival and Service Times: Closed-Form Expressions
Solving Balance Equations via Arc Cuts
Solving Balance Equations Using Generating Functions
Solving Balance Equations Using Reversibility
Reference Notes

Exponential Interarrival and Service Times: Numerical Techniques and Approximations
Multidimensional Birth and Death Chains
Multidimensional Markov Chains
Finite-State Markov Chains
Reference Notes

General Interarrival and/or Service Times: Closed-Form Expressions and Approximations
Analyzing Queues Using Discrete Time Markov Chains
Mean Value Analysis
Bounds and Approximations for General Queues
Matrix Geometric Methods for G/G/s Queues
Other General Queues but with Exact Results
Reference Notes

Multiclass Queues under Various Service Disciplines
Evaluating Policies for Classification Based on Types: Priorities
Evaluating Policies for Classification Based on Location: Polling Models
Evaluating Policies for Classification Based on Knowledge of Service Times
Optimal Service-Scheduling Policies
Reference Notes

Exact Results in Network of Queues: Product Form
Acyclic Queueing Networks with Poisson Flows
Open Jackson Networks
Closed Jackson Networks
Other Product-Form Networks
Reference Notes

Approximations for General Queueing Networks
Single-Server and Single-Class General Queueing Networks
Multiclass and Multiserver Open Queueing Networks with FCFS
Multiclass and Single-Server Open Queueing Networks with Priorities
Reference Notes

Fluid Models for Stability, Approximations, and Analysis of Time-Varying Queues
Deterministic Fluid Queues: An Introduction
Fluid Models for Stability Analysis of Queueing Networks
Diffusion Approximations for Performance Analysis
Fluid Models for Queues with Time-Varying Parameters
Reference Notes

Stochastic Fluid-Flow Queues: Characteristics and Exact Analysis
Single Buffer with Markov Modulated Fluid Source
First Passage Times
Reference Notes

Stochastic Fluid-Flow Queues: Bounds and Tail Asymptotics
Introduction and Preliminaries
Performance Analysis of a Single Queue
Multiclass Fluid Queues
Reference Notes

Appendix A: Random Variables
Appendix B: Stochastic Processes

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