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Optimal Design of Queueing Systems




ISBN 9781584880769
Published March 27, 2009 by Chapman and Hall/CRC
384 Pages - 75 B/W Illustrations

 
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Book Description

The First Comprehensive Book on the Subject

Focusing on the underlying structure of a system, Optimal Design of Queueing Systems explores how to set the parameters of a queueing system, such as arrival and service rates, before putting it into operation. It considers various objectives, comparing individually optimal (Nash equilibrium), socially optimal, class optimal, and facility optimal flow allocations.

After an introduction to basic design models, the book covers the optimal arrival rate model for a single-facility, single-class queue as well as dynamic algorithms for finding individually or socially optimal arrival rates and prices. It then examines several special cases of multiclass queues, presents models in which the service rate is a decision variable, and extends models and techniques to multifacility queueing systems. Focusing on networks of queues, the final chapters emphasize the qualitative properties of optimal solutions.

Written by a long-time, recognized researcher on models for the optimal design and control of queues and networks of queues, this book frames the issues in the general setting of a queueing system. It shows how design models can control flow to achieve a variety of objectives.

Table of Contents

Preface

Introduction to Design Models

Optimal Service Rate

Optimal Arrival Rate

Optimal Arrival Rate and Service Rate

Optimal Arrival Rates for a Two-Class System

Optimal Arrival Rates for Parallel Queues

Optimal Arrival Rates in a Single-Class Queue

A Model with General Utility and Cost Functions

Generalizations of Basic Model

GI/GI/1 Queue with Probabilistic Joining Rule

Uniform Value Distribution: Stability

Power Criterion

Bidding for Priorities

Dynamic Adaptive Algorithms: Stability and Chaos

Basic Model

Discrete-Time Dynamic Adaptive Model

Discrete-Time Dynamic Algorithms: Variants

Continuous-Time Dynamic Adaptive Algorithms

Continuous-Time Dynamic Algorithm: Variants

Optimal Arrival Rates in a Multiclass Queue

General Multiclass Model: Formulation

General Multiclass Model: Optimal Solutions

General Multiclass Model: Dynamic Algorithms

Waiting Costs Dependent on Total Arrival Rate

Linear Utility Functions: Class Dominance

Examples with Different Utility Functions

Multiclass Queue with Priorities

Figures for FIFO Examples

Optimal Service Rates in a Single-Class Queue

The Basic Model

Models with Fixed Toll and Fixed Arrival Rate

Models with Variable Toll and Fixed Arrival Rate

Models with Fixed Toll and Variable Arrival Rate

Models with Variable Toll and Variable Arrival Rate

Multifacility Queueing Systems: Parallel Queues

Optimal Arrival Rates

Optimal Service Rates

Optimal Arrival Rates and Service Rates

Single-Class Networks of Queues

Basic Model

Individually Optimal Arrival Rates and Routes

Socially Optimal Arrival Rates and Routes

Comparison of S.O. and Toll-Free I.O. Solutions

Facility Optimal Arrival Rates and Routes

Multiclass Networks of Queues

General Model

Fixed Routes: Optimal Solutions

Fixed Routes: Dynamic Adaptive Algorithms

Fixed Routes: Homogeneous Waiting Costs

Variable Routes: Homogeneous Waiting Costs

Appendix: Scheduling a Single-Server Queue

Strong Conservation Laws

Work-Conserving Scheduling Systems

GI/GI/1 WCSS with Non-Preemptive Scheduling Rules

GI/GI/1 Queue: Preemptive-Resume Scheduling Rules

References

Index

Endnotes appear in each chapter.

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