Optimal Design of Queueing Systems

by Stidham Jr.; Shaler

• ISBN13: 9781584880769
• ISBN10: 1584880767
• Edition: 1st
• Format: Hardcover
• Copyright: 2009-03-27
• Publisher: Chapman & Hall/

Summary

Over the last 30 years, research on optimal design and control of queuing systems has flowered. Although many books exist on descriptive queuing theory, until now, none has addressed the topic from the perspective of optimization. Emphasizing economic interpretation of the output of optimization models, this text offers a thorough examination of this important and rapidly expanding area. With the numerous, established applications in manufacturing and telecommunications and new applications continually being discovered, this book becomes a vital reference for professionals and an outstanding textbook for operations research, computer science, and electrical engineering students.

Table of Contents

List of Figures	p. v
Preface	p. ix
Introduction to Design Models	p. 1
Optimal Service Rate	p. 3
Optimal Arrival Rate	p. 6
Optimal Arrival Rate and Service Rate	p. 13
Optimal Arrival Rates for a Two-Class System	p. 16
Optimal Arrival Rates for Parallel Queues	p. 21
Endnotes	p. 26
Optimal Arrival Rates in a Single-Class Queue	p. 29
A Model with General Utility and Cost Functions	p. 29
Generalizations of Basic Model	p. 42
GI/GI/1 Queue with Probabilistic Joining Rule	p. 45
Uniform Value Distribution: Stability	p. 68
Power Criterion	p. 72
Bidding for Priorities	p. 77
Endnotes	p. 80
Dynamic Adaptive Algorithms: Stability and Chaos	p. 83
Basic Model	p. 84
Discrete-Time Dynamic Adaptive Model	p. 85
Discrete-Time Dynamic Algorithms: Variants	p. 98
Continuous-Time Dynamic Adaptive Algorithms	p. 101
Continuous-Time Dynamic Algorithm: Variants	p. 106
Endnotes	p. 107
Optimal Arrival Rates in a Multiclass Queue	p. 109
General Multiclass Model: Formulation	p. 109
General Multiclass Model: Optimal Solutions	p. 113
General Multiclass Model: Dynamic Algorithms	p. 124
Waiting Costs Dependent on Total Arrival Rate	p. 129
Linear Utility Functions: Class Dominance	p. 134
Examples with Different Utility Functions	p. 153
Multiclass Queue with Priorities	p. 158
Endnotes	p. 170
Figures for FIFO Examples	p. 172
Optimal Service Rates in a Single-Class Queue	p. 177
The Basic Model	p. 178
Models with Fixed Toll and Fixed Arrival Rate	p. 182
Models with Variable Toll and Fixed Arrival Rate	p. 184
Models with Fixed Toll and Variable Arrival Rate	p. 185
Models with Variable Toll and Variable Arrival Rate	p. 199
Endnotes	p. 215
Multi-Facility Queueing Systems: Parallel Queues	p. 217
Optimal Arrival Rates	p. 217
Optimal Service Rates	p. 255
Optimal Arrival Rates and Service Rates	p. 258
Endnotes	p. 277
Single-Class Networks of Queues	p. 279
Basic Model	p. 279
Individually Optimal Arrival Rates and Routes	p. 280
Socially Optimal Arrival Rates and Routes	p. 282
Comparison of S.O. and Toll-Free I.O. Solutions	p. 284
Facility Optimal Arrival Rates and Routes	p. 307
Endnotes	p. 314
Multiclass Networks of Queues	p. 317
General Model	p. 317
Fixed Routes: Optimal Solutions	p. 330
Fixed Routes: Dynamic Adaptive Algorithms	p. 334
Fixed Routes: Homogeneous Waiting Costs	p. 338
Variable Routes: Homogeneous Waiting Costs	p. 339
Endnotes	p. 342
Scheduling a Single-Server Queue	p. 343
Strong Conservation Laws	p. 343
Work-Conserving Scheduling Systems	p. 344
GI/GI/1 WCSS with Nonpreemptive Scheduling Rules	p. 351
GI/GI/1 Queue: Preemptive-Resume Scheduling Rules	p. 355
Endnotes	p. 357
References	p. 359
Index	p. 369
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