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Optimal Design of Queueing Systems - Shaler Stidham Jr

Optimal Design of Queueing Systems


Published: 8th April 2009
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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.

List of Figuresp. v
Prefacep. ix
Introduction to Design Modelsp. 1
Optimal Service Ratep. 3
Optimal Arrival Ratep. 6
Optimal Arrival Rate and Service Ratep. 13
Optimal Arrival Rates for a Two-Class Systemp. 16
Optimal Arrival Rates for Parallel Queuesp. 21
Endnotesp. 26
Optimal Arrival Rates in a Single-Class Queuep. 29
A Model with General Utility and Cost Functionsp. 29
Generalizations of Basic Modelp. 42
GI/GI/1 Queue with Probabilistic Joining Rulep. 45
Uniform Value Distribution: Stabilityp. 68
Power Criterionp. 72
Bidding for Prioritiesp. 77
Endnotesp. 80
Dynamic Adaptive Algorithms: Stability and Chaosp. 83
Basic Modelp. 84
Discrete-Time Dynamic Adaptive Modelp. 85
Discrete-Time Dynamic Algorithms: Variantsp. 98
Continuous-Time Dynamic Adaptive Algorithmsp. 101
Continuous-Time Dynamic Algorithm: Variantsp. 106
Endnotesp. 107
Optimal Arrival Rates in a Multiclass Queuep. 109
General Multiclass Model: Formulationp. 109
General Multiclass Model: Optimal Solutionsp. 113
General Multiclass Model: Dynamic Algorithmsp. 124
Waiting Costs Dependent on Total Arrival Ratep. 129
Linear Utility Functions: Class Dominancep. 134
Examples with Different Utility Functionsp. 153
Multiclass Queue with Prioritiesp. 158
Endnotesp. 170
Figures for FIFO Examplesp. 172
Optimal Service Rates in a Single-Class Queuep. 177
The Basic Modelp. 178
Models with Fixed Toll and Fixed Arrival Ratep. 182
Models with Variable Toll and Fixed Arrival Ratep. 184
Models with Fixed Toll and Variable Arrival Ratep. 185
Models with Variable Toll and Variable Arrival Ratep. 199
Endnotesp. 215
Multi-Facility Queueing Systems: Parallel Queuesp. 217
Optimal Arrival Ratesp. 217
Optimal Service Ratesp. 255
Optimal Arrival Rates and Service Ratesp. 258
Endnotesp. 277
Single-Class Networks of Queuesp. 279
Basic Modelp. 279
Individually Optimal Arrival Rates and Routesp. 280
Socially Optimal Arrival Rates and Routesp. 282
Comparison of S.O. and Toll-Free I.O. Solutionsp. 284
Facility Optimal Arrival Rates and Routesp. 307
Endnotesp. 314
Multiclass Networks of Queuesp. 317
General Modelp. 317
Fixed Routes: Optimal Solutionsp. 330
Fixed Routes: Dynamic Adaptive Algorithmsp. 334
Fixed Routes: Homogeneous Waiting Costsp. 338
Variable Routes: Homogeneous Waiting Costsp. 339
Endnotesp. 342
Scheduling a Single-Server Queuep. 343
Strong Conservation Lawsp. 343
Work-Conserving Scheduling Systemsp. 344
GI/GI/1 WCSS with Nonpreemptive Scheduling Rulesp. 351
GI/GI/1 Queue: Preemptive-Resume Scheduling Rulesp. 355
Endnotesp. 357
Referencesp. 359
Indexp. 369
Table of Contents provided by Ingram. All Rights Reserved.

ISBN: 9781584880769
ISBN-10: 1584880767
Audience: Tertiary; University or College
Format: Hardcover
Language: English
Number Of Pages: 371
Published: 8th April 2009
Publisher: CRC PR INC
Country of Publication: US
Dimensions (cm): 23.62 x 16.26  x 2.54
Weight (kg): 0.66
Edition Number: 1