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9781584880769

Optimal Design of Queueing Systems

by ;
  • ISBN13:

    9781584880769

  • ISBN10:

    1584880767

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

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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 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.

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