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.
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.
