1st Edition

Optimal Design of Queueing Systems

By Shaler Stidham Jr. Copyright 2010
    384 Pages 75 B/W Illustrations
    by Chapman & Hall

    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.


    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



    Endnotes appear in each chapter.


    Shaler Stidham Jr.