Controlled Queueing Systems: 1st Edition (Hardback) book cover

Controlled Queueing Systems

1st Edition

By Mikhail Yu. Kitaev, Vladimir V. Rykov

CRC Press

304 pages

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Hardback: 9780849328626
pub: 1995-08-30

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This is the first book completely devoted to controlled queueing systems. The book gathers the newest results of the theory of Markov decision processes related to queueing models and demonstrates their applications to main types of control in queueing systems, including control of arrivals, control of service mechanism, and control of service discipline. Emphasis is placed on conditions providing further "good" structural properties of Markov optimal strategies such as monotonicity, threshold or hysteretic character, and priority.

Each chapter is followed by exercises, most of which allow the reader to complete technical fragments of proofs. The text assumes the reader is familiar with standard courses of analysis, probability theory, and queueing theory.

Table of Contents

Semi-Regenerative Decision Models

Description of Basic Decision Model

Rigorous Definitions and Assumptions

Examples of Controlled Queues

Optimization Problems

Renewal Kernels of the Decision Model

Special Classes of Strategies

Sufficiency of Markov Strategies

Dynamic Programming

Discounting in Continuous Time

Dynamic Programming Equation

Bellman Functions

Finite-Horizon Problem

Infinite-Horizon Discounted-Cost Problem

Random-Horizon Problem

Average Cost Criterion

Preliminaries: Weak Topology, Limit Passages

Preliminaries: Taboo Probabilities, Limit Theorems for Markov Renewal Processes

Notation, Recurrence-Communication Assumptions, Examples

Existence of Optimal Policies

Existence of Optimal Strategies: General Criterion

Existence of Optimal Strategies: Sufficient Conditions

Optimality Equation

Constrained Average-Cost Problem

Average-Cost Optimality as Limiting Case of Discounted-Cost Optimality

Continuously Controlled Markov Jump Processes

Facts About Measurability of Stochastic Processes

Marked Point Processes and Random Measures

The Predictable s-Algebra

Dual Predictable Projections of Random Measures

Definition of Controlled Markov Jump Process

An M/M/1 Queue With Controllable Input and Service Rate

Dynamic Programming

Optimization Problems

Structured Optimization Problems for Decision Processes

Convex Regularization

Submodular and Supermodular Functions

Existence of Monotone Solutions for Optimization Problems

Processes with Bounded Drift

Birth and Death Processes

Control of Arrivals

The Model Description

Finite-Horizon Discounted-Cost Problem

Cost Functionals

Infinite-Horizon Case with and without Discounting

Optimal Dynamic Pricing Policy: Model; Results

Control of Service Mechanism

Description of the System

Static Optimization Problem

Optimal Policies for the Queueing Process

Service System with Two Interacting Servers

Analysis of Optimality Equation

Optimal Control in Models with Several Classes of Customers

Description of Models and Processes

Associated Controlled Processes

Existence of Optimal Simple Strategies for the Systems with Alternating Priority

Existence of Optimal Simple Strategy for the System with Feedback

Equations for Stationary Distributions

Stationary Characteristics of the Systems with Alternating Priority

Stationary Characteristics of the System with Feedback

Models with Alternating Priority: Linear Programming Problem

Linear Programming Problem in the Model with Feedback

Model with Periods of Idleness and Discounted-Cost Criterion

Basic Formulas

Construction of Optimal Modified Priority Discipline



Each chapter also includes an Introduction, and a Remarks and Exercises section

About the Authors

Kitaev\, Mikhail Yu.; Rykov\, Vladimir V.

Subject Categories

BISAC Subject Codes/Headings:
BUSINESS & ECONOMICS / Operations Research
TECHNOLOGY & ENGINEERING / Operations Research