With the boom of big data and machine learning and the subsequent need for parallel processing technologies, fork-join queues are more relevant now than ever before. In this book, new estimates of the average response time in fork-join queues are proposed, which form the basis for new research opportunities.
Analysis of Fork-Join Systems: Network of Queues with Precedence Constraints explores numerical approaches to estimate the average response time of fork-join queueing networks and offers never before published simple expressions for the mean response time as conjectures. Extensive experiments are included to demonstrate the remarkable accuracy of the conjectures and algorithms used in the estimation of the average response time.
Graduate students, professors, and researchers in the fields of operations research, management science, industrial engineering, computer science, and electrical engineering will find this book very useful. Students, as well as researchers in both academia and industry, will also find this book of great help when looking for results related to fork-join queues
Author(s): Samyukta Sethuraman
Series: Emerging Operations Research Methodologies and Applications
Publisher: CRC Press
Year: 2022
Language: English
Pages: 103
City: Boca Raton
Cover
Half Title
Series Page
Title Page
Copyright Page
Dedication
Contents
List of Figures
List of Tables
Preface
Author Biography
CHAPTER 1: Basic Queueing Theory
1.1. DISCRETE SINGLE-STATION QUEUEING SYSTEMS
1.2. KENDALL NOTATION
1.3. QUEUEING SYSTEM PERFORMANCE
1.3.1. Flow Conservation and Stability
1.3.2. Performance Metrics
1.3.3. Little’s Law
1.3.4. PASTA
CHAPTER 2: Introduction to Fork-Join Queues
2.1. INTRODUCTION
2.2. RESPONSE TIME IN FORK-JOIN QUEUES
2.3. APPLICATIONS
2.3.1. Parallel Computing
2.3.2. Manufacturing Systems
2.3.3. Health Care Systems
2.3.4. Wireless Sensor Networks
2.4. ORGANIZATION
CHAPTER 3: Literature Review
3.1. FORK-JOIN QUEUEING SYSTEMS WITH A SINGLE LEVEL OF TASKS
3.2. GENERALIZED FORK-JOIN QUEUEING SYSTEMS
CHAPTER 4: Symmetric n-Dimensional Fork-Join Queues
4.1. SYSTEM DEFINITION
4.2. RESPONSE TIME ESTIMATION
4.2.1. Exponential Service Time Distribution
4.2.2. General Service Time Distribution
4.2.3. Numerical Examples
4.3. RESULTS AND COMPARISONS
4.3.1. Comparison with Simulations
4.3.2. Approximation by Nelson and Tantawi
4.3.3. Approximation by Varma and Makowski
4.3.4. Approximation by Ko and Serfozo
4.3.5. Approximation by Thomasian and Tantawi
4.4. CONCLUSIONS
CHAPTER 5: Relaxed Fork-Join Queueing Networks
5.1. SYMMETRIC TANDEM FORK-JOIN QUEUEING NETWORK
5.1.1. Response Time Estimation
5.1.2. Numerical Example
5.1.3. Experimental Results
5.2. HETEROGENEOUS FORK-JOIN QUEUES
5.2.1. System Definition
5.2.2. Response Time Estimation
5.2.3. Numerical Example and Results
5.3. (n, k) FORK-JOIN QUEUES
5.3.1. Comparison with Simulations
5.4. CONCLUSIONS
Bibliography
Index
