Analysis of Fork-Join Systems: Network of Queues with Precedence Constraints
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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 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
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