Introduction to Matrix-Analytic Methods in Queues 2: Analytical and Simulation Approach - Queues and Simulation

✍ Scribed by Srinivas R. Chakravarthy

• Publisher: Wiley-ISTE
• Year: 2022
• Tongue: English
• Leaves: 442
• Series: Mathematics and Statistics
• Category: Library

✦ Synopsis

Matrix-analytic methods (MAM) were introduced by Professor Marcel Neuts and have been applied to a variety of stochastic models since.

In order to provide a clear and deep understanding of MAM while showing their power, this book presents MAM concepts and explains the results using a number of worked-out examples. This book's approach will inform and kindle the interest of researchers attracted to this fertile field.

To allow readers to practice and gain experience in the algorithmic and computational procedures of MAM, Introduction to Matrix-Analytic Methods in Queues 2 provides a number of computational exercises. It also incorporates simulation as another tool for studying complex stochastic models, especially when the state space of the underlying stochastic models under analytic study grows exponentially.

This book's detailed approach will make it more accessible for readers interested in learning about MAM in stochastic models.

✦ Table of Contents

Cover
Title Page
Copyright Page
Contents
List of Notations
Preface
Chapter 1. Single-Server Queues Embedded at Departure Epochs
1.1. BMAP/G/1 queue
1.2. MAP/G/1 queue
1.3. PH/G/1 queue
1.4. M/G/1 queue
1.5. PH/M/1 queue
1.6. M/M/1 queue
1.7. Exercises
Chapter 2. Single-Server Queues Embedded at Arrival Epochs
2.1. GI/PH/1 queue
2.2. GI/M/1 queue
2.3. M/PH/1 queue
2.4. M/M/1 queue
2.5. Exercises
Chapter 3. Single-Server Queues Based on Arbitrary Epochs
3.1. BMAP/PH/1 queue
3.2. MAP/PH/1 queueing model
3.3. PH/PH/1 queue
3.4. PH/M/1 queue
3.5. M/PH/1 queue
3.6. M/M/1 queue
3.7. Exercises
Chapter 4. Busy Period in Queues
4.1. Busy period in M/G/1-type queues (scalar case)
4.2. Busy period in M/G/1-type queues (matrix case)
4.3. Busy period in GI/M/1-type queues (scalar case)
4.4. Busy period in GI/PH/1-type queues
4.5. BMAP/PH/1 queue
4.6. Busy period in QBD-type queues
4.7. When the fundamental period is not the busy period
4.8. GI/G/1 queues
4.9. Exercises
Chapter 5. Multi-Server Queues
5.1. BMAP/PH/c queue
5.2. MAP/PH/3 queue
5.3. BMAP/M/c queue
5.3.1. MAP/M/c queue
5.3.2. M/M/c queue
5.4. GI/PH/c queue
5.5. Exercises
Chapter 6. Finite-Capacity Queues
6.1. Finite-capacity queues with single server
6.1.1. BMAP/PH/1/K queue
6.1.2. MAP/PH/1/K queue
6.1.3. PH/M/1/K queue
6.1.4. M/PH/1/K queue
6.1.5. M/M/1/K queue
6.2. Finite-capacity queues with multiple servers
6.2.1. BMAP/M/c/K queue
6.2.2. MAP/M/c/K queue
6.2.3. PH/M/c/K queue
6.2.4. M/M/c/K queue
6.3. Exercises
Chapter 7. Simulation
7.1. Introduction to ARENA
7.2. Model building using ARENA
7.3. GI/G/c queues
7.3.1. ARENA modules for GI/G/c queues
7.3.2. Validation of GI/G/1 queues
7.3.3. Simulated examples for GI/G/1 queues
7.3.4. Validation of GI/G/c queues
7.3.5. Simulated examples of GI/G/c queues
7.4. BMAP/G/c queues
7.4.1. ARENA modules for BMAP/G/c queues
7.4.2. Validation of BMAP/G/1 queues
7.4.3. Simulated examples for BMAP/G/1 queues
7.4.4. Validation of BMAP/M/c queues
7.4.5. Simulated examples for BMAP/G/c queues
7.5. Exercises
References
Index
Summary of Volume 1
EULA