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Delayed and Network Queues

Book Description

Presents an introduction to differential equations, probability, and stochastic processes with real-world applications of queues with delay and delayed network queues

Featuring recent advances in queueing theory and modeling, Delayed and Network Queues provides the most up-to-date theories in queueing model applications. Balancing both theoretical and practical applications of queueing theory, the book introduces queueing network models as tools to assist in the answering of questions on cost and performance that arise throughout the life of a computer system and signal processing. Written by well-known researchers in the field, the book presents key information for understanding the essential aspects of queues with delay and networks of queues with unreliable nodes and vacationing servers.

  • Beginning with simple analytical fundamentals, the book contains a selection of realistic and advanced queueing models that address current deficiencies. In addition, the book presents the treatment of queues with delay and networks of queues, including possible breakdowns and disruptions that may cause delay. Delayed and Network Queues also features:
  • Numerous examples and exercises with applications in various fields of study such as mathematical sciences, biomathematics, engineering, physics, business, health industry, and economics
  • A wide array of practical applications of network queues and queueing systems, all of which are related to the appropriate stochastic processes
  • Up-to-date topical coverage such as single- and multiserver queues with and without delays, along with the necessary fundamental coverage of probability and difference equations
  • Discussions on queueing models such as single- and multiserver Markovian queues with balking, reneging, delay, feedback, splitting, and blocking, as well as their role in the treatment of networks of queues with and without delay and network reliability

Delayed and Network Queues is an excellent textbook for upper-undergraduate and graduate-level courses in applied mathematics, queueing theory, queueing systems, probability, and stochastic processes. The book is also an ideal reference for academics and practitioners in mathematical sciences, biomathematics, operations research, management, engineering, physics, business, economics, health industry, and industrial engineering.

Aliakbar Montazer Haghighi, PhD, is Professor and Head of the Department of Mathematics at Prairie View A&M University, USA, as well as founding Editor-in-Chief of Applications and Applied Mathematics: An International Journal (AAM). His research interests include probability, statistics, stochastic processes, and queueing theory. Among his research publications and books, Dr. Haghighi is the coauthor of Difference and Differential Equations with Applications in Queueing Theory (Wiley, 2013).

Dimitar P. Mishev, PhD, is Professor in the Department of Mathematics at Prairie View A&M University, USA. His research interests include differential and difference equations and queueing theory. The author of numerous research papers and three books, Dr. Mishev is the coauthor of Difference and Differential Equations with Applications in Queueing Theory (Wiley, 2013).

Table of Contents

  1. Cover
  2. Title Page
  3. Copyright
  4. Dedication
  5. Preface
  6. Chapter 1: Preliminaries
    1. 1.1 Basics of Probability
    2. 1.2 Discrete Random Variables and Distributions
    3. 1.3 Discrete Moments
    4. 1.4 Continuous Random Variables, Density, and Cumulative Distribution Functions
    5. 1.5 Continuous Random Vector
    6. 1.6 Functions of Random Variables
    7. 1.7 Continuous Moments
    8. 1.8 Difference Equations
    9. 1.9 Methods of Solving Linear Difference Equations with Constant Coefficients
    10. Exercises
  7. Chapter 2: Stochastic Processes
    1. 2.1 Introduction and Basic Definitions
    2. 2.2 Markov Chain
    3. 2.3 Markov Process
    4. 2.4 Random Walk
    5. 2.5 Up-and-Down Biased Coin Design as a Random Walk
    6. Exercises
  8. Chapter 3: Birth and Death Processes
    1. 3.1 Overviews of the Birth and Death Processes
    2. 3.2 Finite B–D Process
    3. 3.3 Pure Birth Process (Poisson Process)
    4. 3.4 Pure Death Process (Poisson Death Process)
    5. Exercises
  9. Chapter 4: Standard Queues
    1. 4.1 Introduction of Queues (General Birth and Death Process)
    2. 4.2 Remarks on Non-Markovian Queues
    3. 4.3 Stationary M/M/1 Queueing Process
    4. 4.4 A Parallel M/M/C/K with Baking and Reneging
    5. 4.5 Stationary M/M/1/K Queueing Process
    6. 4.6 Busy Period of an M/M/1/K Queue
    7. 4.7 Stationary M/M/1 and M/M/1/K Queueing Processes with Feedback
    8. 4.8 Queues with Bulk Arrivals and Batch Service
    9. 4.9 A Priority Queue with Balking and Reneging
    10. 4.10 Discrete Time M/M/1 Queueing Process, Combinatorics Method (Lattice Paths)
    11. 4.11 Stationary M/M/C Queueing Process
    12. Exercises
  10. Chapter 5: Queues with Delay
    1. 5.1 Introduction
    2. 5.2 A Queuing System with Delayed Service
    3. 5.3 An M/G/1 Queue with Server Breakdown and with Multiple Working Vacation
    4. 5.4 A Bulk Queuing System Under N-Policy with Bilevel Service Delay Discipline and Start-Up Time
    5. 5.5 Interrelationship between N-policy M/G/1/K and F-policy G/M/1/K Queues with Start-up Time
    6. 5.6 A Transient M/M/1 Queue Under (M, N)-Policy, Lattice Path Method
    7. 5.7 Stationary M/M/1 Queuing Process with Delayed Feedback
    8. 5.8 Single-Server Queue with Unreliable Server and Breakdowns with an Optional Second Service
    9. 5.9 A Bulk Arrival Retrial Queue with Unreliable Server
    10. 5.10 Multiserver Queue with Retrial Feedback Queuing System with Two Orbits
    11. 5.11 Steady-State Stability Condition of a Retrial Queuing System with Two Orbits, Reneging, and Feedback
    12. 5.12 Batch Arrival Queue with General Service in two Fluctuating Modes and Reneging During Vacation and Breakdowns
    13. Exercises
  11. Chapter 6: Networks of Queues with Delay
    1. 6.1 Introduction to Networks of Queues
    2. 6.2 Historical Notes on Networks of Queues
    3. 6.3 Jackson's Network of Queues
    4. 6.4 Robustness of Networks of Queues
    5. 6.5 A MAP Single-Server Queueing System with Delayed Feedback as a Network of Queues
    6. 6.6 Unreliable Networks of Queueing System Models
    7. 6.7 Assessment of Reliability of a Network of Queues
    8. 6.8 Effect of Network Service Breakdown
    9. Exercises
  12. References
  13. Index
  14. End User License Agreement