Delayed and Network Queues (eBook)

Aliakbar Montazer Haghighi, Dimitar P. Mishev (Autoren)

eBook Download: PDF

2016
John Wiley & Sons (Verlag)
978-1-119-02214-5 (ISBN)

Infos

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).

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).

Inhalt

Cover 1
Title Page 5
Copyright 6
Dedication 7
Contents 9
Preface 13
Chapter 1 Preliminaries 17
1.1 Basics of Probability 17
1.1.1 Introduction 17
1.1.2 Conditional Probability 18
1.2 Discrete Random Variables and Distributions 20
1.3 Discrete Moments 24
1.4 Continuous Random Variables, Density, and Cumulative Distribution Functions 29
1.5 Continuous Random Vector 33
1.6 Functions of Random Variables 35
1.7 Continuous Moments 39
1.8 Difference Equations 41
1.8.1 Introduction 41
1.8.2 Basic Definitions and Properties 41
1.9 Methods of Solving Linear Difference Equations with Constant Coefficients 43
1.9.1 Characteristic Equation Method 43
1.9.2 Recursive Method 45
1.9.3 Generating Function Method 46
1.9.4 Laplace Transform Method 48
Exercises 52
Chapter 2 Stochastic Processes 55
2.1 Introduction and Basic Definitions 55
2.2 Markov Chain 59
2.2.1 Classification of States 69
2.3 Markov Process 74
2.3.1 Markov Process with Discrete Space State 74
2.4 Random Walk 77
2.5 Up-and-Down Biased Coin Design as a Random Walk 85
Exercises 91
Chapter 3 Birth and Death Processes 93
3.1 Overviews of the Birth and Death Processes 93
3.2 Finite B-D Process 102
3.3 Pure Birth Process (Poisson Process) 110
3.4 Pure Death Process (Poisson Death Process) 112
Exercises 113
Chapter 4 Standard Queues 117
4.1 Introduction of Queues (General Birth and Death Process) 117
4.1.1 Mechanism, Characteristics, and Types of Queues 119
4.2 Remarks on Non-Markovian Queues 124
4.2.1 Takács's Waiting Time Paradox 124
4.2.2 Virtual Waiting Time and Takács's Integro-Differential Equation 125
4.2.3 The Unfinished Work 129
4.3 Stationary M/M/1 Queueing Process 132
4.4 A Parallel M/M/C/K with Baking and Reneging 135
4.5 Stationary M/M/1/K Queueing Process 136
4.6 Busy Period of an M/M/1/K Queue 138
4.7 Stationary M/M/1 and M/M/1/K Queueing Processes with Feedback 140
4.7.1 Stationary Distribution of the Sojourn Time of a Task 142
4.7.2 Distribution of the Total Time of Service by a Task 144
4.7.3 Stationary Distribution of the Feedback Queue Size 145
4.7.4 Stationary Distribution of ??????n (Sojourn Time of the nth task) 146
4.8 Queues with Bulk Arrivals and Batch Service 147
4.9 A Priority Queue with Balking and Reneging 149
4.10 Discrete Time M/M/1 Queueing Process, Combinatorics Method (Lattice Paths) 153
4.10.1 The Basic Ballot Problem 154
4.10.2 Ballot Problem (based on Takács 1997) 156
4.10.3 Transient Solution of the M/M/1 by Lattice Path Method 165
4.11 Stationary M/M/C Queueing Process 169
4.11.1 A Stationary Multiserver Queue 170
Exercises 172
Chapter 5 Queues With Delay 175
5.1 Introduction 175
5.2 A Queuing System with Delayed Service 179
5.3 An M/G/1 Queue with Server Breakdown and with Multiple Working Vacation 188
5.3.1 Mathematical Formulation of the Model 189
5.3.2 Steady-State Mean Number of Tasks in the System 189
5.3.3 A Special Case 199
5.4 A Bulk Queuing System Under N-Policy with Bilevel Service Delay Discipline and Start-Up Time 201
5.4.1 Analysis of the Model 202
5.5 Interrelationship between N-Policy M/G/1/K and F-Policy G/M/1/K Queues with Start-up Time 204
5.5.1 N-Policy M/G/1/K Queuing System with Exponential Start-up Time 205
5.5.2 F-Policy G/E/1/K Queuing System with Exponential Start-up Time 211
5.6 A Transient M/M/1 Queue Under (M, N)-Policy, Lattice Path Method 215
5.6.1 Solution in Discrete Time 216
5.6.2 Solution in Continuous Time 222
5.7 Stationary M/M/1 Queuing Process with Delayed Feedback 224
5.7.1 Distribution of the Queue Length 225
5.7.2 Mean Queue Length and Waiting Time 229
5.8 Single-Server Queue with Unreliable Server and Breakdowns with an Optional Second Service 238
5.9 A Bulk Arrival Retrial Queue with Unreliable Server 245
5.9.1 The Model 247
5.9.2 Model Analysis 249
5.9.3 Steady-State System Analysis 253
5.9.4 Performance Measures 260
5.9.5 Numerical Illustration 264
5.10 Multiserver Queue with Retrial Feedback Queuing System with Two Orbits 269
5.11 Steady-State Stability Condition of a Retrial Queuing System with Two Orbits, Reneging, and Feedback 274
5.11.1 Necessary Stability Condition for the Steady-State System 275
5.12 Batch Arrival Queue with General Service in Two Fluctuating Modes and Reneging During Vacation and Breakdowns 279
5.12.1 The Model 279
5.12.2 Analysis 281
Exercises 282
Chapter 6 Networks of Queues with Delay 283
6.1 Introduction to Networks of Queues 283
6.2 Historical Notes on Networks of Queues 286
6.3 Jackson's Network of Queues 288
6.3.1 Jackson's Model 289
6.4 Robustness of Networks of Queues 314
6.5 A MAP Single-Server Queueing System with Delayed Feedback as a Network of Queues 318
6.5.1 Description of the Model 320
6.5.2 Service Station 323
6.5.3 Stepwise Explicit Joint Distribution of the Number of Tasks in the System: General Case When Batch Sizes Vary Between a Minimum k and a Maximum K 335
6.6 Unreliable Networks of Queueing System Models 352
6.6.1 Unreliable Network Model of Goodman and Massey 353
6.6.2 Unreliable Network of Queues Model of Mylosz and Daduna 356
6.6.3 Unreliable Network of Queues Model of Gautam Choudhury, Jau-Chuan Ke, and Lotfi Tadj: A Queueing System with Two Network Phases of Services, Unreliable Server, Repair Time Delay under N-Policy 364
6.7 Assessment of Reliability of a Network of Queues 379
6.8 Effect of Network Service Breakdown 381
6.8.1 The Model (CoginfoCom System) 382
6.8.2 Analysis 384
6.8.3 Numerical Example 386
Exercises 390
References 393
Index 407
EULA 417

Rezensionen

"The references are in their majority very recent and well balanced"...."I find the (perhaps tangential) remarks on history, applications, and implementation a welcome addition to the text that should/will interest new researchers in the field" Maria Vlasiou on behalf of Mathematical Reviews, October 2017

Produkt-Details

• Erscheint lt. Verlag: 8.9.2016
• Sprache: englisch
• Themenwelt: Mathematik / Informatik ► Mathematik ► Angewandte Mathematik
• Themenwelt: Mathematik / Informatik ► Mathematik ► Statistik
• Themenwelt: Mathematik / Informatik ► Mathematik ► Wahrscheinlichkeit / Kombinatorik
• Themenwelt: Technik
• Schlagworte: and stochastic processes • Betriebswirtschaft • Betriebswirtschaft u. Operationsforschung • Business & Management • <p>differential equations • Management Science/Operational Research • network queues • Probability • Production Operations Management • Produktionssteuerung • queueing theory </p> • queuing theory • single- and multi-server queues • Statistics • Statistik • Warteschlange • Warteschlangentheorie • Wirtschaft u. Management
• ISBN-10: 1-119-02214-2 / 1119022142
• ISBN-13: 978-1-119-02214-5 / 9781119022145