Vacation Queueing Models (eBook)

Theory and Applications

Naishuo Tian, Zhe George Zhang (Autoren)

eBook Download: PDF

2006 | 2006
XII, 386 Seiten
Springer US (Verlag)
978-0-387-33723-4 (ISBN)

Infos

This book discusses systematically the many variations of vacation policy. The book discusses a variety of typical vacation model applications. The presentation style is unique compared with the books published in the same field - a 'theorem and proof' format is used. Also, this is the first time G1/M/1 multi-server vacation models, both continuous and discrete, and the optimization and control issues have been presented in book form.

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A classical queueing model consists of three parts - arrival process, service process, and queue discipline. However, a vacation queueing model has an additional part - the vacation process which is governed by a vacation policy - that can be characterized by three aspects: 1) vacation start-up rule; 2) vacation termination rule, and 3) vacation duration distribution. Hence, vacation queueing models are an extension of classical queueing theory.Vacation Queueing Models: Theory and Applications discusses systematically and in detail the many variations of vacation policy. By allowing servers to take vacations makes the queueing models more realistic and flexible in studying real-world waiting line systems. Integrated in the book's discussion are a variety of typical vacation model applications that include call centers with multi-task employees, customized manufacturing, telecommunication networks, maintenance activities, etc. Finally, contents are presented in a "e;theorem and proof"e; format and it is invaluable reading for operations researchers, applied mathematicians, statisticians; industrial, computer, electrical and electronics, and communication engineers; computer, management scientists; and graduate students in the above disciplines.

Inhalt

Contents 6
Preface 10
Acknowledgements 12
1 Introduction 13
1.1 Queuing Systems with Server Vacations 13
1.2 Vacation Policies 15
1.3 Stochastic Decompositions in Vacation Models 16
1.4 Bibliographic Notes 17
2 M/G/1 Type Vacation Models: Exhaustive Service 20
2.1 M/G/1 Queue with Multiple Adaptive Vacations 21
2.2 Some Classical M/G/1 Vacation Models 30
2.3 M/G/1 Queue with Multiple Adaptive Vacations 38
2.4 Discrete-Time Geo/G/1 Queue with Vacations 46
2.6 General-Service Bulk Queue with Vacations 65
2.7 Finite-Buffer M/G/1 Queue with Vacations 80
2.8 Bibliographic Notes 84
3 M/G/1 Type Vacation Models: Nonexhaustive Service 87
3.1 Regeneration Cycle Method 87
3.2 Gated Service M/G/1 Vacation Models 91
3.3 Limited Service M/G/1 Vacation Models 100
3.4 Decrementing Service M/G/1 Vacation Models 125
3.5 Bibliographic Notes 136
4 General-Input Single Server Vacation Models 138
4.1 GI/M/1 Type Structure Matrix 138
4.2 GI/M/1 Queue with Multiple Vacations 143
4.3 GI/M/1 Queue with Single Vacation 160
4.4 GI/M/1 Queue with N-Threshold Policies 171
4.5 General-Input Bulk Queue with Vacations 179
4.6 Finite-Buffer GI/M/1 Vacation Model 188
4.7 Discrete-Time GT/ Geo/1 Queue with Vacations 192
4.8 Bibliographic Notes 200
5 Markovian Multiserver Vacation Models 202
5.1 Introducion to Multiserver Vacation Models 202
5.2 Quasi-Birth-and-Death Process Approach 205
5.3 M/M/c Queue with Synchonous Vacations 212
5.4 M/M/c Queue with Asynchonous Vacations 229
5.5 M/M/c Queue with Synchonous Vacations of Some Servers 244
5.6 M/M/c Queue with Asynchonous Vacations of Some Servers 266
5.7 Bibliographic Notes 275
6 General-Input Multiserver Vacation Models 277
6.1 GI/M/c Queue with Exponential Vacations 277
6.1 GI/M/c Queue with PH Vacations 288
6.3 Bibliographic Notes 303
7 Optimization in Vacation Models 305
7.1 M/G/1 Queue with Threshold Policies 305
7.2 Dynamic Control in M/G/1 System with Vacation of Multiple Types 326
7.3 M/M/c Queue with Threshold Policies 338
7.4 Bibliographic Notes 349
8 Application of Vacation Models 351
8.1 Modeling the Flexible Production System 351
8.2 Modeling the Stochastic Service System with Multitask Servers 353
8.3 Modeling SVCC-Based ATM Networks 358
9 References 367
Index 391

Produkt-Details

• Erscheint lt. Verlag: 11.10.2006
• Reihe/Serie: International Series in Operations Research & Management Science
• Reihe/Serie: International Series in Operations Research & Management Science
• Zusatzinfo: XII, 386 p. 8 illus.
• Verlagsort: New York
• Sprache: englisch
• Themenwelt: Mathematik / Informatik ► Informatik
• Themenwelt: Mathematik / Informatik ► Mathematik ► Statistik
• Themenwelt: Mathematik / Informatik ► Mathematik ► Wahrscheinlichkeit / Kombinatorik
• Themenwelt: Technik
• Themenwelt: Wirtschaft ► Allgemeines / Lexika
• Themenwelt: Wirtschaft ► Betriebswirtschaft / Management ► Logistik / Produktion
• Themenwelt: Wirtschaft ► Betriebswirtschaft / Management ► Planung / Organisation
• Schlagworte: Applications • Electronics • embedded Markov chains • Manufacturing • Markov • Matrix geometric solution • Model • Models • Operations Research • Optimization • Queueing • semi-Markov decision process • stochastic decomposition • Stochastic Processes • theory • Tian • vacation • Zhang
• ISBN-10: 0-387-33723-7 / 0387337237
• ISBN-13: 978-0-387-33723-4 / 9780387337234