Retrial Queueing Systems (eBook)
XIII, 318 Seiten
Springer Berlin (Verlag)
978-3-540-78725-9 (ISBN)
The application of auto-repeat facilities in telephone systems, as well as the use of random access protocols in computer networks, have led to growing interest in retrial queueing models. Since much of the theory of retrial queues is complex from an analytical viewpoint, with this book the authors give a comprehensive and updated text focusing on approximate techniques and algorithmic methods for solving the analytically intractable models.
Retrial Queueing Systems: A Computational Approach also
- Presents motivating examples in telephone and computer networks.
- Establishes a comparative analysis of the retrial queues versus standard queues with waiting lines and queues with losses.
- Integrates a wide range of techniques applied to the main M/G/1 and M/M/c retrial queues, and variants with general retrial times, finite population and the discrete-time case.
- Surveys basic results of the matrix-analytic formalism and emphasizes the related tools employed in retrial queues.
- Discusses a few selected retrial queues with QBD, GI/M/1 and M/G/1 structures.
- Features an abundance of numerical examples, and updates the existing literature.
The book is intended for an audience ranging from advanced undergraduates to researchers interested not only in queueing theory, but also in applied probability, stochastic models of the operations research, and engineering. The prerequisite is a graduate course in stochastic processes, and a positive attitude to the algorithmic probability.
Preface 7
Contents 11
Part I An Introduction to Retrial Queueing Systems 15
1 Introduction and Motivating Examples 16
1.1 Introduction 16
1.2 Some Examples in Telephone Systems 17
1.3 Some Examples in Computer Networks 20
1.4 Bibliographical Notes 23
2 A General Overview 24
2.1 The Mathematical Formalism 24
2.2 Comparing Standard and Retrial Queueing Systems 29
2.3 Short Description of Some Advanced Retrial Queueing Systems 44
2.4 Bibliographical Notes 47
Part II Computational Analysis of Performance Descriptors 50
3 Limiting Distribution of the System State 52
3.1 The M/G/1 Retrial Queue 52
3.2 The M/G/1 Queue with General Retrial Times 64
3.3 The Geo/G/1 Retrial Queue 69
3.4 The M/M/c Retrial Queue 77
3.5 A Multiserver Retrial Queue with Finite Population 100
3.6 Bibliographical Notes 104
4 Busy Period 108
4.1 The M/G/1 Retrial Queue 108
4.2 The M/M/c Retrial Queue 124
4.3 Bibliographical Notes 142
5 Waiting Time 144
5.1 The M/G/1 Retrial Queue 144
5.2 The M/M/c Retrial Queue 162
5.3 Bibliographical Notes 171
6 Other Descriptors 172
6.1 Attempts Since the Last Service Completion 172
6.2 Successful versus Blocked Events 177
6.3 Server Idle Periods 187
6.4 Time to Reach a Certain Orbit Level 192
6.5 Bibliographical Notes 195
Part III Retrial Queueing Systems Analyzed Through the Matrix- Analytic Formalism 198
7 The Matrix-Analytic Formalism 200
7.1 A General Overview 200
7.2 Some General Tools for QBD Structures 207
7.3 Some General Tools for GI/M/1 and M/G/1 Structures 211
7.4 Bibliographical Notes 216
8 Selected Retrial Queues with QBD Structure 220
8.1 The MAP/PH/1 Retrial Queue 220
8.2 The MAP/M/c Retrial Queue 232
8.3 A Queue with Finite Population and PH Service and Retrial Times 246
8.4 Bibliographical Notes 250
9 Selected Retrial Queues with GI/M/1 and M/G/1 Structures 254
9.1 The Geo/Geo/c Retrial Queue 254
9.2 The BMAP/SM/1 Retrial Queue 268
9.3 Bibliographical Notes 279
References 282
Author Index 324
Subject Index 328
| Erscheint lt. Verlag | 7.5.2008 |
|---|---|
| Zusatzinfo | XIII, 318 p. |
| Verlagsort | Berlin |
| Sprache | englisch |
| Themenwelt | Mathematik / Informatik ► Mathematik ► Statistik |
| Mathematik / Informatik ► Mathematik ► Wahrscheinlichkeit / Kombinatorik | |
| Technik | |
| Wirtschaft ► Betriebswirtschaft / Management ► Planung / Organisation | |
| Schlagworte | Calculus • Computational Approach • Matrix-Analytic Methods • Operations Research • Performance Descriptors • Queueing Systems • Retrial Queues • stochastic model • stochastic models • Stochastic Processes • Structured Markov Chains |
| ISBN-10 | 3-540-78725-9 / 3540787259 |
| ISBN-13 | 978-3-540-78725-9 / 9783540787259 |
| Haben Sie eine Frage zum Produkt? |
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