Artalejo / Gómez-Corral Retrial Queueing Systems

A Computational Approach
1. Auflage 2008
ISBN: 978-3-540-78725-9
Verlag: Springer Berlin Heidelberg
Format: PDF
Kopierschutz: 1 - PDF Watermark

E-Book, Englisch, 318 Seiten

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.

Autoren/Hrsg.

Artalejo, J. R.

Gómez-Corral, Antonio

Inhaltsverzeichnis

1;Preface;7
2;Contents;11
3;Part I An Introduction to Retrial Queueing Systems;15
3.1;1 Introduction and Motivating Examples;16
3.1.1;1.1 Introduction;16
3.1.2;1.2 Some Examples in Telephone Systems;17
3.1.3;1.3 Some Examples in Computer Networks;20
3.1.4;1.4 Bibliographical Notes;23
3.2;2 A General Overview;24
3.2.1;2.1 The Mathematical Formalism;24
3.2.2;2.2 Comparing Standard and Retrial Queueing Systems;29
3.2.3;2.3 Short Description of Some Advanced Retrial Queueing Systems;44
3.2.4;2.4 Bibliographical Notes;47
4;Part II Computational Analysis of Performance Descriptors;50
4.1;3 Limiting Distribution of the System State;52
4.1.1;3.1 The M/G/1 Retrial Queue;52
4.1.2;3.2 The M/G/1 Queue with General Retrial Times;64
4.1.3;3.3 The Geo/G/1 Retrial Queue;69
4.1.4;3.4 The M/M/c Retrial Queue;77
4.1.5;3.5 A Multiserver Retrial Queue with Finite Population;100
4.1.6;3.6 Bibliographical Notes;104
4.2;4 Busy Period;108
4.2.1;4.1 The M/G/1 Retrial Queue;108
4.2.2;4.2 The M/M/c Retrial Queue;124
4.2.3;4.3 Bibliographical Notes;142
4.3;5 Waiting Time;144
4.3.1;5.1 The M/G/1 Retrial Queue;144
4.3.2;5.2 The M/M/c Retrial Queue;162
4.3.3;5.3 Bibliographical Notes;171
4.4;6 Other Descriptors;172
4.4.1;6.1 Attempts Since the Last Service Completion;172
4.4.2;6.2 Successful versus Blocked Events;177
4.4.3;6.3 Server Idle Periods;187
4.4.4;6.4 Time to Reach a Certain Orbit Level;192
4.4.5;6.5 Bibliographical Notes;195
5;Part III Retrial Queueing Systems Analyzed Through the Matrix- Analytic Formalism;198
5.1;7 The Matrix-Analytic Formalism;200
5.1.1;7.1 A General Overview;200
5.1.2;7.2 Some General Tools for QBD Structures;207
5.1.3;7.3 Some General Tools for GI/M/1 and M/G/1 Structures;211
5.1.4;7.4 Bibliographical Notes;216
5.2;8 Selected Retrial Queues with QBD Structure;220
5.2.1;8.1 The MAP/PH/1 Retrial Queue;220
5.2.2;8.2 The MAP/M/c Retrial Queue;232
5.2.3;8.3 A Queue with Finite Population and PH Service and Retrial Times;246
5.2.4;8.4 Bibliographical Notes;250
5.3;9 Selected Retrial Queues with GI/M/1 and M/G/1 Structures;254
5.3.1;9.1 The Geo/Geo/c Retrial Queue;254
5.3.2;9.2 The BMAP/SM/1 Retrial Queue;268
5.3.3;9.3 Bibliographical Notes;279
6;References;282
7;Author Index;324
8;Subject Index;328