Retrial Queueing Systems: A Computational Approach Book

Pt. I An Introduction to Retrial Queueing Systems

1 Introduction and Motivating Examples 3

1.1 Introduction 3

1.2 Some Examples in Telephone Systems 4

1.3 Some Examples in Computer Networks 7

1.4 Bibliographical Notes 10

2 A General Overview 11

2.1 The Mathematical Formalism 11

2.2 Comparing Standard and Retrial Queueing Systems 16

2.3 Short Description of Some Advanced Retrial Queueing Systems 31

2.4 Bibliographical Notes 34

Pt. II Computational Analysis of Performance Descriptors

3 Limiting Distribution of the System State 39

3.1 The M/G/1 Retrial Queue 39

3.2 The M/G/1 Queue with General Retrial Times 51

3.3 The Geo/G/1 Retrial Queue 56

3.4 The M/M/c Retrial Queue 64

3.5 A Multiserver Retrial Queue with Finite Population 87

3.6 Bibliographical Notes 91

4 Busy Period 95

4.1 The M/G/1 Retrial Queue 95

4.2 The M/M/c Retrial Queue 111

4.3 Bibliographical Notes 129

5 Waiting Time 131

5.1 The M/G/1 Retrial Queue 131

5.2 The M/M/c Retrial Queue 149

5.3 Bibliographical Notes 158

6 Other Descriptors 159

6.1 Attempts Since the Last Service Completion 159

6.2 Successful versus Blocked Events 164

6.3 Server Idle Periods 174

6.4 Time to Reach a Certain Orbit Level 179

6.5 Bibliographical Notes 182

Pt. III Retrial Queueing Systems Analyzed Through the Matrix-Analytic Formalism

7 The Matrix-Analytic Formalism 187

7.1 A General Overview 187

7.2 Some General Tools for QBD Structures 194

7.3 Some General Tools for GI/M/1 and M/G/1 Structures 198

7.4 Bibliographical Notes 203

8 Selected Retrial Queues with QBD Structure 207

8.1 The MAP/PH/1 Retrial Queue 207

8.2 The MAP/M/c Retrial Queue 219

8.3 A Queue with FinitePopulation and PH Service and Retrial Times 233

8.4 Bibliographical Notes 237

9 Selected Retrial Queues with GI/M/1 and M/G/1 Structures 241

9.1 The Geo/Geo/c Retrial Queue 241

9.2 The BMAP/SM/1 Retrial Queue 255

9.3 Bibliographical Notes 266

References 269

Author Index 311

Subject Index 315