Queueing Theory 1

Advanced Trends
1. Auflage 2021
ISBN: 978-1-78945-001-9
Verlag: Wiley

Buch, Englisch, 336 Seiten, Format (B × H): 161 mm x 240 mm, Gewicht: 665 g

The aim of this book is to reflect the current cutting-edge thinking and established practices in the investigation of queueing systems and networks.
This first volume includes ten chapters written by experts well-known in their areas. The book studies the analysis of queues with interdependent arrival and service times, characteristics of fluid queues, modifications of retrial queueing systems and finite-source retrial queues with random breakdowns, repairs and customers’ collisions. Some recent tendencies in the asymptotic analysis include the average and diffusion approximation of Markov queueing systems and networks, the diffusion and Gaussian limits of multi-channel queueing networks with rather general input flow, and the analysis of two-time-scale nonhomogenous Markov chains using the large deviations principle.

The book also analyzes transient behavior of infinite-server queueing models with a mixed arrival process, the strong stability of queueing systems and networks, and applications of fast simulation methods for solving high-dimension combinatorial problems.

Autoren/Hrsg.

Weitere Mitwirkende

Anisimov, Vladimir

Limnios, Nikolaos

Fachgebiete

• Mathematik | Informatik Mathematik Stochastik Wahrscheinlichkeitsrechnung
• Wirtschaftswissenschaften Betriebswirtschaft Unternehmensforschung

Inhaltsverzeichnis

Preface xi

Chapter 1. Discrete Time Single-server Queues with Interdependent Interarrival and Service Times 1
Attahiru Sule ALFA

1.1. Introduction 1

1.2. The Geo/Geo/1 case 3

1.2.1. Arrival probability as a function of service completion probability 4

1.2.2. Service times dependent on interarrival times 6

1.3. The PH/PH/1 case 7

1.3.1. A review of discrete PH distribution 7

1.3.2. The PH/PH/1 system 9

1.4. The model with multiple interarrival time distributions 10

1.4.1. Preliminaries 11

1.4.2. A queueing model with interarrival times dependent on service times 13

1.5. Interdependent interarrival and service times 15

1.5.1. A discrete time queueing model with bivariate geometric distribution 16

1.5.2. Matrix equivalent model 17

1.6. Conclusion 18

1.7. Acknowledgements 18

1.8. References 18

Chapter 2. Busy Period, Congestion Analysis and Loss Probability in Fluid Queues 21
Fabrice GUILLEMIN, Marie-Ange REMICHE and Bruno SERICOLA

2.1. Introduction 21

2.2. Modeling a link under congestion and buffer fluctuations 24

2.2.1. Model description 25

2.2.2. Peaks and valleys 26

2.2.3. Minimum valley height in a busy period 28

2.2.4. Maximum peak level in a busy period 33

2.2.5. Maximum peak under a fixed fluid level 37

2.3. Fluid queue with finite buffer 42

2.3.1. Congestion metrics 42

2.3.2. Minimum valley height in a busy period 43

2.3.3. Reduction of the state space 46

2.3.4. Distributions of t1(x) and V1(x) 47

2.3.5. Sequences of idle and busy periods 49

2.3.6. Joint distributions of loss periods and loss volumes 51

2.3.7. Total duration of losses and volume of information lost 56

2.4. Conclusion 59

2.5. References 60

Chapter 3. Diffusion Approximation of Queueing Systems and Networks 63

Über Autor(innen)

Vladimir Anisimov is Full Professor in Applied Statistics. He works in the Center for Design & Analysis at Amgen Inc. in London, UK. His research interests include probability models and stochastic processes, clinical trials modeling, applied statistics, queueing models and asymptotic techniques.
Nikolaos Limnios is Full Professor in Applied Mathematics at the University of Technology of Compiègne, part of the Sorbonne University Group, in France. His research interests include stochastic processes and statistics, Markov and semi-Markov processes, random evolutions with applications in reliability, queueing systems, earthquakes and biology.