Queueing Theory 2. Nikolaos Limnios
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Table of Contents
1 Cover
4 Preface
5 1 Stability Analysis of Queueing Systems based on Synchronization of the Input and Majorizing Output Flows 1.1. Introduction 1.2. Model description 1.3. Auxiliary service process 1.4. Instability result for the case ρ ≥ 1 1.5. Stochastic boundedness for the case ρ < 1 1.6. Queueing system with unreliable servers and preemptive resume service discipline 1.7. Discrete-time queueing system with interruptions and preemptive repeat different service discipline 1.8. Queueing system with a preemptive priority discipline 1.9. Queueing system with simultaneous service of a customer by a random number of servers 1.10. Applications to transport systems analysis 1.11. Conclusion 1.12. Acknowledgment 1.13. References
6 2 Queueing Models in Services – Analytical and Simulation Approach 2.1. Introduction 2.2. Phase-type distributions and the batch Markovian arrival process 2.3. Generation of MAP processes for numerical purposes 2.4. Analysis of selected queueing models of BMAP/G/c type 2.5. Simulated models of BM AP/G/c type queues 2.6. Analysis of selected queueing models of BMAP/G/c type with a vacation 2.7. Acknowledgment 2.8. References
7 3 Distributions and Random Processes Related to Queueing and Reliability Models 3.1. Some useful notations, relationships and interpretations 3.2. Unreliable service model and reliability maintenance 3.3. Characterizations of exponential and geometric distributions via properties of service times 3.4 Probability distributions almost having lack of memory property 3.5. Random processes with a periodic nature 3.6. Conclusions 3.7. References
8 4 The Impact of Information Structure on Strategic Behavior in Queueing Systems 4.1. Introduction 4.2. Game-theoretical framework in queueing 4.3. The unobservable model 4.4. The observable model 4.5. Comparison of the unobservable and the observable models 4.6. Partially observable models 4.7. Heterogeneously observable models 4.8. Observable-with-delay models 4.9. Conclusions and literature review for further study 4.10. Acknowledgments 4.11. References
9 5 Non-extensive Maximum Entropy Formalisms and Inductive Inference of a Stable M/G/1 Queue with Heavy Tails 5.1 Introduction 5.2 General systems and inductive ME formalisms 5.3. NME formalisms and EME consistency axioms 5.4. A stable M/G/1 queue with long-range interactions 5.5. Numerical experiments and interpretations 5.6. Conclusions 5.7. Acknowledgments 5.8. Appendix: Rényi’s NME formalisms versus EME consistency axioms 5.9. References
10 6 Inventory with Positive Service Time: a Survey 6.1. Introduction 6.2. Queueing inventory models 6.3. Acknowledgment 6.4. References
11 7 A Stability Analysis Method of Regenerative Queueing Systems 7.1. Introduction