Оглавление
Nikolaos Limnios. Queueing Theory 2
Table of Contents
List of Illustrations
List of Tables
Guide
Pages
Queueing Theory 2. Advanced Trends
Preface
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
2. Queueing Models in Services – Analytical and Simulation Approach
2.1. Introduction
2.2. Phase-type distributions and the batch Markovian arrival process
2.2.1. Phase-type distributions
2.2.2. Some useful results related to continuous PH distributions
2.2.3. 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
2.4.1. MAP/PH/1 queueing model
2.4.2. The system performance measures
2.4.3. Illustrative numerical examples for MAP/PH/1
2.4.4. MAP/M/c queueing model
2.4.5. The system performance measures
2.4.6. Illustrative numerical examples for MAP/M/c
2.5. Simulated models of BM AP/G/c type queues
2.5.1. Simulated model validation using MAP/M/c type queues
2.5.2. Simulated model validation using MAP/PH/1 type queues
2.5.3. Selected simulated models of BMAP/G/c type queues
2.6. Analysis of selected queueing models of BMAP/G/c type with a vacation
2.6.1. MAP/PH/1 queueing model with a vacation
2.6.2. The system performance measures
2.6.3. Illustrative numerical examples for MAP/PH/1 with a vacation
2.6.4. Validation of simulated model for vacation type queues
2.6.5. Selected simulated models of BMAP/G/c type queues with a vacation
2.7. Acknowledgment
2.8. References
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
3.3.1. Instant repairs: characterization of geometric distribution
3.3.2. Instant repairs: characterizations of the exponential distribution
3.3.3. Various simplifying conditions
3.3.4. Unreliable service, repair times included
3.4 Probability distributions almost having lack of memory property
3.4.1. Service time on an unreliable server: instantaneous repairs
3.4.2. Properties of ALM distributions, and equivalent presentations
3.4.2.1. Probability density
3.4.2.2. The failure rate λ(t) and Hazard rate Λ(t) functions
3.4.2.3. ALM is the waiting time to the first success of extended in time Bernoulli trials
3.4.3. Periodicity in natural phenomena
3.5. Random processes with a periodic nature
3.5.1. Counting processes
3.5.2. Characterization of an NPP
3.5.3. Applications in risk modeling
3.6. Conclusions
3.7. References
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
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. 5.2.1 “Classical” Shannon’s EME formalism with short-range interactions
5.2.2. Rényi’s and Tsallis’s NME formalisms with long-range interactions
5.3. NME formalisms and EME consistency axioms
5.4. A stable M/G/1 queue with long-range interactions
5.4.1. Background: Shannon’s EME state probability of a stable M/G/1 queue
5.4.2 Tsallis’ and Rényi’s NME state probabilities of a stable M/G/1 queue
5.4.3. Exact Rényi’s and Tsallis’ NME state probabilities with distinct GEq-type service time distributions
5.4.3.1 The underlying service time probability density functions
5.5. Numerical experiments and interpretations
5.6. Conclusions
5.7. Acknowledgments
5.8. Appendix: Rényi’s NME formalisms versus EME consistency axioms. 5.8.1. Uniqueness
5.8.2. Invariance
5.8.3. System independence
5.8.4. Subset independence
5.9. References
6. Inventory with Positive Service Time: a Survey
6.1. Introduction
6.2. Queueing inventory models
6.2.1. Single-commodity queueing-inventory systems
6.2.1.1. Queueing-inventory system with a product form solution
6.2.1.2. Queueing-inventory system with postponed work
6.2.1.3. Multiserver queueing-inventory system
6.2.1.4. Queueing systems with perishable inventory
6.2.2. Production inventory systems
6.2.3. Multicommodity queueing-inventory system
6.3.2.1. Queueing-inventory models with multiclass customers
6.2.4. Retrial queues with inventory
6.2.5. Queues requiring additional items for service
6.2.5.1. Miscellaneous items
6.2.6. Queueing-inventory: some work in progress and suggestions for future studies
6.3. Acknowledgment
6.4. References
7. A Stability Analysis Method of Regenerative Queueing Systems
7.1. Introduction
7.2. Preliminaries
7.3. The single-server system
7.4. The zero-delayed multiserver system
7.5. The delayed multiserver system: finiteness of the first regeneration period
7.6. Instability
7.6.1. Some comments on the method
7.7. Related research
7.8. Acknowledgments
7.9. References
8. Transient Analysis of Markovian Queueing Systems: a Survey with Focus on Closed-forms and Uniformization
8.1. Introduction
8.2. Basics on Markovian queues
8.2.1 Markov models
8.2.1.1. Some notation for basic queues
8.2.2. Uniformization
8.3. First examples
8.3.1. The Ehrenfest model in continuous-time
8.3.2. The M/M/∞ model
8.3.3. A queue with no server and catastrophes
8.3.4. The fundamental M/M/1 model
8.3.4.1. A different approach
8.3.5. M/M/1 with bounded waiting room: the M/M/1/Hmodel
8.3.5.1. The M/M/1 as the limit of the M/M/1/Hwhen H → ∞
8.3.6. Comments
8.4. An uniformization-based path for the M/M/1 with matrix generating functions
8.4.1. General case
8.4.2. Mean number of customers at time t in the M/M/1
8.5. An uniformization-based path using duality
8.5.1. Duality
8.5.2. The path toward the transient state distributions using duality
8.5.3. Application to theM/M/1 queueing system
8.5.4. Application to theM/M/1/Hqueueing system
8.5.5. Application to anM/M/1/Hmodel with catastrophes
8.6. Other transient results
8.6.1. Busy period of theM/M/1
8.6.2. Max backlog of the M/M/1 over a finite time interval
8.6.3. M/E/1
8.7. Conclusion
8.8. References
List of Authors
Index. A, B
C, D
E, F
G, H, I
L, M
N, P
Q
R
S
T, U
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