Queueing theory 2 : advanced trends

Queueing theory 2 advanced trends

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 second volume includes eight chapters written by experts wellknown in their areas. The book conducts a stability analysis of certain types of mul...

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Detalles Bibliográficos
Otros Autores: Limnios, Nikolaos, editor (editor), Anisimov, Vladimir, editor
Formato: Libro electrónico
Idioma:Inglés
Publicado: Hoboken, New Jersey : John Wiley & Sons, Incorporated [2020]
Colección:Sciences (Editions Eshel)
Materias:
Queuing theory.
Ver en Biblioteca Universitat Ramon Llull:https://discovery.url.edu/permalink/34CSUC_URL/1im36ta/alma991009724215706719
Tabla de Contenidos:
  • Cover
  • Half-Title Page
  • Title Page
  • Copyright Page
  • Contents
  • 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 &lt
  • 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 BMAP/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
  • 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
  • 3.4.3. 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
  • 5.5. 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
  • 6.2.2. Production inventory systems
  • 6.2.3. Multicommodity queueing-inventory system
  • 6.2.4. Retrial queues with inventory
  • 6.2.5. Queues requiring additional items for service
  • 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
  • 8.2.2. Uniformization
  • 8.3. First examples
  • 8.3.1. The Ehrenfest model in continuous-time
  • 8.3.2. The M/M/8 model
  • 8.3.3. A queue with no server and catastrophes
  • 8.3.4. The fundamental M/M/1 model
  • 8.3.5. M/M/1 with bounded waiting room: the M/M/1/H model
  • 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 the M/M/1 queueing system
  • 8.5.4. Application to the M/M/1/H queueing system
  • 8.5.5. Application to an M/M/1/H model with catastrophes
  • 8.6. Other transient results
  • 8.6.1. Busy period of the M/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
  • EULA.

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