Queueing theory 2 : advanced trends / / edited by Vladimir Anisimov, Nikolaos Limnios

• Pubblicazione: Hoboken, New Jersey : , : John Wiley & Sons, Incorporated, , [2020]; ©2020
• Descrizione fisica: 1 online resource (328 pages) : illustrations
• Disciplina: 519.82
• Soggetto topico: Queuing theory
• Soggetto genere / forma: Electronic books.
• Persona (resp. second.): LimniosNikolaos; AnisimovVladimir
• Note generali: Includes index.
• Nota di contenuto: 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 < -- 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.
• Titolo autorizzato: Queueing theory 2
• ISBN: 1-119-75522-0; 1-119-75523-9; 1-119-75521-2
• Formato: Materiale a stampa
• Livello bibliografico: Monografia
• Lingua di pubblicazione: Inglese
• Record Nr.: 9910554880903321
• Lo trovi qui: Univ. Federico II