Queueing theory 1 : advanced trends

Queueing theory 1 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 first volume includes ten chapters written by experts well-known in their areas. The book studies the analysis of queues with interdependent arri...

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Detalles Bibliográficos
Otros Autores: Limnios, N. (Nikolaos), editor (editor), Anisimov, Vladimir, editor
Formato: Libro electrónico
Idioma:Inglés
Publicado: London, England ; Hoboken, New Jersey : ISTE Ltd [2020]
Edición:1st edition
Materias:
Queuing theory.
Ver en Biblioteca Universitat Ramon Llull:https://discovery.url.edu/permalink/34CSUC_URL/1im36ta/alma991009724215606719
Tabla de Contenidos:
  • Cover
  • Half-Title Page
  • Title Page
  • Copyright Page
  • Contents
  • Preface
  • 1 Discrete Time Single-server Queues with Interdependent Interarrival and Service Times
  • 1.1. Introduction
  • 1.2. The Geo/Geo/1 case
  • 1.2.1. Arrival probability as a function of service completion probability
  • 1.2.2. Service times dependent on interarrival times
  • 1.3. The PH/PH/1 case
  • 1.3.1. A review of discrete PH distribution
  • 1.3.2. The PH/PH/1 system
  • 1.4. The model with multiple interarrival time distributions
  • 1.4.1. Preliminaries
  • 1.4.2. A queueing model with interarrival times dependent on service times
  • 1.5. Interdependent interarrival and service times
  • 1.5.1. A discrete time queueing model with bivariate geometric distribution
  • 1.5.2. Matrix equivalent model
  • 1.6. Conclusion
  • 1.7. Acknowledgements
  • 1.8. References
  • 2 Busy Period, Congestion Analysis and Loss Probability in Fluid Queues
  • 2.1. Introduction
  • 2.2. Modeling a link under congestion and buffer fluctuations
  • 2.2.1. Model description
  • 2.2.2. Peaks and valleys
  • 2.2.3. Minimum valley height in a busy period
  • 2.2.4. Maximum peak level in a busy period
  • 2.2.5. Maximum peak under a fixed fluid level
  • 2.3. Fluid queue with finite buffer
  • 2.3.1. Congestion metrics
  • 2.3.2. Minimum valley height in a busy period
  • 2.3.3. Reduction of the state space
  • 2.3.4. Distributions of t1(x) and V1(x)
  • 2.3.5. Sequences of idle and busy periods
  • 2.3.6. Joint distributions of loss periods and loss volumes
  • 2.3.7. Total duration of losses and volume of information lost
  • 2.4. Conclusion
  • 2.5. References
  • 3 Diffusion Approximation of Queueing Systems and Networks
  • 3.1. Introduction
  • 3.2. Markov queueing processes
  • 3.3. Average and diffusion approximation
  • 3.3.1. Average scheme
  • 3.3.2. Diffusion approximation scheme.
  • 3.3.3. Stationary distribution
  • 3.4. Markov queueing systems
  • 3.4.1. Collective limit theorem in R1
  • 3.4.2. Systems of M/M type
  • 3.4.3. Repairman problem
  • 3.5. Markov queueing networks
  • 3.5.1. Collective limit theorems in RN
  • 3.5.2. Markov queueing networks
  • 3.5.3. Superposition of Markov processes
  • 3.6. Semi-Markov queueing systems
  • 3.7. Acknowledgements
  • 3.8. References
  • 4 First-come First-served Retrial Queueing System by Laszlo Lakatos and its Modifications
  • 4.1. Introduction
  • 4.2. A contribution by Laszlo Lakatos and his disciples
  • 4.3. A contribution by E.V. Koba
  • 4.4. An Erlangian and hyper-Erlangian approximation for a Laszlo Lakatos-type queueing system
  • 4.5. Two models with a combined queueing discipline
  • 4.6. References
  • 5 Parameter Mixing in Infinite-server Queues
  • 5.1. Introduction
  • 5.2. The M./Coxn/8 queue
  • 5.2.1. The differential equation
  • 5.2.2. Calculating moments
  • 5.2.3. Steady state
  • 5.2.4. M./M/8
  • 5.3. Mixing in Markov-modulated infinite-server queues
  • 5.3.1. The differential equation
  • 5.3.2. Calculating moments
  • 5.4. Discussion and future work
  • 5.5. References
  • 6 Application of Fast Simulation Methods of Queueing Theory for Solving Some High-dimension Combinatorial Problems
  • 6.1. Introduction
  • 6.2. Upper and lower bounds for the number of some k-dimensional subspaces of a given weight over a finite field
  • 6.2.1. A general fast simulation algorithm
  • 6.2.2. An auxiliary algorithm
  • 6.2.3. Exact analytical formulae for the cases k = 1 and k = 2
  • 6.2.4. The upper and lower bounds for the probability P{Y.(r)}
  • 6.2.5. Numerical results
  • 6.3. Evaluation of the number of "good" permutations by fast simulation on the SCIT-4 multiprocessor computer complex
  • 6.3.1. Modified fast simulation method
  • 6.3.2. Numerical results
  • 6.4. References.
  • 7 Diffusion and Gaussian Limits for Multichannel Queueing Networks
  • 7.1. Introduction
  • 7.2. Model description and notation
  • 7.3. Local approach to prove limit theorems
  • 7.3.1. Network of the [GI|M|8]r-type in heavy traffic
  • 7.4. Limit theorems for networks with controlled input flow
  • 7.4.1. Diffusion approximation of [SM|M|8]r-networks
  • 7.4.2. Asymptotics of stationary distribution for [SM|GI|8]r-networks
  • 7.4.3. Convergence to Ornstein-Uhlenbeck process
  • 7.5. Gaussian approximation of networks with input flow of general structure
  • 7.5.1. Gaussian approximation of [G|M|8]r-networks
  • 7.5.2. Criterion of Markovian behavior for r-dimensional Gaussian processes
  • 7.5.3. Non-Markov Gaussian approximation of [G|GI|8]r-networks
  • 7.6. Limit processes for network with time-dependent input flow
  • 7.6.1. Gaussian approximation of Mt|M|∞ r-networks in heavy traffic
  • 7.6.2. Limit process in case of asymptotically large initial load
  • 7.7. Conclusion
  • 7.8. Acknowledgements
  • 7.9. References
  • 8 Recent Results in Finite-source Retrial Queues with Collisions
  • 8.1. Introduction
  • 8.2. Model description and notations
  • 8.3. Systems with a reliable server
  • 8.3.1. M/M/1 systems
  • 8.3.2. M/GI/1 system
  • 8.4. Systems with an unreliable server
  • 8.4.1. M/M/1 system
  • 8.4.2. M/GI/1 system
  • 8.4.3. Stochastic simulation of special systems
  • 8.4.4. Gamma distributed retrial times
  • 8.4.5. The effect of breakdowns disciplines
  • 8.5. Conclusion
  • 8.6. Acknowledgments
  • 8.7. References
  • 9 Strong Stability of Queueing Systems and Networks: a Survey and Perspectives
  • 9.1. Introduction
  • 9.2. Preliminary and notations
  • 9.3. Strong stability of queueing systems
  • 9.3.1. M/M/1 queue
  • 9.3.2. PH/M/1 and M/PH/1 queues
  • 9.3.3. G/M/1 and M/G/1 queues
  • 9.3.4. Other queues
  • 9.3.5. Queueing networks.
  • 9.3.6. Non-parametric perturbation
  • 9.4. Conclusion and further directions
  • 9.5. References
  • 10 Time-varying Queues: a Two-time-scale Approach
  • 10.1. Introduction
  • 10.2. Time-varying queues
  • 10.3. Main results
  • 10.3.1. Large deviations of two-time-scale queues
  • 10.3.2. Computation of H(y, t)
  • 10.3.3. Applications to queueing systems
  • 10.4. Concluding remarks
  • 10.5. References
  • List of Authors
  • Index
  • EULA.

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