Queueing theory 1 : advanced trends / / edited by Vladimir Anisimov, Nikolaos Limnios

• Pubblicazione: London, England ; ; Hoboken, New Jersey : , : ISTE Ltd. : , : John Wiley & Sons, Incorporated, , [2020]; ©2020
• Descrizione fisica: 1 online resource (335 pages) : illustrations
• Disciplina: 519.82
• Soggetto topico: Queuing theory
• Soggetto genere / forma: Electronic books.
• Persona (resp. second.): LimniosN (Nikolaos); AnisimovVladimir
• Note generali: Includes index.
• Nota di contenuto: 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.
• Titolo autorizzato: Queueing theory 1
• ISBN: 1-119-75542-5; 1-119-75541-7
• Formato: Materiale a stampa
• Livello bibliografico: Monografia
• Lingua di pubblicazione: Inglese
• Record Nr.: 9910554883003321
• Lo trovi qui: Univ. Federico II