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| 020 ## - INTERNATIONAL STANDARD BOOK NUMBER |
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| International Standard Book Number |
9781789450019 |
| 020 ## - INTERNATIONAL STANDARD BOOK NUMBER |
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| International Standard Book Number |
9781119755432 |
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(electronic bk. : oBook) |
| 020 ## - INTERNATIONAL STANDARD BOOK NUMBER |
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| International Standard Book Number |
1119755433 |
| Qualifying information |
(electronic bk. : oBook) |
| 024 7# - OTHER STANDARD IDENTIFIER |
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| Standard number or code |
10.1002/9781119755432 |
| Source of number or code |
doi |
| 035 ## - SYSTEM CONTROL NUMBER |
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| System control number |
(OCoLC)1250024317 |
| 040 ## - CATALOGING SOURCE |
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| Original cataloging agency |
DG1 |
| Language of cataloging |
eng |
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rda |
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pn |
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DG1 |
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OCLCO |
| 041 ## - LANGUAGE CODE |
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| Language code of text/sound track or separate title |
eng. |
| 050 #4 - LIBRARY OF CONGRESS CALL NUMBER |
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| Classification number |
T57.9 |
| 082 04 - DEWEY DECIMAL CLASSIFICATION NUMBER |
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| Classification number |
519.8/2 |
| Edition number |
23 |
| 245 00 - TITLE STATEMENT |
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| Title |
Queueing theory. |
| Number of part/section of a work |
1, |
| Name of part/section of a work |
Advanced trends / |
| Statement of responsibility, etc |
Coordinated by Vladimir Anisimov, Nikolaos Limnios. |
| 264 #1 - PUBLICATION, DISTRIBUTION, ETC. (IMPRINT) |
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| Place of publication, distribution, etc |
London, UK : |
| Name of publisher, distributor, etc |
ISTE, Ltd. ; |
| Place of publication, distribution, etc |
Hoboken, NJ : |
| Name of publisher, distributor, etc |
Wiley, |
| Date of publication, distribution, etc |
[2021] |
| 300 ## - PHYSICAL DESCRIPTION |
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| Extent |
1 online resource. |
| 336 ## - CONTENT TYPE |
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text |
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txt |
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rdacontent. |
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computer |
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rdamedia. |
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online resource |
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cr |
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rdacarrier. |
| 340 ## - PHYSICAL MEDIUM |
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rdacc |
| Authority record control number or standard number |
http://rdaregistry.info/termList/RDAColourContent/1003. |
| 490 1# - SERIES STATEMENT |
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| Series statement |
Mathematics, Queueing theory and applications. |
| 504 ## - BIBLIOGRAPHY, ETC. NOTE |
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| Bibliography, etc |
Includes bibliographical references and index. |
| 505 0# - CONTENTS |
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| Formatted contents note |
Table of Contents<br/><br/>Preface xi<br/><br/>Chapter 1. Discrete Time Single-server Queues with Interdependent Interarrival and Service Times 1<br/>Attahiru Sule ALFA<br/><br/>1.1. Introduction 1<br/><br/>1.2. The Geo/Geo/1 case 3<br/><br/>1.2.1. Arrival probability as a function of service completion probability 4<br/><br/>1.2.2. Service times dependent on interarrival times 6<br/><br/>1.3. The PH/PH/1 case 7<br/><br/>1.3.1. A review of discrete PH distribution 7<br/><br/>1.3.2. The PH/PH/1 system 9<br/><br/>1.4. The model with multiple interarrival time distributions 10<br/><br/>1.4.1. Preliminaries 11<br/><br/>1.4.2. A queueing model with interarrival times dependent on service times 13<br/><br/>1.5. Interdependent interarrival and service times 15<br/><br/>1.5.1. A discrete time queueing model with bivariate geometric distribution 16<br/><br/>1.5.2. Matrix equivalent model 17<br/><br/>1.6. Conclusion 18<br/><br/>1.7. Acknowledgements 18<br/><br/>1.8. References 18<br/><br/>Chapter 2. Busy Period, Congestion Analysis and Loss Probability in Fluid Queues 21<br/>Fabrice GUILLEMIN, Marie-Ange REMICHE and Bruno SERICOLA<br/><br/>2.1. Introduction 21<br/><br/>2.2. Modeling a link under congestion and buffer fluctuations 24<br/><br/>2.2.1. Model description 25<br/><br/>2.2.2. Peaks and valleys 26<br/><br/>2.2.3. Minimum valley height in a busy period 28<br/><br/>2.2.4. Maximum peak level in a busy period 33<br/><br/>2.2.5. Maximum peak under a fixed fluid level 37<br/><br/>2.3. Fluid queue with finite buffer 42<br/><br/>2.3.1. Congestion metrics 42<br/><br/>2.3.2. Minimum valley height in a busy period 43<br/><br/>2.3.3. Reduction of the state space 46<br/><br/>2.3.4. Distributions of τ1(x) and V1(x) 47<br/><br/>2.3.5. Sequences of idle and busy periods 49<br/><br/>2.3.6. Joint distributions of loss periods and loss volumes 51<br/><br/>2.3.7. Total duration of losses and volume of information lost 56<br/><br/>2.4. Conclusion 59<br/><br/>2.5. References 60<br/><br/>Chapter 3. Diffusion Approximation of Queueing Systems and Networks 63<br/>Dimitri KOROLIOUK and Vladimir S. KOROLIUK<br/><br/>3.1. Introduction 63<br/><br/>3.2. Markov queueing processes 64<br/><br/>3.3. Average and diffusion approximation 65<br/><br/>3.3.1. Average scheme 65<br/><br/>3.3.2. Diffusion approximation scheme 68<br/><br/>3.3.3. Stationary distribution 73<br/><br/>3.4. Markov queueing systems 78<br/><br/>3.4.1. Collective limit theorem in R1 78<br/><br/>3.4.2. Systems of M/M type 81<br/><br/>3.4.3. Repairman problem 82<br/><br/>3.5. Markov queueing networks 85<br/><br/>3.5.1. Collective limit theorems in RN 85<br/><br/>3.5.2. Markov queueing networks 89<br/><br/>3.5.3. Superposition of Markov processes 91<br/><br/>3.6. Semi–Markov queueing systems 92<br/><br/>3.7. Acknowledgements 96<br/><br/>3.8. References 96<br/><br/>Chapter 4. First-come First-served Retrial Queueing System by Laszlo Lakatos and its Modifications 97<br/>Igor Nikolaevich KOVALENKO†<br/><br/>4.1. Introduction 97<br/><br/>4.2. A contribution by Laszlo Lakatos and his disciples 98<br/><br/>4.3. A contribution by E.V. Koba 98<br/><br/>4.4. An Erlangian and hyper-Erlangian approximation for a Laszlo Lakatos-type queueing system 99<br/><br/>4.5. Two models with a combined queueing discipline 102<br/><br/>4.6. References 104<br/><br/>Chapter 5. Parameter Mixing in Infinite-server Queues 107<br/>Lucas VAN KREVELD and Onno BOXMA<br/><br/>5.1. Introduction 107<br/><br/>5.2. The MΛ/Coxn/∞ queue 109<br/><br/>5.2.1. The differential equation 110<br/><br/>5.2.2. Calculating moments 113<br/><br/>5.2.3. Steady state 120<br/><br/>5.2.4. MΛ/M/∞ 125<br/><br/>5.3. Mixing in Markov-modulated infinite-server queues 131<br/><br/>5.3.1. The differential equation 131<br/><br/>5.3.2. Calculating moments 133<br/><br/>5.4. Discussion and future work 142<br/><br/>5.5. References 143<br/><br/>Chapter 6. Application of Fast Simulation Methods of Queueing Theory for Solving Some High-dimension Combinatorial Problems 145<br/>Igor KUZNETSOV and Nickolay KUZNETSOV<br/><br/>6.1. Introduction 146<br/><br/>6.2. Upper and lower bounds for the number of some k-dimensional subspaces of a given weight over a finite field 147<br/><br/>6.2.1. A general fast simulation algorithm 149<br/><br/>6.2.2. An auxiliary algorithm 153<br/><br/>6.2.3. Exact analytical formulae for the cases k = 1 and k = 2 155<br/><br/>6.2.4. The upper and lower bounds for the probability P{Yω(r)} 158<br/><br/>6.2.5. Numerical results 164<br/><br/>6.3. Evaluation of the number of “good” permutations by fast simulation on the SCIT-4 multiprocessor computer complex 167<br/><br/>6.3.1. Modified fast simulation method 168<br/><br/>6.3.2. Numerical results 171<br/><br/>6.4. References 174<br/><br/>Chapter 7. Diffusion and Gaussian Limits for Multichannel Queueing Networks 177<br/>Eugene LEBEDEV and Hanna LIVINSKA<br/><br/>7.1. Introduction 177<br/><br/>7.2. Model description and notation 182<br/><br/>7.3. Local approach to prove limit theorems 184<br/><br/>7.3.1. Network of the [GI|M|∞]r-type in heavy traffic 185<br/><br/>7.4. Limit theorems for networks with controlled input flow 190<br/><br/>7.4.1. Diffusion approximation of [SM|M|∞]r-networks 190<br/><br/>7.4.2. Asymptotics of stationary distribution for [SM|GI|∞]r-networks 192<br/><br/>7.4.3. Convergence to Ornstein–Uhlenbeck process 194<br/><br/>7.5. Gaussian approximation of networks with input flow of general structure 195<br/><br/>7.5.1. Gaussian approximation of [G|M|∞]r-networks 195<br/><br/>7.5.2. Criterion of Markovian behavior for r-dimensional Gaussian processes 197<br/><br/>7.5.3. Non-Markov Gaussian approximation of [G|GI|∞]r-networks 198<br/><br/>7.6. Limit processes for network with time-dependent input flow 201<br/><br/>7.6.1. Gaussian approximation of [Mt|M|∞]r -networks in heavy traffic 201<br/><br/>7.6.2. Limit process in case of asymptotically large initial load 205<br/><br/>7.7. Conclusion 207<br/><br/>7.8. Acknowledgements 208<br/><br/>7.9. References 208<br/><br/>Chapter 8. Recent Results in Finite-source Retrial Queues with Collisions 213<br/>Anatoly NAZAROV, János SZTRIK and Anna KVACH<br/><br/>8.1. Introduction 213<br/><br/>8.2. Model description and notations 216<br/><br/>8.3. Systems with a reliable server 220<br/><br/>8.3.1. M/M/1 systems 220<br/><br/>8.3.2. M/GI/1 system 224<br/><br/>8.4. Systems with an unreliable server 229<br/><br/>8.4.1. M/M/1 system 229<br/><br/>8.4.2. M/GI/1 system 237<br/><br/>8.4.3. Stochastic simulation of special systems 240<br/><br/>8.4.4. Gamma distributed retrial times 242<br/><br/>8.4.5. The effect of breakdowns disciplines 243<br/><br/>8.5. Conclusion 251<br/><br/>8.6. Acknowledgments 253<br/><br/>8.7. References 253<br/><br/>Chapter 9. Strong Stability of Queueing Systems and Networks: a Survey and Perspectives 259<br/>Boualem RABTA, Ouiza LEKADIR and Djamil AÏSSANI<br/><br/>9.1. Introduction 259<br/><br/>9.2. Preliminary and notations 261<br/><br/>9.3. Strong stability of queueing systems 263<br/><br/>9.3.1. M/M/1 queue 264<br/><br/>9.3.2. PH/M/1 and M/PH/1 queues 269<br/><br/>9.3.3. G/M/1 and M/G/1 queues 270<br/><br/>9.3.4. Other queues 276<br/><br/>9.3.5. Queueing networks 277<br/><br/>9.3.6. Non-parametric perturbation 286<br/><br/>9.4. Conclusion and further directions 287<br/><br/>9.5. References 287<br/><br/>Chapter 10. Time-varying Queues: a Two-time-scale Approach 293<br/>George YIN, Hanqin ZHANG and Qing ZHANG<br/><br/>10.1. Introduction 293<br/><br/>10.2. Time-varying queues 295<br/><br/>10.3. Main results 298<br/><br/>10.3.1. Large deviations of two-time-scale queues 298<br/><br/>10.3.2. Computation of H(y, t) 301<br/><br/>10.3.3. Applications to queueing systems 303<br/><br/>10.4. Concluding remarks 309<br/><br/>10.5. References 310<br/><br/>List of Authors 313<br/><br/>Index 315 |
| 520 ## - SUMMARY, ETC. |
|---|
| Summary, etc |
Description<br/>The aim of this book is to reflect the current cutting-edge thinking and established practices in the investigation of queueing systems and networks.<br/><br/>This first volume includes ten chapters written by experts well-known in their areas. The book studies the analysis of queues with interdependent arrival and service times, characteristics of fluid queues, modifications of retrial queueing systems and finite-source retrial queues with random breakdowns, repairs and customers’ collisions. Some recent tendencies in the asymptotic analysis include the average and diffusion approximation of Markov queueing systems and networks, the diffusion and Gaussian limits of multi-channel queueing networks with rather general input flow, and the analysis of two-time-scale nonhomogenous Markov chains using the large deviations principle.<br/><br/>The book also analyzes transient behavior of infinite-server queueing models with a mixed arrival process, the strong stability of queueing systems and networks, and applications of fast simulation methods for solving high-dimension combinatorial problems. |
| 545 0# - BIOGRAPHICAL OR HISTORICAL DATA |
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| Biographical or historical note |
About the Author<br/><br/>Vladimir Anisimov is Full Professor in Applied Statistics. He works in the Center for Design & Analysis at Amgen Inc. in London, UK. His research interests include probability models and stochastic processes, clinical trials modeling, applied statistics, queueing models and asymptotic techniques.<br/><br/>Nikolaos Limnios is Full Professor in Applied Mathematics at the University of Technology of Compiègne, part of the Sorbonne University Group, in France. His research interests include stochastic processes and statistics, Markov and semi-Markov processes, random evolutions with applications in reliability, queueing systems, earthquakes and biology. |
| 650 #0 - SUBJECT ADDED ENTRY--TOPICAL TERM |
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| Topical term or geographic name as entry element |
Queuing theory. |
| Authority record control number |
http://id.loc.gov/authorities/subjects/sh85109832. |
| 655 #4 - INDEX TERM--GENRE/FORM |
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| Genre/form data or focus term |
Electronic books. |
| 700 1# - ADDED ENTRY--PERSONAL NAME |
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| Personal name |
Anisimov, Vladimir |
| Fuller form of name |
(Vladimir Timofeevich), |
| Authority record control number |
http://id.loc.gov/authorities/names/no2014003833 |
| Relator term |
editor. |
| 700 1# - ADDED ENTRY--PERSONAL NAME |
|---|
| Personal name |
Limnios, N. |
| Fuller form of name |
(Nikolaos), |
| Authority record control number |
http://id.loc.gov/authorities/names/n98057246 |
| Relator term |
editor. |
| 830 #0 - SERIES ADDED ENTRY--UNIFORM TITLE |
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| Uniform title |
Mathematics, Queueing theory and applications. |
| 856 ## - ELECTRONIC LOCATION AND ACCESS |
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| Uniform Resource Identifier |
https://onlinelibrary.wiley.com/doi/book/10.1002/9781119755432 |
| Link text |
Full text is available at Wiley Online Library Click here to view. |
| 942 ## - ADDED ENTRY ELEMENTS |
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| Source of classification or shelving scheme |
|
| Item type |
EBOOK |