Probability, Markov Chains, Queues, and Simulation: The Mathematical Basis of Performance Modeling
Probability, Markov Chains, Queues, and Simulation provides a modern and authoritative treatment of the mathematical processes that underlie performance modeling. The detailed explanations of mathematical derivations and numerous illustrative examples make this textbook readily accessible to graduat...
Gespeichert in:
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| Format: | Elektronisch E-Book |
| Sprache: | English |
| Veröffentlicht: |
Princeton, NJ
Princeton University Press
[2009]
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| Schlagworte: | |
| Online-Zugang: | FAB01 FAW01 FCO01 FHA01 FKE01 FLA01 UBA01 UPA01 Volltext |
| Zusammenfassung: | Probability, Markov Chains, Queues, and Simulation provides a modern and authoritative treatment of the mathematical processes that underlie performance modeling. The detailed explanations of mathematical derivations and numerous illustrative examples make this textbook readily accessible to graduate and advanced undergraduate students taking courses in which stochastic processes play a fundamental role. The textbook is relevant to a wide variety of fields, including computer science, engineering, operations research, statistics, and mathematics. The textbook looks at the fundamentals of probability theory, from the basic concepts of set-based probability, through probability distributions, to bounds, limit theorems, and the laws of large numbers. Discrete and continuous-time Markov chains are analyzed from a theoretical and computational point of view. Topics include the Chapman-Kolmogorov equations; irreducibility; the potential, fundamental, and reachability matrices; random walk problems; reversibility; renewal processes; and the numerical computation of stationary and transient distributions. The M/M/1 queue and its extensions to more general birth-death processes are analyzed in detail, as are queues with phase-type arrival and service processes. The M/G/1 and G/M/1 queues are solved using embedded Markov chains; the busy period, residual service time, and priority scheduling are treated. Open and closed queueing networks are analyzed. The final part of the book addresses the mathematical basis of simulation. Each chapter of the textbook concludes with an extensive set of exercises. An instructor's solution manual, in which all exercises are completely worked out, is also available (to professors only). Numerous examples illuminate the mathematical theories Carefully detailed explanations of mathematical derivations guarantee a valuable pedagogical approach Each chapter concludes with an extensive set of exercises |
| Beschreibung: | 1 online resource (776 pages) |
| ISBN: | 9781400832811 |
| DOI: | 10.1515/9781400832811 |
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| 520 | |a Probability, Markov Chains, Queues, and Simulation provides a modern and authoritative treatment of the mathematical processes that underlie performance modeling. The detailed explanations of mathematical derivations and numerous illustrative examples make this textbook readily accessible to graduate and advanced undergraduate students taking courses in which stochastic processes play a fundamental role. The textbook is relevant to a wide variety of fields, including computer science, engineering, operations research, statistics, and mathematics. The textbook looks at the fundamentals of probability theory, from the basic concepts of set-based probability, through probability distributions, to bounds, limit theorems, and the laws of large numbers. Discrete and continuous-time Markov chains are analyzed from a theoretical and computational point of view. Topics include the Chapman-Kolmogorov equations; irreducibility; the potential, fundamental, and reachability matrices; random walk problems; reversibility; renewal processes; and the numerical computation of stationary and transient distributions. The M/M/1 queue and its extensions to more general birth-death processes are analyzed in detail, as are queues with phase-type arrival and service processes. The M/G/1 and G/M/1 queues are solved using embedded Markov chains; the busy period, residual service time, and priority scheduling are treated. Open and closed queueing networks are analyzed. The final part of the book addresses the mathematical basis of simulation. Each chapter of the textbook concludes with an extensive set of exercises. An instructor's solution manual, in which all exercises are completely worked out, is also available (to professors only). Numerous examples illuminate the mathematical theories Carefully detailed explanations of mathematical derivations guarantee a valuable pedagogical approach Each chapter concludes with an extensive set of exercises | ||
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Datensatz im Suchindex
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| discipline | Allgemeine Naturwissenschaft Wirtschaftswissenschaften |
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| id | DE-604.BV046285697 |
| illustrated | Not Illustrated |
| indexdate | 2024-07-10T08:40:35Z |
| institution | BVB |
| isbn | 9781400832811 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-031663273 |
| oclc_num | 1130278405 |
| open_access_boolean | |
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| owner_facet | DE-1046 DE-Aug4 DE-859 DE-860 DE-739 DE-1043 DE-858 DE-384 |
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| publishDate | 2009 |
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| publisher | Princeton University Press |
| record_format | marc |
| spelling | Stewart, William J. 1946- Verfasser (DE-588)124089143 aut Probability, Markov Chains, Queues, and Simulation The Mathematical Basis of Performance Modeling William J. Stewart Princeton, NJ Princeton University Press [2009] © 2009 1 online resource (776 pages) txt rdacontent c rdamedia cr rdacarrier Probability, Markov Chains, Queues, and Simulation provides a modern and authoritative treatment of the mathematical processes that underlie performance modeling. The detailed explanations of mathematical derivations and numerous illustrative examples make this textbook readily accessible to graduate and advanced undergraduate students taking courses in which stochastic processes play a fundamental role. The textbook is relevant to a wide variety of fields, including computer science, engineering, operations research, statistics, and mathematics. The textbook looks at the fundamentals of probability theory, from the basic concepts of set-based probability, through probability distributions, to bounds, limit theorems, and the laws of large numbers. Discrete and continuous-time Markov chains are analyzed from a theoretical and computational point of view. Topics include the Chapman-Kolmogorov equations; irreducibility; the potential, fundamental, and reachability matrices; random walk problems; reversibility; renewal processes; and the numerical computation of stationary and transient distributions. The M/M/1 queue and its extensions to more general birth-death processes are analyzed in detail, as are queues with phase-type arrival and service processes. The M/G/1 and G/M/1 queues are solved using embedded Markov chains; the busy period, residual service time, and priority scheduling are treated. Open and closed queueing networks are analyzed. The final part of the book addresses the mathematical basis of simulation. Each chapter of the textbook concludes with an extensive set of exercises. An instructor's solution manual, in which all exercises are completely worked out, is also available (to professors only). Numerous examples illuminate the mathematical theories Carefully detailed explanations of mathematical derivations guarantee a valuable pedagogical approach Each chapter concludes with an extensive set of exercises MATHEMATICS / Applied bisacsh Markov processes Probabilities - Computer simulation Probabilities -- Computer simulation Probabilities Computer simulation Queuing theory Wahrscheinlichkeitsrechnung (DE-588)4064324-4 gnd rswk-swf Warteschlangentheorie (DE-588)4255044-0 gnd rswk-swf Leistungsbewertung (DE-588)4167271-9 gnd rswk-swf Computersimulation (DE-588)4148259-1 gnd rswk-swf Mathematische Methode (DE-588)4155620-3 gnd rswk-swf Datenverarbeitungssystem (DE-588)4125229-9 gnd rswk-swf Markov-Prozess (DE-588)4134948-9 gnd rswk-swf Wahrscheinlichkeitsrechnung (DE-588)4064324-4 s Markov-Prozess (DE-588)4134948-9 s Warteschlangentheorie (DE-588)4255044-0 s Computersimulation (DE-588)4148259-1 s 1\p DE-604 Datenverarbeitungssystem (DE-588)4125229-9 s Leistungsbewertung (DE-588)4167271-9 s Mathematische Methode (DE-588)4155620-3 s 2\p DE-604 https://doi.org/10.1515/9781400832811 Verlag URL des Erstveröffentlichers Volltext 1\p cgwrk 20201028 DE-101 https://d-nb.info/provenance/plan#cgwrk 2\p cgwrk 20201028 DE-101 https://d-nb.info/provenance/plan#cgwrk |
| spellingShingle | Stewart, William J. 1946- Probability, Markov Chains, Queues, and Simulation The Mathematical Basis of Performance Modeling MATHEMATICS / Applied bisacsh Markov processes Probabilities - Computer simulation Probabilities -- Computer simulation Probabilities Computer simulation Queuing theory Wahrscheinlichkeitsrechnung (DE-588)4064324-4 gnd Warteschlangentheorie (DE-588)4255044-0 gnd Leistungsbewertung (DE-588)4167271-9 gnd Computersimulation (DE-588)4148259-1 gnd Mathematische Methode (DE-588)4155620-3 gnd Datenverarbeitungssystem (DE-588)4125229-9 gnd Markov-Prozess (DE-588)4134948-9 gnd |
| subject_GND | (DE-588)4064324-4 (DE-588)4255044-0 (DE-588)4167271-9 (DE-588)4148259-1 (DE-588)4155620-3 (DE-588)4125229-9 (DE-588)4134948-9 |
| title | Probability, Markov Chains, Queues, and Simulation The Mathematical Basis of Performance Modeling |
| title_auth | Probability, Markov Chains, Queues, and Simulation The Mathematical Basis of Performance Modeling |
| title_exact_search | Probability, Markov Chains, Queues, and Simulation The Mathematical Basis of Performance Modeling |
| title_full | Probability, Markov Chains, Queues, and Simulation The Mathematical Basis of Performance Modeling William J. Stewart |
| title_fullStr | Probability, Markov Chains, Queues, and Simulation The Mathematical Basis of Performance Modeling William J. Stewart |
| title_full_unstemmed | Probability, Markov Chains, Queues, and Simulation The Mathematical Basis of Performance Modeling William J. Stewart |
| title_short | Probability, Markov Chains, Queues, and Simulation |
| title_sort | probability markov chains queues and simulation the mathematical basis of performance modeling |
| title_sub | The Mathematical Basis of Performance Modeling |
| topic | MATHEMATICS / Applied bisacsh Markov processes Probabilities - Computer simulation Probabilities -- Computer simulation Probabilities Computer simulation Queuing theory Wahrscheinlichkeitsrechnung (DE-588)4064324-4 gnd Warteschlangentheorie (DE-588)4255044-0 gnd Leistungsbewertung (DE-588)4167271-9 gnd Computersimulation (DE-588)4148259-1 gnd Mathematische Methode (DE-588)4155620-3 gnd Datenverarbeitungssystem (DE-588)4125229-9 gnd Markov-Prozess (DE-588)4134948-9 gnd |
| topic_facet | MATHEMATICS / Applied Markov processes Probabilities - Computer simulation Probabilities -- Computer simulation Probabilities Computer simulation Queuing theory Wahrscheinlichkeitsrechnung Warteschlangentheorie Leistungsbewertung Computersimulation Mathematische Methode Datenverarbeitungssystem Markov-Prozess |
| url | https://doi.org/10.1515/9781400832811 |
| work_keys_str_mv | AT stewartwilliamj probabilitymarkovchainsqueuesandsimulationthemathematicalbasisofperformancemodeling |