Buch, Englisch, Band 24, 490 Seiten, HC runder Rücken kaschiert, Format (B × H): 160 mm x 241 mm, Gewicht: 1950 g
Reihe: International Series in Operations Research & Management Science
Buch, Englisch, Band 24, 490 Seiten, HC runder Rücken kaschiert, Format (B × H): 160 mm x 241 mm, Gewicht: 1950 g
Reihe: International Series in Operations Research & Management Science
ISBN: 978-0-7923-8617-9
Verlag: Springer US
The work of major research scholars in this field comprises the individual chapters of Computational Probability. The first chapter describes, in nonmathematical terms, the challenges in computational probability. Chapter 2 describes the methodologies available for obtaining the transition matrices for Markov chains, with particular emphasis on stochastic Petri-nets. Chapter 3 discusses how to find transient probabilities and transient rewards for these Markov chains. The next two chapters indicate how to find steady-state probabilities for Markov chains with a finite number of states. Both direct and iterative methods are described in Chapter 4. Details of these methods are given in Chapter 5. Chapters 6 and 7 deal with infinite-state Markov chains, which occur frequently in queueing, because there are times one does not want to set a bound for all queues. Chapter 8 deals with transforms, in particular Laplace transforms. The work of Ward Whitt and his collaborators, who have recently developed a number of numerical methods for Laplace transform inversions, is emphasized in this chapter. Finally, if one wants to optimize a system, one way to do the optimization is through Markov decision making, described in Chapter 9. Markov modeling has found applications in many areas, three of which are described in detail:Chapter 10 analyzes discrete-time queues, Chapter 11 describes networks of queues, and Chapter 12 deals with reliability theory.
Zielgruppe
Research
Autoren/Hrsg.
Fachgebiete
- Wirtschaftswissenschaften Betriebswirtschaft Wirtschaftsmathematik und -statistik
- Mathematik | Informatik Mathematik Stochastik Wahrscheinlichkeitsrechnung
- Wirtschaftswissenschaften Volkswirtschaftslehre Volkswirtschaftslehre Allgemein Ökonometrie
- Interdisziplinäres Wissenschaften Wissenschaften: Forschung und Information Datenanalyse, Datenverarbeitung
- Mathematik | Informatik Mathematik Stochastik Mathematische Statistik
Weitere Infos & Material
1 Computational Probability: Challenges and Limitations.- 2 Tools for Formulating Markov Models.- 3 Transient Solutions for Markov Chains.- 4 Numerical Methods for Computing Stationary Distributions of Finite Irreducible Markov Chains.- 5 Stochastic Automata Networks.- 6 Matrix Analytic Methods.- 7 Use of Characteristic Roots for Solving Infinite State Markov Chains.- 8 An Introduction to Numerical Transform Inversion and Its Application to Probability Models.- 9 Optimal Control of Markov Chains.- 10 On Numerical Computations of Some Discrete-Time Queues.- 11 The Product Form Tool for Queueing Networks.- 12 Techniques for System Dependability Evaluation.