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Max Plus at Work : Modeling and Analysis of Synchronized Systems: A Course on Max-Plus Algebra and Its Applications /
Trains pull into a railroad station and must wait for each other before leaving again in order to let passengers change trains. How do mathematicians then calculate a railroad timetable that accurately reflects their comings and goings? One approach is to use max-plus algebra, a framework used to mo...
| Autores principales: | , , |
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| Formato: | Electrónico eBook |
| Idioma: | Inglés |
| Publicado: |
Oxfordshire, England :
Princeton University Press,
2006.
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| Colección: | Book collections on Project MUSE.
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| Temas: | |
| Acceso en línea: | Texto completo |
MARC
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| 020 | |a 9781400865239 | ||
| 020 | |z 9780691117638 | ||
| 040 | |a MdBmJHUP |c MdBmJHUP | ||
| 100 | 1 | |a Heidergott, Bernd, |e author. | |
| 245 | 1 | 0 | |a Max Plus at Work : |b Modeling and Analysis of Synchronized Systems: A Course on Max-Plus Algebra and Its Applications / |c Bernd Heidergott, Geert Jan Olsder, Jacob van der Woude. |
| 264 | 1 | |a Oxfordshire, England : |b Princeton University Press, |c 2006. | |
| 264 | 3 | |a Baltimore, Md. : |b Project MUSE, |c 0000 | |
| 264 | 4 | |c ©2006. | |
| 300 | |a 1 online resource: |b illustrations | ||
| 336 | |a text |b txt |2 rdacontent | ||
| 337 | |a computer |b c |2 rdamedia | ||
| 338 | |a online resource |b cr |2 rdacarrier | ||
| 490 | 0 | |a Princeton Series in Applied Mathematics | |
| 505 | 0 | |a Cover; Title; Copyright; Contents; Preface; Chapter 0. Prolegomenon; 0.1 Introductory Example; 0.2 On the Notation; 0.3 On Eigenvalues and Eigenvectors; 0.4 Some Modeling Issues; 0.5 Counter and Dater Descriptions; 0.6 Exercises; 0.7 Notes; PART I. MAX-PLUS ALGEBRA; Chapter 1. Max-Plus Algebra; 1.1 Basic Concepts and Definitions; 1.2 Vectors and Matrices; 1.3 A First Max-Plus Model; 1.4 The Projective Space; 1.5 Exercises; 1.6 Notes; Chapter 2. Spectral Theory; 2.1 Matrices and Graphs; 2.2 Eigenvalues and Eigenvectors; 2.3 Solving Linear Equations; 2.4 Exercises; 2.5 Notes. | |
| 505 | 0 | |a Chapter 3. Periodic Behavior and the Cycle-Time Vector3.1 Cyclicity and Transient Time; 3.2 The Cycle-Time Vector: Preliminary Results; 3.3 The Cycle-Time Vector: General Results; 3.4 A Sunflower Bouquet; 3.5 Exercises; 3.6 Notes ; Chapter 4. Asymptotic Qualitative Behavior; 4.1 Periodic Regimes; 4.2 Characterization of the Eigenspace; 4.3 Primitive Matrices; 4.4 Limits in the Projective Space; 4.5 Higher-Order Recurrence Relations; 4.6 Exercises; 4.7 Notes; Chapter 5. Numerical Procedures for Eigenvalues of Irreducible Matrices; 5.1 Karp''s Algorithm; 5.2 The Power Algorithm; 5.3 Exercises. | |
| 505 | 0 | |a 5.4 NotesChapter 6. A Numerical Procedure for Eigenvalues of Reducible Matrices; 6.1 Howard''s Algorithm; 6.2 Examples; 6.3 Howard''s Algorithm for Higher-Order Models; 6.4 Exercises; 6.5 Notes; PART II. TOOLS AND APPLICATIONS; Chapter 7. Petri Nets; 7.1 Petri Nets and Event Graphs; 7.2 The Autonomous Case; 7.3 The Nonautonomous Case; 7.4 Exercises; 7.5 Notes; Chapter 8. The Dutch Railway System Captured in a Max-Plus Model; 8.1 The Line System; 8.2 Construction of the Timed Event Graph; 8.3 State Space Description; 8.4 Application of Howard''s Algorithm; 8.5 Exercises; 8.6 Notes. | |
| 505 | 0 | |a Chapter 9. Delays, Stability Measures, and Results for the Whole Network9.1 Propagation of Delays; 9.2 Results for the Whole Dutch Intercity Network; 9.3 Other Modeling Issues ; 9.4 Exercises; 9.5 Notes; Chapter 10. Capacity Assessment; 10.1 Capacity Assessment with Different Types of Trains; 10.2 Capacity Assessment for a Series of Tunnels; 10.3 Exercises; 10.4 Notes; PART III. EXTENSIONS; Chapter 11. Stochastic Max-Plus Systems; 11.1 Basic Definitions and Examples; 11.2 The Subadditive Ergodic Theorem; 11.3 Matrices with Fixed Support; 11.4 Beyond Fixed Support; 11.5 Exercises; 11.6 Notes. | |
| 505 | 0 | |a Chapter 12. Min-Max-Plus Systems and Beyond12.1 Min-Max-Plus Systems; 12.2 Links to Other Mathematical Areas; 12.3 Exercises; 12.4 Notes; Chapter 13. Continuous and Synchronized Flows on Networks; 13.1 Dater and Counter Descriptions; 13.2 Continuous Flows without Capacity Constraints; 13.3 Continuous Flows with Capacity Constraints; 13.4 Exercises; 13.5 Notes; Bibliography; List of Symbols; Index. | |
| 520 | |a Trains pull into a railroad station and must wait for each other before leaving again in order to let passengers change trains. How do mathematicians then calculate a railroad timetable that accurately reflects their comings and goings? One approach is to use max-plus algebra, a framework used to model Discrete Event Systems, which are well suited to describe the ordering and timing of events. This is the first textbook on max-plus algebra, providing a concise and self-contained introduction to the topic. Applications of max-plus algebra abound in the world around us. Traffic systems, compu. | ||
| 546 | |a In English. | ||
| 588 | |a Description based on print version record. | ||
| 650 | 7 | |a System theory. |2 fast |0 (OCoLC)fst01141423 | |
| 650 | 7 | |a Matrices. |2 fast |0 (OCoLC)fst01012399 | |
| 650 | 7 | |a MATHEMATICS |x Algebra |x General. |2 bisacsh | |
| 650 | 7 | |a MATHEMATICS |x Algebra |x Intermediate. |2 bisacsh | |
| 650 | 0 | |a System theory |v Textbooks. | |
| 650 | 0 | |a Matrices |v Textbooks. | |
| 655 | 7 | |a Textbooks. |2 fast |0 (OCoLC)fst01423863 | |
| 655 | 7 | |a Electronic books. |2 local | |
| 700 | 1 | |a Woude, J. W. van der, |e author. | |
| 700 | 1 | |a Olsder, Geert Jan, |e author. | |
| 710 | 2 | |a Project Muse. |e distributor | |
| 830 | 0 | |a Book collections on Project MUSE. | |
| 856 | 4 | 0 | |z Texto completo |u https://projectmuse.uam.elogim.com/book/35304/ |
| 945 | |a Project MUSE - Custom Collection | ||