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Max Plus at work : modeling and analysis of synchronized systems : a course on Max-Plus algebra and its applications / Bernd Heidergott, Geert Jan Olsder, Jacob van der Woude.

By: Heidergott, Bernd [author.].
Contributor(s): Olsder, Geert Jan [author.] | Woude, J. W. van der [author.].
Material type: materialTypeLabelBookSeries: Princeton series in applied mathematics: Publisher: Princeton, New Jersey ; Oxfordshire, England : Princeton University Press, 2006Copyright date: �2006Description: 1 online resource (226 pages) : illustrations.Content type: text Media type: computer Carrier type: online resourceISBN: 9781400865239; 1400865239; 0691117632; 9780691117638.Subject(s): Matrices -- Textbooks | System theory -- Textbooks | MATHEMATICS -- Algebra -- Intermediate | MATHEMATICS -- Algebra -- General | Matrices | System theoryGenre/Form: Electronic books. | Electronic books. | Textbooks.Additional physical formats: Print version:: Max Plus at work : modeling and analysis of synchronized systems : a course on Max-Plus algebra and its applications.DDC classification: 512 Online resources: Click here to access online
Contents:
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.
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.
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.
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.
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.
Summary: 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.
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Includes bibliographical references and index.

Print version record.

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.

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.

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.

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.

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.

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.

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