The Resource Max Plus at work : modeling and analysis of synchronized systems : a course on MaxPlus algebra and its applications, Bernd Heidergott, Geert Jan Olsder, Jacob van der Woude
Max Plus at work : modeling and analysis of synchronized systems : a course on MaxPlus algebra and its applications, Bernd Heidergott, Geert Jan Olsder, Jacob van der Woude
 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 maxplus 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 maxplus algebra, providing a concise and selfcontained introduction to the topic. Applications of maxplus algebra abound in the world around us. Traffic systems, compu
 Language
 eng
 Extent
 1 online resource (226 pages)
 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. MAXPLUS ALGEBRA; Chapter 1. MaxPlus Algebra; 1.1 Basic Concepts and Definitions; 1.2 Vectors and Matrices; 1.3 A First MaxPlus 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 CycleTime Vector3.1 Cyclicity and Transient Time; 3.2 The CycleTime Vector: Preliminary Results; 3.3 The CycleTime 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 HigherOrder 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 HigherOrder 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 MaxPlus 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 MaxPlus 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. MinMaxPlus Systems and Beyond12.1 MinMaxPlus 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
 Isbn
 9781400865239
 Label
 Max Plus at work : modeling and analysis of synchronized systems : a course on MaxPlus algebra and its applications
 Title
 Max Plus at work
 Title remainder
 modeling and analysis of synchronized systems : a course on MaxPlus algebra and its applications
 Statement of responsibility
 Bernd Heidergott, Geert Jan Olsder, Jacob van der Woude
 Language
 eng
 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 maxplus 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 maxplus algebra, providing a concise and selfcontained introduction to the topic. Applications of maxplus algebra abound in the world around us. Traffic systems, compu
 Cataloging source
 E7B
 Illustrations
 illustrations
 Index
 index present
 Language note
 In English
 Literary form
 non fiction
 Nature of contents

 dictionaries
 bibliography
 Series statement
 Princeton Series in Applied Mathematics
 Label
 Max Plus at work : modeling and analysis of synchronized systems : a course on MaxPlus algebra and its applications, Bernd Heidergott, Geert Jan Olsder, Jacob van der Woude
 Bibliography note
 Includes bibliographical references and index
 Carrier category
 online resource
 Carrier category code
 cr
 Carrier MARC source
 rdacarrier
 Color
 multicolored
 Content category
 text
 Content type code
 txt
 Content type MARC source
 rdacontent
 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. MAXPLUS ALGEBRA; Chapter 1. MaxPlus Algebra; 1.1 Basic Concepts and Definitions; 1.2 Vectors and Matrices; 1.3 A First MaxPlus 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 CycleTime Vector3.1 Cyclicity and Transient Time; 3.2 The CycleTime Vector: Preliminary Results; 3.3 The CycleTime 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 HigherOrder 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 HigherOrder 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 MaxPlus 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 MaxPlus 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. MinMaxPlus Systems and Beyond12.1 MinMaxPlus 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
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 unknown
 http://library.link/vocab/discovery_link
 {'f': 'http://opac.lib.rpi.edu/record=b4332604'}
 Extent
 1 online resource (226 pages)
 Form of item
 online
 Isbn
 9781400865239
 Media category
 computer
 Media MARC source
 rdamedia
 Media type code
 c
 Other physical details
 illustrations.
 Specific material designation
 remote
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