Max Plus at Work : Modeling and Analysis of Synchronized Systems: a Course on Max-Plus Algebra and Its Applications.
Heidergott, Bernd.
Max Plus at Work : Modeling and Analysis of Synchronized Systems: a Course on Max-Plus Algebra and Its Applications. - 1st ed. - 1 online resource (226 pages) - Princeton Series in Applied Mathematics Series ; v.48 . - Princeton Series in Applied Mathematics Series .
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 Vector -- 3.1 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 Notes -- Chapter 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 Network -- 9.1 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 Beyond -- 12.1 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.
No detailed description available for "Max Plus at Work".
9781400865239
Matrices.
Electronic books.
QA188 / .H445 2006
Max Plus at Work : Modeling and Analysis of Synchronized Systems: a Course on Max-Plus Algebra and Its Applications. - 1st ed. - 1 online resource (226 pages) - Princeton Series in Applied Mathematics Series ; v.48 . - Princeton Series in Applied Mathematics Series .
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 Vector -- 3.1 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 Notes -- Chapter 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 Network -- 9.1 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 Beyond -- 12.1 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.
No detailed description available for "Max Plus at Work".
9781400865239
Matrices.
Electronic books.
QA188 / .H445 2006