{"product_id":"max-plus-at-work-9780691117638","title":"Max Plus at Work","description":"\u003cb\u003eBook Synopsis\u003c\/b\u003e\u003cbr\u003eProvides a self-contained introduction to max-plus algebra. This book explores the introduction of max-plus algebra and of system descriptions based upon it. It deals with a real application, namely the design of timetables for railway networks. It also examines various extensions, such as stochastic systems and min-max-plus systems.\u003cbr\u003e\u003cbr\u003e\u003cb\u003eTrade Review\u003c\/b\u003e\u003cbr\u003e\"\u003ci\u003eMax Plus at Work\u003c\/i\u003e is the best English textbook for learning eigenvector eigenvalues and the asymptotic regime of max-plus systems.\"\u003cb\u003e—J. P. Quadrat, Director of Research, International Research Institute\u003c\/b\u003e\u003cbr\u003e\"This book is very accessible, providing many examples and a clear road map for learning about max-plus algebra.\"\u003cb\u003e—Bart De Schutter, Delft University of Technology\u003c\/b\u003e\u003cbr\u003e\u003cbr\u003e\u003cb\u003eTable of Contents\u003c\/b\u003e\u003cbr\u003ePreface ix     Chapter 0. Prolegomenon 1  0.1 Introductory Example 1  0.2 On the Notation 3  0.3 On Eigenvalues and Eigenvectors 6  0.4 Some Modeling Issues 7  0.5 Counter and Dater Descriptions 8  0.6 Exercises 9  0.7 Notes 10      PART I. MAX-PLUS ALGEBRA 11      Chapter 1. Max-Plus Algebra 13  1.1 Basic Concepts and Definitions 13  1.2 Vectors and Matrices 17  1.3 A First Max-Plus Model 20  1.4 The Projective Space 24  1.5 Exercises 25  1.6 Notes 26      Chapter 2. Spectral Theory 28  2.1 Matrices and Graphs 28  2.2 Eigenvalues and Eigenvectors 36  2.3 Solving Linear Equations 42  2.4 Exercises 44  2.5 Notes 45      Chapter 3. Periodic Behavior and the Cycle-Time Vector 47  3.1 Cyclicity and Transient Time 48  3.2 The Cycle-Time Vector: Preliminary Results 56  3.3 The Cycle-Time Vector: General Results 62  3.4 A Sunflower Bouquet 67  3.5 Exercises 69  3.6 Notes 70      Chapter 4. Asymptotic Qualitative Behavior 72  4.1 Periodic Regimes 72  4.2 Characterization of the Eigenspace 74  4.3 Primitive Matrices 79  4.4 Limits in the Projective Space 80  4.5 Higher-Order Recurrence Relations 82  4.6 Exercises 83  4.7 Notes 84      Chapter 5. Numerical Procedures for Eigenvalues of Irreducible Matrices 85  5.1 Karp's Algorithm 85  5.2 The Power Algorithm 91  5.3 Exercises 94  5.4 Notes 94      Chapter 6. A Numerical Procedure for Eigenvalues of Reducible Matrices 95  6.1 Howard's Algorithm 96  6.2 Examples 102  6.3 Howard's Algorithm for Higher-Order Models 108  6.4 Exercises 110  6.5 Notes 111      PART II. TOOLS AND APPLICATIONS 113      Chapter 7. Petri Nets 115  7.1 Petri Nets and Event Graphs 115  7.2 The Autonomous Case 119  7.3 The Nonautonomous Case 122  7.4 Exercises 124  7.5 Notes 125      Chapter 8. The Dutch Railway System Captured in a Max-Plus Model 126  8.1 The Line System 126  8.2 Construction of the Timed Event Graph 130  8.3 State Space Description 132  8.4 Application of Howard's Algorithm 137  8.5 Exercises 138  8.6 Notes 139      Chapter 9. Delays, Stability Measures, and Results for the Whole Network 140  9.1 Propagation of Delays 140  9.2 Results for the Whole Dutch Intercity Network 145  9.3 Other Modeling Issues 148  9.4 Exercises 151  9.5 Notes 152      Chapter 10. Capacity Assessment 153  10.1 Capacity Assessment with Different Types of Trains 153  10.2 Capacity Assessment for a Series of Tunnels 154  10.3 Exercises 158  10.4 Notes 159      PART III. EXTENSIONS 161      Chapter 11. Stochastic Max-Plus Systems 163  11.1 Basic Definitions and Examples 164  11.2 The Subadditive Ergodic Theorem 167  11.3 Matrices with Fixed Support 171  11.4 Beyond Fixed Support 174  11.5 Exercises 175  11.6 Notes 176      Chapter 12. Min-Max-Plus Systems and Beyond 177  12.1 Min-Max-Plus Systems 177  12.2 Links to Other Mathematical Areas 187  12.3 Exercises 189  12.4 Notes 190      Chapter 13. Continuous and Synchronized Flows on Networks 191  13.1 Dater and Counter Descriptions 191  13.2 Continuous Flows without Capacity Constraints 192  13.3 Continuous Flows with Capacity Constraints 197  13.4 Exercises 199  13.5 Notes 200      Bibliography 201  List of Symbols 206  Index 209","brand":"Princeton University Press","offers":[{"title":"Default Title","offer_id":49403731804503,"sku":"9780691117638","price":73.8,"currency_code":"GBP","in_stock":true}],"url":"https:\/\/bookcurl.com\/products\/max-plus-at-work-9780691117638","provider":"Book Curl","version":"1.0","type":"link"}