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

• Autore: Heidergott Bernd
• Pubblicazione: Princeton, New Jersey ; ; Oxfordshire, England : , : Princeton University Press, , 2006; ©2006
• Descrizione fisica: 1 online resource (226 p.)
• Disciplina: 512
• Soggetto topico: Matrices; System theory
• Persona (resp. second.): OlsderGeert Jan; WoudeJ. W. van der
• Note generali: Description based upon print version of record.
• Nota di bibliografia: Includes bibliographical references and index.
• Nota di contenuto: Front matter -- Contents -- Preface -- Chapter Zero. Prolegomenon -- PART I. Max-Plus Algebra -- Chapter One. Max-Plus Algebra -- Chapter Two. Spectral Theory -- Chapter Three. Periodic Behavior and the Cycle-Time Vector -- Chapter Four. Asymptotic Qualitative Behavior -- Chapter Five. Numerical Procedures for Eigenvalues of Irreducible Matrices -- Chapter Six. A Numerical Procedure for Eigenvalues of Reducible Matrices -- PART II. Tools and Applications -- Chapter Seven. Petri Nets -- Chapter Eight. The Dutch Railway System Captured in a Max-Plus Model -- Chapter Nine. Delays, Stability Measures, and Results for the Whole Network -- Chapter Ten. Capacity Assessment -- PART III. Extensions -- Chapter Eleven. Stochastic Max-Plus Systems -- Chapter Twelve. Min-Max-Plus Systems and Beyond -- Chapter Thirteen. Continuous and Synchronized Flows on Networks -- Bibliography -- List of Symbols -- Index
• Sommario/riassunto: 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, computer communication systems, production lines, and flows in networks are all based on discrete even systems, and thus can be conveniently described and analyzed by means of max-plus algebra. The book consists of an introduction and thirteen chapters in three parts. Part One explores the introduction of max-plus algebra and of system descriptions based upon it. Part Two deals with a real application, namely the design of timetables for railway networks. Part Three examines various extensions, such as stochastic systems and min-max-plus systems. The text is suitable for last-year undergraduates in mathematics, and each chapter provides exercises, notes, and a reference section.
• Titolo autorizzato: Max Plus at work
• ISBN: 1-4008-6523-9
• Formato: Materiale a stampa
• Livello bibliografico: Monografia
• Lingua di pubblicazione: Inglese
• Record Nr.: 9910812330103321
• Lo trovi qui: Univ. Federico II
• Serie: Princeton series in applied mathematics.