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.

• Superior document: Title is part of eBook package: De Gruyter Princeton Series in Applied Mathematics eBook-Package
• VerfasserIn: Heidergott, Bernd,; Olsder, Geert Jan,; van der Woude, Jacob,
• Place / Publishing House: Princeton, NJ : : Princeton University Press, , [2014]; ©2006
• Year of Publication: 2014
• Language: English
• Series: Princeton Series in Applied Mathematics ; 48
• Physical Description: 1 online resource (224 p.) :; 9 halftones. 36 line illus.

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.

Table of Contents

Frontmatter -- 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