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2003•Unpublished venueRequires access

ON THE BEHAVIOUR OF CLASSES OF MIN-MAX-PLUS SYSTEMS

G. Soto y Koelemeijer

Open publisher page 36 citations

Abstract

Discrete Event Systems are systems, the time evolution of which can be described by the occurence of events. Well-known examples of DESs are manufacturing systems and transportation networks. An important class of DESs can be described by the so-called (max,+) algebra, in which, compared to the usual arithmetic, the operator + is replaced by the operator max and the operator * is replaced by +. In this thesis we model a railroad network by means of the (max,+) algebra. Furthermore, we develop some theory concerning graphs corresponding to the (max,+) matrix. An extension of the (max,+) algebra is considered, that is, bipartite (min,max,+) systems and seperated (min,max,+) systems. Some theory is developed concerning the existence of the eigenvalue for these types of sytems. Furthermore, we have studied whether it is possible to model railroad networks by means of these kind of systems.

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What this paper is about

Discrete Event Systems are systems, the time evolution of which can be described by the occurence of events. Well-known examples of DESs are manufacturing systems and transportation networks. An important class of DESs can be described by the so-called (max,+) algebra, in which, compared to the usual arithmetic, the operator + is replaced by the operator max and the operator * is replaced by +. In this thesis we model a railroad network by means of the (max,+) algebra. Furthermore, we develop some theory concerning graphs corresponding to the (max,+) matrix. An extension of the (max,+) algebra is considered, that is, bipartite (min,max,+) systems and seperated (min,max,+) systems. Some theory is developed concerning the existence of the eigenvalue for these types of sytems. Furthermore, we have studied whether it is possible to model railroad networks by means of these kind of systems.

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Available abstract

Discrete Event Systems are systems, the time evolution of which can be described by the occurence of events. Well-known examples of DESs are manufacturing systems and transportation networks. An important class of DESs can be described by the so-called (max,+) algebra, in which, compared to the usual arithmetic, the operator + is replaced by the operator max and the operator * is replaced by +. In this thesis we model a railroad network by means of the (max,+) algebra. Furthermore, we develop some theory concerning graphs corresponding to the (max,+) matrix. An extension of the (max,+) algebra is considered, that is, bipartite (min,max,+) systems and seperated (min,max,+) systems. Some theory is developed concerning the existence of the eigenvalue for these types of sytems. Furthermore, we have studied whether it is possible to model railroad networks by means of these kind of systems.

Key concepts: Mathematics, Operator (biology), Bipartite graph, Eigenvalues and eigenvectors, Algebra over a field, Extension (predicate logic), Class (philosophy), Operator algebra

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