
Synchronization and Linearity : An Algebra for Discrete Event Systems F. BACCELLI, INRIA, Sophia Antipolis, France, now with ENS Ulm, Paris, France G. COHEN, Ecole des Mines de Paris, Fontainebleau, France, now with CERMICSENPC, Marne la Vallée, France G.J. OLSDER, Delft University of Technology, The Netherlands, J.P. QUADRAT, INRIA, Rocquencourt, France.

This book proposes a unified mathematical treatment of a class of 'linear' discrete event systems, which contains important subclasses of Petri nets and queuing networks with synchronization constraints. The linearity has to be understood with respect to nonstandard algebraic structures, e.g. the 'maxplus algebra'. A calculus is developed based on such structures, which is followed by tools for computing the time behaviour to such systems. This algebraic vision lays the foundation of a bona fide 'discrete event system theory', which is shown to parallel the classical linear system theory in several ways.
This class of synchronized systems finds its main current industrial applications in the modeling, optimization and control of communications networks, computer architectures, manufacturing and transportation systems. The book should hence appeal to students and researchers in probabilitystatistics, applied mathematics, (industrial and electrical) engineering, operations research, as well as computer and management scientists.
CONTENTS
 Preface