On max-algebraic models for transportation networks
Reinout E. de Vries, Bart De Schutter, Bart De Moor · 1998
We will consider the modeling and analysis of public transportation networks which evolve according to a timetable. Some results are summarized. A way to control these networks is introduced. 1 Introduction Transportation networks are examples of what are known as Discrete Event Systems (DES). The evolution of these systems is determined by the occurrence of certain events. In a transportion network, e.g. a railway network, examples of discrete events are the departure from or arrival at a station of a train. The evolution of a class of DES, viz. those which involve synchronization constraints, can be described by linear models provided that the max-algebra structure is used. In transportation networks such constraints follow from the demand that trains should connect. The max-algebra consists of the real numbers and minus innity together with the operations maximization and addition. For an extensive discussion of the max-algebra and its applications in the modeling of DES we refer...