The dynamical properties of a discrete event model of a public transportation network

We consider the well-known model of a public transportation network described by linear equations in the algebra on the set of real numbers whose operations are maximum and addition. In order to study the stability properties of the train schedule in this network we suggest a representation of the model as a discrete event system. The available stability theorems for invariant sets of the discrete event systems describing the situation of trains going on schedule enable us to make some statements concerning the properties of a schedule in this model of railroad transport.