Multilevel models for railway traffic control

Assumes that the railway stations are basic point controlled elements of the network. The flow continuity equation for a railway station is based on the assumption that in the station trains can be accumulated. The network can be assumed to be a system of stations interconnected by means of railway tracks. Under this assumption a model of a railway network has been formulated in which flow concentration in particular stations are state variables, streams of trains entering the stations are inputs and streams of trains exiting the stations are outputs. The boundaries on the capacity of a railway network and the traffic capacity of stations can be taken into account by imposing inequality conditions on the model variables. The control problem consists in controlling streams of trains leaving railway stations such that it assures maximal railway station efficiency and maximal flow capacity of railway lines.