Konferensartikel

Max-plus algebra provides mathematical methods for solving nonlinear problems that can be given the form of linear problems. Problems of this type, sometimes of an administrative nature, arise in areas such as manufacturing, transportation, allocation of resources, and information processing technology. Train networks can be modelled as a directed graph, in which nodes correspond to arrivals and departures at stations, and arcs to travelling times. A particular difficulty is represented by meeting conditions in a single-track railway system. Compared to earlier work which typically include numerical optimization, max-plus formalism is used throughout this paper. The stability and sensitivity of the timetable is analyzed, and different types of delays and delay behavior are discussed and simulated. Interpretation of the recovery matrix is also done. A simple train network with real world background is used for illustration.

train schedules, meeting conditions, max-plus algebra, discrete-event systems, delay sensitivity, recovery matrix