Ausgewählte Aspekte der Verspätungsfortpflanzung in Netzen

Random external disruptions impacting upon the overall system cause delays relative to the scheduled status to arise in the running of trains. Suitable measures need to be adopted right from the planning stage in order to accommodate such disruptions and hence ensure a high quality of traffic. This is why timetables contain a) buffer times between trains and b) recovery margins in the driving and stopping times of trains. Forcing up the quality of traffic merely with the aid of extensive recovery allowances leads to longer running times, however. Crucial to achieving patterns that are both stable and robust, therefore, is not just how many recovery margins there are but also where they are positioned in the timetable. In order to gauge the quality of traffic achievable in a timetable or, more generally, in an operating concept, it is necessary to predict how potential delays will propagate through the railway network. Random variables are used to model the types of delays arising with the aid of distribution or density functions. Subjecting delay propagation to analytical mapping allows dependable computations to be speedily achieved even for large networks. Unlike in Monte-Carlo simulation, where concrete realisations of the delay situation are generated for each simulation run, analytical methods directly process the distribution functions of the underlying random variables. Events that in practice lead to alterations in a delay are mapped by manipulating the distribution functions in analytical methods. Guaranteeing the accuracy and efficiency of this kind of method entails selecting a class of distribution functions for the modelling of delays that ensures sufficiently accurate adaptation to the real world whilst not giving rise to runtime and storage-space problems when performing computing operations. Existing modelling approaches either fail to embrace all requisite manipulations of random variables or else only allow such computing operations to be carried out approximatively. Furthermore, it is impossible as a result to make reliable pronouncements on issues of procedural theory for propagation calculation exercises. The key objective of the present work is to elaborate a class of distribution function that enables delay propagation to be speedily computed but also allows the quality of the computing process to be controlled. The form of modelling adopted is additionally taken as the basis for addressing issues of procedural theory as they arise in the context of networks. The practicability of the form of modelling selected is then investigated by applying the basic idea, thus far used solely to examine timetabling stability, to the real-time prediction of delays in arrival. Not only is the method’s usefulness shown to obtain, the results also reveal that it is possible, by including historical data in calculations, to attain a higher predictive power than in the method adopted hitherto